The figure shows an arrangement of four charged particles, with θ = 20.0° and d1 = 3.00 cm, which is the distance from the origin to a charge q1. Charge q1 is unknown, but q2= +7.00×10‒19 C and q3 = q4 = ‒2.00×10‒19 C. If there is no nett electrostatic force on q1 due to the other charges (the nett electrostatic force on q1 is zero), calculate the distance from the origin to q2, given by d2, in cm. Assume that all forces apart from the electrostatic forces in the system are negligible
Answers
Answer:
[tex]d_2=3.16cm[/tex]
Explanation:
So, in order to solve this problem, we must start by building a diagram of the problem itself. (See attached picture) And together with the diagram, we must build a free body diagram, which will include the forces that are being applied on the given charged particle together with their directions.
In this case we only care about the x-direction of the force, since the y-forces cancel each other. So if we do a sum of forces on the x-direction, we get the following:
[tex]\sum{F_{x}}=0[/tex]
so:
[Tex]-F_{12}+F_{13x}+F_{14x}=0[/tex]
Since [tex]F_{13x}=F_{14x}[/tex] we can simplify the equation as:
[tex]-F_{12}+2F_{13x}=0[/tex]
we can now solve this for [tex]F_{12}[/tex] so we get:
[tex]F_{12}=2F_{13x}[/tex]
Now we can substitute with the electrostatic force formula, so we get:
[tex]k_{e}\frac{q_{1}q_{2}}{r_{12}^{2}}=2k_{e}\frac{q_{1}q_{3}}{r_{13}^{2}}cos \theta[/tex]
We can cancel [tex]k_{e}[/tex] and [tex]q_{1}[/tex]
so the simplified equation is:
[tex]\frac{q_{2}}{r_{12}^{2}}=2\frac{q_{3}}{r_{13}^{2}}cos \theta[/tex]
From the given diagram we know that:
[tex]cos \theta = \frac{d_{1}}{r_{13}}[/tex]
so when solving for [tex]r_{13}[/tex] we get:
[tex]r_{13}=\frac{d_{1}}{cos\theta}[/tex]
and if we square both sides of the equation, we get:
[tex]r_{13}^{2}=\frac{d_{1}^{2}}{cos^{2}\theta}[/tex]
and we can substitute this into our equation:
[tex]\frac{q_{2}}{r_{12}^{2}}=2\frac{q_{3}}{d_{1}^{2}}cos^{3} \theta[/tex]
so we can now solve this for [tex]r_{12}[/tex] so we get:
[tex]r_{12}=\sqrt{\frac{d_{1}^{2}q_{2}}{2q_{3}cos^{3}\theta}}[/tex]
which can be rewritten as:
[tex]r_{12}=d_{1}\sqrt{\frac{q_{2}}{2q_{3}cos^{3}\theta}}[/tex]
and now we can substitute values.
[tex]r_{12}=(3cm)\sqrt{\frac{7x10^{-19}C}{2(2x10^{-19}C)cos^{3}(20^{o})}}[/tex]
which solves to:
[tex]r_{12}=6.16cm[/tex]
now, we must find [tex]d_{2}[/tex] by using the following equation:
[tex]r_{12}=d_{1}+d_{2}[/tex]
when solving for [tex]d_{2}[/tex] we get:
[tex]d_{2}=r_{12}-d_{1}[/tex]
when substituting we get:
[tex]d_{2}=6.16cm-3cm[/tex]
so:
[tex]d_{2}=3.16cm[/tex]
Related Questions
Potential difference of a battery is 2.2 V when it is connected
across a resistance of 5 ohm, if suddenly the potential difference
falls to 1.8V, its internal resistance will be
Answers
Answer:
1.1ohms
Explanation:
According to ohms law E = IR
If potential difference of a battery is 2.2 V when it is connected across a resistance of 5 ohm and if suddenly the voltage Falls to 1.8V then the current in the 5ohms resistor I = V/R = 1.8/5
I = 0.36A (This will be the load current).
Before we can calculate the value of the internal resistance, we need to know the voltage drop across the internal resistance.
Voltage drop = 2.2V - 1.8V = 0.4V
Then we calculate the internal resistance using ohms law.
According to the law, V = Ir
V= voltage drop
I is the load current
r = internal resistance
0.4 = 0.36r
r = 0.4/0.36
r = 1.1 ohms
An electron of mass 9.11 x 10^-31 kg has an initial speed of 4.00 x 10^5 m/s. It travels in a straight line, and its speed increases to 6.60 x10^5 m/s in a distance of 5.40 cm. Assume its acceleration is constant.
Required:
a. Determine the magnitude of the force exerted on the electron.
b. Compare this force (F) with the weight of the electron (Fg), which we ignored.
Answers
Answer:
a. F = 2.32*10^-18 N
b. The force F is 2.59*10^11 times the weight of the electron
Explanation:
a. In order to calculate the magnitude of the force exerted on the electron you first calculate the acceleration of the electron, by using the following formula:
[tex]v^2=v_o^2+2ax[/tex] (1)
v: final speed of the electron = 6.60*10^5 m/s
vo: initial speed of the electron = 4.00*10^5 m/s
a: acceleration of the electron = ?
x: distance traveled by the electron = 5.40cm = 0.054m
you solve the equation (2) for a and replace the values of the parameters:
[tex]a=\frac{v^2-v_o^2}{2x}=\frac{(6.60*10^5m/s)^2-(4.00*10^5m/s)^2}{2(0.054m)}\\\\a=2.55*10^{12}\frac{m}{s^2}[/tex]
Next, you use the second Newton law to calculate the force:
[tex]F=ma[/tex]
m: mass of the electron = 9.11*10^-31kg
[tex]F=(9.11*10^{-31}kg)(2.55*10^{12}m/s^2)=2.32*10^{-18}N[/tex]
The magnitude of the force exerted on the electron is 2.32*10^-18 N
b. The weight of the electron is given by:
[tex]F_g=mg=(9.11*10^{-31}kg)(9.8m/s^2)=8.92*10^{-30}N[/tex]
The quotient between the weight of the electron and the force F is:
[tex]\frac{F}{F_g}=\frac{2.32*10^{-18}N}{8.92*10^{-30}N}=2.59*10^{11}[/tex]
The force F is 2.59*10^11 times the weight of the electron
Dr. Jones performed an experiment to monitor the effects of sunlight exposure on stem density in aquatic plants. In the study, Dr. Jones measured the mass and volume of stems grown in 5 levels of sun exposure. The data is represented below.
Sun exposure Stem mass (g) Stem volume (mL)
30 275 1100
45 415 1215
60 563 1425
75 815 1610
90 954 1742
a. Convert the mass measurements to kilograms (kg) and the volume measurements to cubic meters (mº).
b. Calculate the density of the samples using the equation d = m/v. d = density m = mass (kg) v = volume (m)
c. Convert the density values to scientific notation.
Answers
Given that,
Sun exposure = 30%, 45%, 60%, 75%, 90%
Stem mass (g) = 275, 415, 563, 815, 954
Stem volume (ml) = 1100, 1215, 1425, 1610, 1742
(a). We need to convert the mass measurements to kilograms (kg) and the volume measurements to cubic meters
Using conversion of mass
[tex]1\ g=0.001\ kg[/tex]
Conservation of volume
[tex]1\ Lt=0.001\ m^3[/tex]
[tex]1\ mL=1\times10^{-6}\ m^3[/tex]
So, mass in kg
Stem mass (kg) = 0.275, 0.415, 0.563, 0.815, 0.954
Volume in m³,
Stem volume (m³) = 0.0011, 0.001215, 0.001425, 0.001610, 0.001742
(b). We need to calculate the density of the samples
Using formula of density
[tex]\rho=\dfrac{m}{V}[/tex]
Where, m = mass
V = volume
If the m = 0.275 kg and V = 0.0011 m³
Put the value into the formula
[tex]\rho=\dfrac{0.275}{0.0011}[/tex]
[tex]\rho=250\ kg/m^3[/tex]
If the m = 0.415 kg and V = 0.001215 m³
Put the value into the formula
[tex]\rho=\dfrac{0.415}{0.001215}[/tex]
[tex]\rho=341.56\ kg/m^3[/tex]
[tex]\rho=342\ kg/m^3[/tex]
If the m = 0.563 kg and V = 0.001425 m³
Put the value into the formula
[tex]\rho=\dfrac{0.563}{0.001425}[/tex]
[tex]\rho=395.08\ kg/m^3[/tex]
If the m = 0.815 kg and V = 0.001610 m³
Put the value into the formula
[tex]\rho=\dfrac{0.815}{0.001610}[/tex]
[tex]\rho=506.21\ kg/m^3[/tex]
If the m = 0.954 kg and V = 0.001742 m³
Put the value into the formula
[tex]\rho=\dfrac{0.954}{0.001742}[/tex]
[tex]\rho=547.6\ kg/m^3[/tex]
[tex]\rho=548\ kg/m^3[/tex]
(c). We need to convert the density values to scientific notation
In scientific notation
The densities are
[tex]\rho\ (kg/m^3)= 2.50\times10^{2}, 3.42\times10^{2}, 3.95\times10^{2}, 5.06\times10^{2}, 5.48\times10^{2}[/tex]
Hence, This is required solution.
In 1898, the world land speed record was set by Gaston Chasseloup-Laubat driving a car named Jeantaud. His speed was 39.24 mph (63.15 km/h), much lower than the limit on our interstate highways today. Repeat the calculations of Example 2.7 (assume the car accelerates for 6 miles to get up to speed, is then timed for a one-mile distance, and accelerates for another 6 miles to come to a stop) for the Jeantaud car. (Assume the car moves in the +x direction.)
Find the acceleration for the first 6 miles.
Answers
Answer:
the acceleration [tex]a^{\to} = (0.0159 \ \ m/s^2 )i[/tex]
Explanation:
Given that:
the initial speed v₁ = 0 m/s i.e starting from rest ; since the car accelerates at a distance Δx = 6 miles in order to teach that final speed v₂ of 63.15 km/h.
So; the acceleration for the first 6 miles can be calculated by using the formula:
v₂² = v₁² + 2a (Δx)
Making acceleration a the subject of the formula in the above expression ; we have:
v₂² - v₁² = 2a (Δx)
[tex]a = \dfrac{v_2^2 - v_1^2 }{2 \Delta x}[/tex]
[tex]a = \dfrac{(63.15 \ km/s)^2 - (0 \ m/s)^2 }{2 (6 \ miles)}[/tex]
[tex]a = \dfrac{(17.54 \ m/s)^2 - (0 \ m/s)^2 }{2 (9.65*10^3 \ m)}[/tex]
[tex]a =0.0159 \ m/s^2[/tex]
Thus;
Assume the car moves in the +x direction;
the acceleration [tex]a^{\to} = (0.0159 \ \ m/s^2 )i[/tex]
A spherical balloon is made from a material whose mass is 4.30 kg. The thickness of the material is negligible compared to the 1.54-m radius of the balloon. The balloon is filled with helium (He) at a temperature of 289 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m3. Find the absolute pressure of the helium gas.
Answers
Answer:
P = 5.97 × 10^(5) Pa
Explanation:
We are given;
Mass of balloon;m_b = 4.3 kg
Radius;r = 1.54 m
Temperature;T = 289 K
Density;ρ = 1.19 kg/m³
We know that, density = mass/volume
So, mass = Volume x Density
We also know that Force = mg
Thus;
F = mg = Vρg
Where m = mass of balloon(m_b) + mass of helium (m_he)
So,
(m_b + m_he)g = Vρg
g will cancel out to give;
(m_b + m_he) = Vρ - - - eq1
Since a sphere shaped balloon, Volume(V) = (4/3)πr³
V = (4/3)π(1.54)³
V = 15.3 m³
Plugging relevant values into equation 1,we have;
(3 + m_he) = 15.3 × 1.19
m_he = 18.207 - 3
m_he = 15.207 kg = 15207 g
Molecular weight of helium gas is 4 g/mol
Thus, Number of moles of helium gas is ; no. of moles = 15207/4 ≈ 3802 moles
From ideal gas equation, we know that;
P = nRT/V
Where,
P is absolute pressure
n is number of moles
R is the gas constant and has a value lf 8.314 J/mol.k
T is temperature
V is volume
Plugging in the relevant values, we have;
P = (3802 × 8.314 × 289)/15.3
P = 597074.53 Pa
P = 5.97 × 10^(5) Pa
During a particular time interval, the displacement of an object is equal to zero. Must the distance traveled by this object also equal to zero during this time interval? Group of answer choices
Answers
Answer: No, we can have a displacement equal to 0 while the distance traveled is different than zero.
Explanation:
Ok, let's write the definitions:
Displacement: The displacement is equal to the difference between the final position and the initial position.
Distance traveled: Total distance that you moved.
So, for example, if at t = 0s, you are in your house, then you go to the store, and then you return to your house, we have:
The displacement is equal to zero, because the initial position is your house and the final position is also your house, so the displacement is zero.
But the distance traveled is not zero, because you went from you traveled the distance from your house to the store two times.
So no, we can have a displacement equal to zero, but a distance traveled different than zero.
A glass flask whose volume is 1000 cm^3 at a temperature of 1.00°C is completely filled with mercury at the same temperature. When the flask and mercury are warmed together to a temperature of 52.0°C , a volume of 8.50 cm^3 of mercury overflows the flask.Required:If the coefficient of volume expansion of mercury is βHg = 1.80×10^−4 /K , compute βglass, the coefficient of volume expansion of the glass. Express your answer in inverse kelvins.
Answers
Answer:
the coefficient of volume expansion of the glass is [tex]\mathbf{ ( \beta_{glass} )= 1.333 *10^{-5} / K}[/tex]
Explanation:
Given that:
Initial volume of the glass flask = 1000 cm³ = 10⁻³ m³
temperature of the glass flask and mercury= 1.00° C
After heat is applied ; the final temperature = 52.00° C
Temperature change ΔT = 52.00° C - 1.00° C = 51.00° C
Volume of the mercury overflow = 8.50 cm^3 = 8.50 × 10⁻⁶ m³
the coefficient of volume expansion of mercury is 1.80 × 10⁻⁴ / K
The increase in the volume of the mercury = 10⁻³ m³ × 51.00 × 1.80 × 10⁻⁴
The increase in the volume of the mercury = [tex]9.18*10^{-6} \ m^3[/tex]
Increase in volume of the glass = 10⁻³ × 51.00 × [tex]\beta _{glass}[/tex]
Now; the mercury overflow = Increase in volume of the mercury - increase in the volume of the flask
the mercury overflow = [tex](9.18*10^{-6} - 51.00* \beta_{glass}*10^{-3})\ m^3[/tex]
[tex]8.50*10^{-6} = (9.18*10^{-6} -51.00* \beta_{glass}* 10^{-3} )\ m^3[/tex]
[tex]8.50*10^{-6} - 9.18*10^{-6} = ( -51.00* \beta_{glass}* 10^{-3} )\ m^3[/tex]
[tex]-6.8*10^{-7} = ( -51.00* \beta_{glass}* 10^{-3} )\ m^3[/tex]
[tex]6.8*10^{-7} = ( 51.00* \beta_{glass}* 10^{-3} )\ m^3[/tex]
[tex]\dfrac{6.8*10^{-7}}{51.00 * 10^{-3}}= ( \beta_{glass} )[/tex]
[tex]\mathbf{ ( \beta_{glass} )= 1.333 *10^{-5} / K}[/tex]
Thus; the coefficient of volume expansion of the glass is [tex]\mathbf{ ( \beta_{glass} )= 1.333 *10^{-5} / K}[/tex]
Professional baseball player Nolan Ryan could pitch a baseball at approximately 160.0 km/h. At that average velocity, how long (in s) did it take a ball thrown by Ryan to reach home plate, which is 18.4 m from the pitcher's mound
Answers
Answer:
t = 0.414s
Explanation:
In order to calculate the time that the ball takes to reach home plate, you assume that the speed of the ball is constant, and you use the following formula:
[tex]t=\frac{d}{v}[/tex] (1)
d: distance to the plate = 18.4m
v: speed of the ball = 160.0km/h
You first convert the units of the sped of the ball to appropriate units (m/s)
[tex]160.0\frac{km}{h}*\frac{1h}{3600s}*\frac{1000m}{1km}=44.44\frac{m}{s}[/tex]
Then, you replace the values of the speed v and distance s in the equation (1):
[tex]t=\frac{18.4m}{44.44m/s}=0.414s[/tex]
THe ball takes 0.414s to reach the home plate
according to newtons second law of motion, what is equal to the acceleration of an object
Answers
Answer: According to Newtons second Law of motion ;
F = ma (Force equals mass multiplied by acceleration.)
The acceleration is directly proportional to the net force; the net force equals mass times acceleration; the acceleration in the same direction as the net force; an acceleration is produced by a net force
Explanation:
Two guitarists attempt to play the same note of wavelength 6.50 cm at the same time, but one of the instruments is slightly out of tune. Consequently, a 17.0-Hz beat frequency is heard between the two instruments. What were the possible wavelengths of the out-of-tune guitar’s note? Express your answers, separated by commas, in centimeters to three significant figures IN cm.
Answers
Answer:
The two value of the wavelength for the out of tune guitar is
[tex]\lambda _2 = (6.48,6.52) \ cm[/tex]
Explanation:
From the question we are told that
The wavelength of the note is [tex]\lambda = 6.50 \ cm = 0.065 \ m[/tex]
The difference in beat frequency is [tex]\Delta f = 17.0 \ Hz[/tex]
Generally the frequency of the note played by the guitar that is in tune is
[tex]f_1 = \frac{v_s}{\lambda}[/tex]
Where [tex]v_s[/tex] is the speed of sound with a constant value [tex]v_s = 343 \ m/s[/tex]
[tex]f_1 = \frac{343}{0.0065}[/tex]
[tex]f_1 = 5276.9 \ Hz[/tex]
The difference in beat is mathematically represented as
[tex]\Delta f = |f_1 - f_2|[/tex]
Where [tex]f_2[/tex] is the frequency of the sound from the out of tune guitar
[tex]f_2 =f_1 \pm \Delta f[/tex]
substituting values
[tex]f_2 =f_1 + \Delta f[/tex]
[tex]f_2 = 5276.9 + 17.0[/tex]
[tex]f_2 = 5293.9 \ Hz[/tex]
The wavelength for this frequency is
[tex]\lambda_2 = \frac{343 }{5293.9}[/tex]
[tex]\lambda_2 = 0.0648 \ m[/tex]
[tex]\lambda_2 = 6.48 \ cm[/tex]
For the second value of the second frequency
[tex]f_2 = f_1 - \Delta f[/tex]
[tex]f_2 = 5276.9 -17[/tex]
[tex]f_2 = 5259.9 Hz[/tex]
The wavelength for this frequency is
[tex]\lambda _2 = \frac{343}{5259.9}[/tex]
[tex]\lambda _2 = 0.0652 \ m[/tex]
[tex]\lambda _2 = 6.52 \ cm[/tex]
This question involves the concepts of beat frequency and wavelength.
The possible wavelengths of the out-of-tune guitar are "6.48 cm" and "6.52 cm".
The beat frequency is given by the following formula:
[tex]f_b=|f_1-f_2|\\\\[/tex]
f₂ = [tex]f_b[/tex] ± f₁
where,
f₂ = frequency of the out-of-tune guitar = ?
[tex]f_b[/tex] = beat frequency = 17 Hz
f₁ = frequency of in-tune guitar = [tex]\frac{speed\ of\ sound\ in\ air}{\lambda_1}=\frac{343\ m/s}{0.065\ m}=5276.9\ Hz[/tex]
Therefore,
f₂ = 5276.9 Hz ± 17 HZ
f₂ = 5293.9 Hz (OR) 5259.9 Hz
Now, calculating the possible wavelengths:
[tex]\lambda_2=\frac{speed\ of\ sound}{f_2}\\\\\lambda_2 = \frac{343\ m/s}{5293.9\ Hz}\ (OR)\ \frac{343\ m/s}{5259.9\ Hz}\\\\[/tex]
λ₂ = 6.48 cm (OR) 6.52 cm
Learn more about beat frequency here:
https://brainly.com/question/10703578?referrer=searchResults
A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the
Answers
Answer:
F₂ = 925.92 N
Explanation:
In a hydraulic lift the normal stress applied to one arm must be equally transmitted to the other arm. Therefore,
σ₁ = σ₂
F₁/A₁ = F₂/A₂
F₂ = F₁ A₂/A₁
where,
F₂ = Initial force that must be applied to narrow arm = ?
F₁ = Load on Wider Arm to be raised = 12000 N
A₁ = Area of wider arm = πr₁² = π(18 cm)² = 324π cm²
A₂ = Area of narrow arm = πr₂² = π(5 cm)² = 25π cm²
Therefore,
F₂ = (12000 N)(25π cm²)/(324π cm²)
F₂ = 925.92 N
High voltage power is often carried in wire bundles made up of individual strands. In your initial post to the discussion, discuss the forces on the strands of wire due to the current flowing through them. What would happen if the force acted opposite of the known behavior
Answers
Answer:
More current will be loss through the metal wire strands if the force on them was repulsive, and more stress will be induced on the wire strands due to internal and external flexing.
Explanation:
A wire bundle is made up of wire strands bunched together to increase flexibility that is not always possible in a single solid metal wire conductor. In the strands of wire carrying a high voltage power, each strand carries a certain amount of current, and the current through the strands all travel in the same direction. It is know that for two conductors or wire, separated by a certain distance, that carries current flowing through them in the same direction, an attractive force is produced on these wires, one on the other. This effect is due to the magnetic induction of a current carrying conductor. The forces between these strands of the high voltage wire bundle, pulls the wire strands closer, creating more bond between these wire strands and reducing internal flex induced stresses.
If the case was the opposite, and the wires opposed themselves, the effect would be that a lot of cost will be expended in holding these wire strands together. Also, stress within the strands due to the repulsion, will couple with external stress from the flexing of the wire, resulting in the weakening of the material.
The biggest problem will be that more current will be lost in the wire due to increased surface area caused by the repulsive forces opening spaces between the strand. This loss is a s a result of the 'skin effect' in wire transmission, in which current tends to flow close to the surface of the metal wire. The skin effect generates power loss as heat through the exposed surface area.
A person is standing on an elevator initially at rest at the first floor of a high building. The elevator then begins to ascend to the sixth floor, which is a known distance h above the starting point. The elevator undergoes an unknown constant acceleration of magnitude a for a given time interval T. Then the elevator moves at a constant velocity for a time interval 4T. Finally the elevator brakes with an acceleration of magnitude a, (the same magnitude as the initial acceleration), for a time interval T until stopping at the sixth floor.
Answers
Answer:
The found acceleration in terms of h and t is:
[tex]a=\frac{h}{5(t_1)^2}[/tex]
Explanation:
(The complete question is given in the attached picture. We need to find the acceleration in terms of h and t in this question)
We are given 3 stages of movement of elevator. We'll first model them each of the stage one by one to find the height covered in each stage. After that we'll find the total height covered by adding heights covered in each stage, and equate it to Total height h. From that we can find the formula for acceleration.
Stage 1Constant acceleration, starts from rest.
Distance = [tex]y = \frac{1}{2}a(t_1)^2[/tex]
Velocity = [tex]v_1=at_1[/tex]
Stage 2Constant velocity where
Velocity = [tex]v_o=v_1=at_1[/tex]
Distance =
[tex]y_2=v_2(t_2)\\\text{Where~}t_2=4t_1 ~\text{and}~ v_2=v_1=at_1\\y_2=(at_1)(4t_1)\\y_2=4a(t_1)^2\\[/tex]Stage 3Constant deceleration where
Velocity = [tex]v_0=v_1=at_1[/tex]
Distance =
[tex]y_3=v_1t_3-\frac{1}{2}a(t_3)^2\\\text{Where}~t_3=t_1\\y_3=v_1t_1-\frac{1}{2}a(t_1)^2\\\text{Where}~ v_1t_1=a(t_1)^2\\y_3=a(t_1)^2-\frac{1}{2}a(t_1)^2\\\text{Subtracting both terms:}\\y_3=\frac{1}{2}a(t_1)^2[/tex]
Total HeightTotal height = y₁ + y₂ + y₃
Total height = [tex]\frac{1}{2}a(t_1)^2+4a(t_1)^2+\frac{1}{2}a(t_1)^2 = 5a(t_1)^2[/tex]
AccelerationFind acceleration by rearranging the found equation of total height.
Total Height = h
h = 5a(t₁)²
[tex]a=\frac{h}{5(t_1)^2}[/tex]
In 1949, an automobile manufacturing company introduced a sports car (the "Model A") which could accelerate from 0 to speed v in a time interval of Δt. In order to boost sales, a year later they introduced a more powerful engine (the "Model B") which could accelerate the car from 0 to speed 2.92v in the same time interval. Introducing the new engine did not change the mass of the car. Compare the power of the two cars, if we assume all the energy coming from the engine appears as kinetic energy of the car.
Answers
Answer: [tex]\frac{P_B}{P_A}[/tex] = 8.5264
Explanation: Power is the rate of energy transferred per unit of time: P = [tex]\frac{E}{t}[/tex]
The energy from the engine is converted into kinetic energy, which is calculated as: [tex]KE = \frac{1}{2}.m.v^{2}[/tex]
To compare the power of the two cars, first find the Kinetic Energy each one has:
K.E. for Model A
[tex]KE_A = \frac{1}{2}.m.v^{2}[/tex]
K.E. for model B
[tex]KE_B = \frac{1}{2}.m.(2.92v)^{2}[/tex]
[tex]KE_B = \frac{1}{2}.m.8.5264v^{2}[/tex]
Now, determine Power for each model:
Power for model A
[tex]P_{A}[/tex] = [tex]\frac{m.v^{2} }{2.t}[/tex]
Power for model B
[tex]P_B = \frac{m.8.5264.v^{2} }{2.t}[/tex]
Comparing power of model B to power of model A:
[tex]\frac{P_B}{P_A} = \frac{m.8.5264.v^{2} }{2.t}.\frac{2.t}{m.v^{2} }[/tex]
[tex]\frac{P_B}{P_A} =[/tex] 8.5264
Comparing power for each model, power for model B is 8.5264 better than model A.
A 4.5 kg ball swings from a string in a vertical circle such that it has constant sum of kinetic and gravitational potential energy. Ignore any friction forces from the air or in the string. What is the difference in the tension between the lowest and highest points on the circle
Answers
Answer:
88.29 N
Explanation:
mass of the ball = 4.5 kg
weight of the ball will be = mass x acceleration due to gravity(9.81 m/s^2)
weight W = 4.5 x 9.81 = 44.145 N
centrifugal forces Tc act on the ball as it swings.
At the top point of the vertical swing,
Tension on the rope = Tc - W.
At the bottom point of the vertical swing,
Tension on the rope = Tc + W
therefore,
difference in tension between these two points will be;
Net tension = tension at bottom minus tension at the top
= Tc + W - (Tc - W) = Tc + W -Tc + W
= 2W
imputing the value of the weight W, we have
2W = 2 x 44.145 = 88.29 N
A box on a ramp is connected by a rope to a winch. The winch is turned so that the box moves down the ramp at a constant speed. The box experiences kinetic friction with the ramp. Which forces on the box do zero work as the box moves down the ramp?
a. Weight (gravitational force)
b. Normal force
c. Kinetic friction force
d. Tension force
e. None
Answers
Answer:
Option B:
The normal force
Explanation:
The normal force does no work as the box slides down the ramp.
Work can only be done when the force succeeds in moving the object in the direction of the force.
All the other forces involved have a component that is moving the box in their direction.
However, the normal force does not, as it points downwards into the ramp. Since the normal force is pointing into the ramp, and the box is sliding down the ramp, we can say that no work is being done by the normal force because the box is not moving in its direction (which would have been the box moving into the ramp)
A piston of small cross-sectional area a is used in a hydraulic press to exert a small force f on the enclosed liquid. A connecting pipe leads to a larger piston of cross sectional area A. a) What force F will the larger piston sustain
Answers
Answer:
force on larger piston = [tex]\frac{fA}{a}[/tex]
Explanation:
we label the pistons as piston A and piston B
small piston A:
area = a
force = f
large piston B:
area = A
force = ?
Pascal's law of pressure state that the pressure delivered to a liquid is transmitted undiminished to every portion of the fluid.
we know that pressure = force ÷ area
pressure of piston A = [tex]\frac{f}{a}[/tex]
pressure of piston B = [tex]\frac{(force on piston B)}{A}[/tex]
obeying Pascal's law, the system pressures must be equal. Therefore
[tex]\frac{f}{a} = \frac{(force on piston B)}{A}[/tex]
force on large piston (B) = F = [tex]\frac{fA}{a}[/tex]
A Nearsighted Eye. A certain very nearsighted person cannot focus on anything farther than 36.0 cm from the eye. Consider the simplified model of the eye. In a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina.
Required:
a. If the radius of curvature of the cornea is 0.65 cm when the eye is focusing on an object 36.0 cm from the cornea vertex and the indexes of refraction are as described before, what is the distance from the cornea vertex to the retina?
b. What does this tell you about the shape of the nearsighted eye?
1. This distance is greater than for the normal eye.
2. This distance is shorter than for the normal eye.
Answers
Answer:
a) The distance from the cornea vertex to the retina is 2.37 cm
b) This distance is shorter than for the normal eye.
Explanation:
a) Let refractive index of air,
n(air) = x = 1
Let refractive index of lens,
n(lens) = y = 1.4
Object distance, s = 36 cm
Radius of curvature, R = 0.65 cm
The distance from the cornea vertex to the retina is the image distance because image is formed in the retina.
Image distance, s' = ?
(x/s) + (y/s') = (y-x)/R
(1/36) + (1.4/s') = (1.4 - 1)/0.65
1.4/s' = 0.62 - 0.028
1.4/s' = 0.592
s' = 1.4/0.592
s' = 2.37 cm
Distance from the cornea vertex to the retina is 2.37 cm
(b) For a normal eye, the distance between the cornea vertex and the retina is 2.60 cm. Since 2.37 < 2.60, this distance is shorter than for normal eye.
Underline your answer for each situation: If you advance the movie one frame, the knot at point A would be a) in the same place b) higher c) lower d) to the right e) to the left If the person generates a new pulse like the first but more quickly, the pulse would be a) same size b) wider c) narrower If the person generates another pulse like the first but he moves his hand further, the pulse would be a) same size b) taller c) shorter If the person generates another pulse like the first but the rope is tightened, the pulse will move a) at the same rate b) faster c) slower Now the person moves his hand back and forth several times to produce several waves. You freeze the movie and get this snapshot. Underline your answer for each situation: If you advance the movie one frame, the knot at point A would be a) in the same place b) higher c) lower d) to the right e) to the left If you advance the movie one frame, the pattern of the waves will be _________relative to the hand. a) in the same place b) shifted right c) shifted left d) shifted up e) shifted down If the person starts over and moves his hand more quickly, the peaks of the waves will be a) the same distance apart b) further apart c) closer together If you lower the frequency of a wave on a string you will lower its speed. b) increase its wavelength. c). lower its amplitude. d) shorten its period.
Answers
Answer:
a) correct answer is b higher , b) correct answer is b higher , c) correct answer is b faster , d) traveling wave , e)
Explanation:
A traveling wave is described by the expression
y = A sin (kx - wt)
where k is the wave vector and w is the angular velocity
let's examine every situation presented
a) a new faster pulse is generated
A faster pulse should have a higher angular velocity
equal speed is related to the period and frequency
w = 2π f = 2π / T
therefore in this case the period must decrease so that the angular velocity increases
the correct answer is c narrower
b) Generate a pulse, but move your hand more.
Moving the hand increases the amplitude (A) of the pulse
the correct answer is b higher
c) generates a pulse but the force is tightened
Set means that more tension force is applied to the string, so the velicate changes
v = √ (T /μ)
the correct answer is b faster
d) move your hand back and forth
in this case you would see a pulse series whose sum corresponds to a traveling wave
e) Advance a frame the movie
in this case the wave will be displaced a whole period to the right
the correct answer is b
f) move your hand faster
the waves will have a maximum fast, so they are closer
answer C
g) decrease wave frequency
Since the speed of the wave is a constant m ak, decreasing the frequency must increase the wavelength to keep the velocity constant.
the correct answer is b increases its wavelength
a wall, a 55.6 kg painter is standing on a 3.15 m long homogeneous board that is resting on two saw horses. The board’s mass is 14.5 kg. The saw horse on the right is 1.00 m from the right. How far away can the painter walk from the saw horse on the right until the board begins to tip?
Answers
Answer:
0.15 m
Explanation:
First calculating the center of mass from the saw horse
[tex]\frac{3.15}{2} -1=0.575 m[/tex]
from the free body diagram we can write
Taking moment about the saw horse
55.9×9.81×y=14.5×0.575×9.81
y= 0.15 m
So, the painter walk from the saw horse on the right until the board begins to tip is 0.15 m far.
An unknown charged particle passes without deflection through crossed electric and magnetic fields of strengths 187,500 V/m and 0.1250 T, respectively. The particle passes out of the electric field, but the magnetic field continues, and the particle makes a semicircle of diameter 25.05 cm.
Part A. What is the particle's charge-to-mass ratio?
Part B. Can you identify the particle?
a. can't identify
b. proton
c. electron
d. neutron
Answers
Answer:
Explanation:
Given that
The electric fields of strengths E = 187,500 V/m and
and The magnetic fields of strengths B = 0.1250 T
The diameter d is 25.05 cm which is converted to 0.2505m
The radius is (d/2)
= 0.2505m / 2 = 0.12525m
The given formula to find the magnetic force is [tex]F_{ma}=BqV---(i)[/tex]
The given formula to find the electric force is [tex]F_{el}=qE---(ii)[/tex]
The velocity of electric field and magnetic field is said to be perpendicular
Electric field is equal to magnectic field
Equate equation (i) and equation (ii)
[tex]Bqv=qE\\\\v=\frac{E}{B}[/tex]
[tex]v=\frac{187500}{0.125} \\\\v=15\times10^5m/s[/tex]
It is said that the particles moves in semi circle, so we are going to consider using centripetal force
[tex]F_{ce}=\frac{mv^2}{r}---(iii)[/tex]
magnectic field is equal to centripetal force
Lets equate equation (i) and (iii)
[tex]Bqr=\frac{mv^2}{r} \\\\\frac{q}{m}=\frac{v}{Br} \\\\\frac{q}{m} =\frac{15\times 10^5}{0.125\times0.12525} \\\\=\frac{15\times10^5}{0.015656} \\\\=95808383.23\\\\=958.1\times10^5C/kg[/tex]
Therefore, the particle's charge-to-mass ratio is [tex]958.1\times10^5C/kg[/tex]
b)
To identify the particle
Then 1/ 958.1 × 10⁵ C/kg
The charge to mass ratio is very close to that of a proton, which is about 1*10^8 C/kg
Therefore the particle is proton.
A heavy, 6 m long uniform plank has a mass of 30 kg. It is positioned so that 4 m is supported on the deck of a ship and 2 m sticks out over the water. It is held in place only by its own weight. You have a mass of 70 kg and walk the plank past the edge of the ship. How far past the edge do you get before the plank starts to tip, in m
Answers
Answer:
about 1 meter
Explanation:
The distance past the edge that the man will get before the plank starts to tip is; 0.4285 m
We are given;
Mass of plank; m = 30 kg
Length of plank; L = 6m
Mass of man; M = 70 kg
Since the plank has 2 supports which are the deck of the ship, then it means that, we can take moments about the right support before the 2m stick out of the plank.
Thus;
Moment of weight of plank about the right support;
τ_p = mg((L/2) - 2)
τ_p = 30 × 9.8((6/2) - 2)
τ_p = 294 N.m
Moment of weight of man about the right support;
τ_m = Mgx
where x is the distance past the edge the man will get before the plank starts to tip.
τ_m = 70 × 9.8x
τ_m = 686x
Now, moment of the board is counterclockwise while that of the man is clockwise. Thus;
τ_m = τ_p
686x = 294
x = 294/686
x = 0.4285 m
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Two large rectangular aluminum plates of area 180 cm2 face each other with a separation of 3 mm between them. The plates are charged with equal amount of opposite charges, ±17 µC. The charges on the plates face each other. Find the flux (in N · m2/C) through a circle of radius 3.3 cm between the plates when the normal to the circle makes an angle of 4° with a line perpendicular to the plates. Note that this angle can also be given as 180° + 4°. N · m2/C
Answers
Answer:
Φ = 361872 N.m^2 / C
Explanation:
Given:-
- The area of the two plates, [tex]A_p = 180 cm^2[/tex]
- The charge on each plate, [tex]q = 17 * 10^-^6 C[/tex]
- Permittivity of free space, [tex]e_o = 8.85 * 10^-^1^2 \frac{C^2}{N.m^2}[/tex]
- The radius for the flux region, [tex]r = 3.3 cm[/tex]
- The angle between normal to region and perpendicular to plates, θ = 4°
Find:-
Find the flux (in N · m2/C) through a circle of radius 3.3 cm between the plates.
Solution:-
- First we will determine the area of the region ( Ar ) by using the formula for the area of a circle as follows. The region has a radius of r = 3.3 cm:
[tex]A_r = \pi *r^2\\\\A_r = \pi *(0.033)^2\\\\A_r = 0.00342 m^2[/tex]
- The charge density ( σ ) would be considered to be uniform for both plates. It is expressed as the ratio of the charge ( q ) on each plate and its area ( A_p ):
σ = [tex]\frac{q}{A_p} = \frac{17*10^-^6}{0.018} \\[/tex]
σ = 0.00094 C / m^2
- We will assume the electric field due to the positive charged plate ( E+ ) / negative charged plate ( E- ) to be equivalent to the electric field ( E ) of an infinitely large charged plate with uniform charge density.
[tex]E+ = E- = \frac{sigma}{2*e_o} \\\\[/tex]
- The electric field experienced by a region between two infinitely long charged plates with uniform charge density is the resultant effect of both plates. So from the principle of super-position we have the following net uniform electric field ( E_net ) between the two plates:
[tex]E_n_e_t = (E+) + ( E-)\\\\E_n_e_t = \frac{0.00094}{8.85*10^-^1^2} \\\\E_n_e_t = 106214689.26553 \frac{N}{C} \\[/tex]
- From the Gauss-Law the flux ( Φ ) through a region under uniform electric field ( E_net ) at an angle of ( θ ) is:
Φ = E_net * Ar * cos ( θ )
Φ = (106214689.26553) * (0.00342) * cos ( 5 )
Φ = 361872 N.m^2 / C
A 56.0 g ball of copper has a net charge of 2.10 μC. What fraction of the copper’s electrons has been removed? (Each copper atom has 29 protons, and copper has an atomic mass of 63.5.)
Answers
Answer:
The fraction of the cooper's electrons that is removed is [tex]8.5222\times 10^{-11}[/tex].
Explanation:
An electron has a mass of [tex]9.1 \times 10^{-31}\,kg[/tex] and a charge of [tex]-1.6 \times 10^{-19}\,C[/tex]. Based on the Principle of Charge Conservation, [tex]-2.10\times 10^{-6}\,C[/tex] in electrons must be removed in order to create a positive net charge. The amount of removed electrons is found after dividing remove charge by the charge of a electron:
[tex]n_{R} = \frac{-2.10\times 10^{-6}\,C}{-1.6 \times 10^{-19}\,C}[/tex]
[tex]n_{R} = 1.3125 \times 10^{13}\,electrons[/tex]
The number of atoms in 56 gram cooper ball is determined by the Avogadro's Law:
[tex]n_A = \frac{m_{ball}}{M_{Cu}}\cdot N_{A}[/tex]
Where:
[tex]m_{ball}[/tex] - Mass of the ball, measured in kilograms.
[tex]M_{Cu}[/tex] - Atomic mass of cooper, measured in grams per mole.
[tex]N_{A}[/tex] - Avogradro's Number, measured in atoms per mole.
If [tex]m_{ball} = 56\,g[/tex], [tex]M_{Cu} = 63.5\,\frac{g}{mol}[/tex] and [tex]N_{A} = 6.022\times 10^{23}\,\frac{atoms}{mol}[/tex], the number of atoms is:
[tex]n_{A} = \left(\frac{56\,g}{63.5\,\frac{g}{mol} } \right)\cdot \left(6.022\times 10^{23}\,\frac{atoms}{mol} \right)[/tex]
[tex]n_{A} = 5.3107\times 10^{23}\,atoms[/tex]
As there are 29 protons per each atom of cooper, there are 29 electrons per atom. Hence, the number of electrons in cooper is:
[tex]n_{E} = \left(29\,\frac{electrons}{atom} \right)\cdot (5.3107\times 10^{23}\,atoms)[/tex]
[tex]n_{E} = 1.5401\times 10^{23}\,electrons[/tex]
The fraction of the cooper's electrons that is removed is the ratio of removed electrons to total amount of electrons when net charge is zero:
[tex]x = \frac{n_{R}}{n_{E}}[/tex]
[tex]x = \frac{1.3125\times 10^{13}\,electrons}{1.5401\times 10^{23}\,electrons}[/tex]
[tex]x = 8.5222 \times 10^{-11}[/tex]
The fraction of the cooper's electrons that is removed is [tex]8.5222\times 10^{-11}[/tex].
A uniformly charged sphere has a potential on its surface of 450 V. At a radial distance of 8.1 m from this surface, the potential is 150 V. What is the radius of the sphere
Answers
Answer:
The radius of the sphere is 4.05 m
Explanation:
Given;
potential at surface, [tex]V_s[/tex] = 450 V
potential at radial distance, [tex]V_r[/tex] = 150
radial distance, l = 8.1 m
Apply Coulomb's law of electrostatic force;
[tex]V = \frac{KQ}{r} \\\\V_s = \frac{KQ}{r} \\\\V_r = \frac{KQ}{r+ l}[/tex]
[tex]450 = \frac{KQ}{r} ------equation (i)\\\\150 = \frac{KQ}{r+8.1} ------equation (ii)\\\\divide \ equation (i)\ by \ equation \ (ii)\\\\\frac{450}{150} = (\frac{KQ}{r} )*(\frac{r+8.1}{KQ} )\\\\3 = \frac{r+8.1}{r} \\\\3r = r + 8.1\\\\2r = 8.1\\\\r = \frac{8.1}{2} \\\\r = 4.05 \ m[/tex]
Therefore, the radius of the sphere is 4.05 m
A 2.0-kg object moving at 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision.
Answers
Answer:
20 J
Explanation:
From the question, since there is a lost in kinetic energy, Then the collision is an inelastic collision.
m'u'+mu = V(m+m')........... Equation 1
Where m' = mass of the moving object, m = mass of the stick, u' = initial velocity of the moving object, initial velocity of the stick, V = common velocity after collision.
make V the subject of the equation above
V = (m'u'+mu)/(m+m')............. Equation 2
Given: m' = 2 kg, m = 8 kg, u' = 5 m/s, u = 0 m/s (at rest).
Substitute into equation 2
V = [(2×5)+(8×0)]/(2+8)
V = 10/10
V = 1 m/s.
Lost in kinetic energy = Total kinetic energy before collision- total kinetic energy after collision
Total kinetic energy before collision = 1/2(2)(5²) = 25 J
Total kinetic energy after collision = 1/2(2)(1²) +1/2(8)(1²) = 1+4 = 5 J
Lost in kinetic energy = 25-5 = 20 J
The collision is inelastic collision. As a result of collision the kinetic energy lost by the given system is 20 J.
Since there is a lost in kinetic energy, the collision is inelastic collision.
m'u'+mu = V(m+m')
[tex]\bold {V =\dfrac { (m'u'+mu)}{(m+m')} }[/tex]
Where
m' = mass of the moving object = 2 kg
m = mass of the stick = 8 kg,
u' = initial velocity of the moving object = 5 m/s
V = common velocity after collision= ?
u = 0 m/s (at rest).
put the values in the formula,
[tex]\bold {V = \dfrac {(2\times 5)+(8\times 0)}{(2+8)}}\\\\\bold {V = \dfrac {10}{10}}\\\\\bold {V = 1\\ m/s.}[/tex]
kinetic energy before collision
[tex]\bold { = \dfrac 1{2} (2)(5^2) = 25 J}[/tex]
kinetic energy after collision
[tex]\bold { = \dfrac 12(2)(1^2) + \dfrac 12(8)(1^2) = 5\ J}[/tex]
Lost in kinetic energy = 25-5 = 20 J
Therefore, As a result of collision the kinetic energy lost by the given system is 20 J.
To know more about Kinetic energy,
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A fox locates rodents under the snow by the slight sounds they make. The fox then leaps straight into the air and burrows its nose into the snow to catch its meal. If a fox jumps up to a height of 85 cm , calculate the speed at which the fox leaves the snow and the amount of time the fox is in the air. Ignore air resistance.
Answers
Answer:
v = 4.08m/s₂
Explanation:
The robot HooRU is lost in space, floating around aimlessly, and radiates heat into the depths of the cosmos at the rate of 13.1 W. HooRU's surface area is 1.55 m2 and the emissivity of its surface is 0.287. Ignoring the radiation that HooRU absorbs from the cold universe, what is HooRU's temperature T?
Answers
Answer:
The temperature is [tex]T = 168.44 \ K[/tex]
Explanation:
From the question ewe are told that
The rate of heat transferred is [tex]P = 13.1 \ W[/tex]
The surface area is [tex]A = 1.55 \ m^2[/tex]
The emissivity of its surface is [tex]e = 0.287[/tex]
Generally, the rate of heat transfer is mathematically represented as
[tex]H = A e \sigma T^{4}[/tex]
=> [tex]T = \sqrt[4]{\frac{P}{e* \sigma } }[/tex]
where [tex]\sigma[/tex] is the Boltzmann constant with value [tex]\sigma = 5.67*10^{-8} \ W\cdot m^{-2} \cdot K^{-4}.[/tex]
substituting value
[tex]T = \sqrt[4]{\frac{13.1}{ 0.287* 5.67 *10^{-8} } }[/tex]
[tex]T = 168.44 \ K[/tex]
The smallest shift you can reliably measure on the screen is about 0.2 grid units. This shift corresponds to the precision of positions measured with the best Earth-based optical telescopes. If you cannot measure an angle smaller than this, what is the maximum distance at which a star can be located and still have a measurable parallax
Answers
Answer:
The distance is [tex]d = 1.5 *10^{15} \ km[/tex]
Explanation:
From the question we are told that
The smallest shift is [tex]d = 0.2 \ grid \ units[/tex]
Generally a grid unit is [tex]\frac{1}{10}[/tex] of an arcsec
This implies that 0.2 grid unit is [tex]k = \frac{0.2}{10} = 0.02 \ arc sec[/tex]
The maximum distance at which a star can be located and still have a measurable parallax is mathematically represented as
[tex]d = \frac{1}{k}[/tex]
substituting values
[tex]d = \frac{1}{0.02}[/tex]
[tex]d = 50 \ parsec[/tex]
Note [tex]1 \ parsec \ \to 3.26 \ light \ year \ \to 3.086*10^{13} \ km[/tex]
So [tex]d = 50 * 3.08 *10^{13}[/tex]
[tex]d = 1.5 *10^{15} \ km[/tex]
A charged particle q moves at constant velocity through a crossed electric and magnetic fields (E and B, which are both constant in magnitude and direction). Write the magnitude of the electric force on the particle in terms of the variables given. Do the same for the magnetic force
Answers
Answer:
The magnitude of the electric force on the particle in terms of the variables given is, F = qE
The magnitude of the magnetic force on the particle in terms of the variables given is, F = q (v x B)
Explanation:
Given;
a charged particle, q
magnitude of electric field, E
magnitude of magnetic field, B
The magnitude of the electric force on the particle in terms of the variables given;
F = qE
The magnitude of the magnetic force on the particle in terms of the variables given;
F = q (v x B)
where;
v is the constant velocity of the charged particle
Answer:
The magnitude of the electric force acting on a charged particle moving through an electric field = |qE|
The magnitude of the magnetic force of a charged particle moving at a particular velocity through a magnetic field = |qv × B|
Explanation:
The electric force acting on a charged particle, q, moving through an electric field, E, is given as a product of the charge on the particle (a scalar quantity) and the electric field (a vector quantity).
Electric force = qE
The magnitude of the electric force = |qE|
That is, magnitude of the product of the charge and the electric field vector.
The magnetic force acting on a charged particle, q, moving with a velocity, v, through a magnetic field, B is a vector product of qv [a product of the charge of the particle (a scalar quantity) and the velocity of the particle (a vector quantity)] and B (a vector quantity).
It is given mathematically as (qv × B)
The magnitude of the magnetic force is the magnitude of the vector product obtained.
Magnitude of the magnetic force = |qv × B|
Hope this Helps!!!