Answer:
xtotal = 90km
displacement = 18km N
Explanation:
To find the total distance traveled by the car, you first calculate the distance traveled by the car when it travels to north. You use the following formula:
[tex]x=vt[/tex] (1)
x: distance
v: speed of the car = 30 m/s
t: time = one half hour
In order to calculate the distance you convert the time from hours to seconds:
[tex]t=0.5\ h*\frac{3600s}{1\ h}=1800s[/tex]
Then, you replace the values of t and v in the equation (1):
[tex]x=(30m/s)(1800s)=54000m[/tex] (2)
Next, you calculate the distance traveled by the car when it travels to south:
[tex]x'=v't'\\\\v'=40\frac{m}{s}\\\\t'=15\ min[/tex]
You convert the time from minutes to seconds:
[tex]t'=15\ min*\frac{60s}{1min}=900s[/tex]
[tex]x'=(40m/s)(900s)=36000m[/tex]
Finally, you sum both distances x and x':
[tex]x_{total}=x+x'=54000m+36000m=90000m=90km[/tex]
The total distance traveled by the car is 90km
The total displacement is the final distance of the car respect to the starting point of the motion. This is calculated by subtracting x' to x:
[tex]d=x-x'=54000m-36000m=18000m=18km[/tex]
The total displacement of the car is 18km to the north from its starting point of motion.
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.)
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].
The Pauli exclusion principle states that Question 1 options: the wavelength of a photon of light times its frequency is equal to the speed of light. no two electrons in the same atom can have the same set of four quantum numbers. both the position of an electron and its momentum cannot be known simultaneously very accurately. the wavelength and mass of a subatomic particle are related by . an electron can have either particle character or wave character.
Answer:
no two electrons in the same atom can have the same set of four quantum numbers
Explanation:
Pauli 's Theory of Exclusion specifies that for all four of its quantum numbers, neither two electrons in the same atom can have similar value.
In a different way, we can say that no more than two electrons can take up the identical orbital, and two electrons must have adversely spin in the identical orbital
Therefore the second option is correct
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
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 charged Adam or particle is called a
Answer:
A charged atom or particle is called an ion :)
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
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]
which of the following best describes a stable atom?
A box weighing 180 newtons is hanging by rope as shown in the figure. Find the tension T2.
The question is incomplete, however, the correct question is attached
in the image format:
Answer:
B. 171 N
Explanation:
The equation of the forces along the
Horizontal direction:
[tex]T_{2} cos62^{0} = T_{1} cos20^{0}[/tex]...... 1
Verticalb direction:
[tex]T_{1} sin20^{0} = T_{2} sin62^{0}[/tex] = W . . . 2
Where W = 180 N is the weight of the box.
From equation (1),
[tex]= T_{1} =T_{2} \frac{cos62^{0}}{ cos20^{0}}[/tex]
Substituting into equation (2),
[tex](T_{2} \frac{cos62^{0}}{ cos20^{0}})[/tex][tex]sin20^{0} = T_{2} sin62^{0}[/tex]
= [tex]T = \frac{W}{cos62x^{0} tan20x^{0}+sin62x^{0} }[/tex]
=117 N
Thus, the correct answer is option B. 117 N
A coil is connected to a galvanometer, which can measure the current flowing through the coil. You are not allowed to connect a battery to this coil. Given a magnet, a battery and a long piece of wire, can you induce a steady current in that coil?
Answer:
Yes we can induce current in the coil by moving the magnet in and out of the coil steadily.
Explanation:
A current can be induced there using the magnetic field and the coil of wire. Moving the bar magnet around the coil can induce a current and this is called electromagnetic induction.
What is electromagnetic induction ?The generation of an electromotive force across an electrical conductor in a fluctuating magnetic field is known as electromagnetic or magnetic induction.
Induction was first observed in 1831 by Michael Faraday, and James Clerk Maxwell mathematically named it Faraday's law of induction. The induced field's direction is described by Lenz's law.
Electrical equipment like electric motors and generators as well as parts like inductors and transformers have all found uses for electromagnetic induction.
Here, moving the bar magnet around the coil generates the electronic movement followed by a generation of electric current.
Find more on electromagnetic induction :
https://brainly.com/question/13369951
#SPJ6
A double slit illuminated with light of wavelength 588 nm forms a diffraction pattern on a screen 11.0 cm away. The slit separation is 2464 nm. What is the distance between the third and fourth bright fringes away from the central fringe
Answer:
[tex]y_{4}-y_{3}=35.22-11.27=23.95 \mathrm{cm}[/tex]
Explanation:
Given that
Wavelength [tex]\lambda=588 \mathrm{nm}[/tex]
slit separation [tex]\mathrm{d}=2464 \mathrm{nm}[/tex]
slit screen distance [tex]\mathrm{D}=11 \mathrm{cm}[/tex]
We know that for double slit the maxima condition is that
[tex]\operatorname{dsin} \theta=m \lambda[/tex]
[tex]\sin \theta=\frac{m \lambda}{d}[/tex]
[tex]\theta=\sin ^{-1}\left(\frac{\mathrm{m} \lambda}{\mathrm{d}}\right)[/tex]
For small angle approximation, [tex]\sin \theta \approx \tan \theta \approx \theta[/tex]
[tex]\tan \theta=\frac{y_{m}}{D}[/tex]
[tex]y_{m}=D \times \tan \left[\sin ^{-1}\left(\frac{m \lambda}{d}\right)\right][/tex]
Now [tex]y_{4}[/tex] [tex]y_{4}=D \times \tan \left[\sin ^{-1}\left(\frac{4 \lambda}{d}\right)\right]=11 \times \tan \left[\sin ^{-1}\left(\frac{4 \times 588 \mathrm{nm}}{2464 \mathrm{nm}}\right)\right]=35.22 \mathrm{cm}[/tex]
Again [tex]y_{3}=D \times \tan \left[\sin ^{-1}\left(\frac{3 \lambda}{d}\right)\right]=11 \times \tan \left[\sin ^{-1}\left(\frac{3 \times 588 \mathrm{nm}}{2464 \mathrm{nm}}\right)\right]=11.27 \mathrm{cm}[/tex]
Hence [tex]y_{4}-y_{3}=35.22-11.27=23.95 \mathrm{cm}[/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.
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
In a hydraulic lift, if the pressure exerted on the liquid by one piston is increased by 100 N/m2 , how much additional weight can the other piston slowly lift if its cross sectional area is 25 m2
Answer:
The additional weight and mass needed for lifting the other piston slowly is 2500 N and 254.92 kg, respectively.
Explanation:
By means of the Pascal's Principle, the hydraulic lift can be modelled by the following two equations:
Hydraulic Lift - Before change
[tex]P = \frac{F}{A}[/tex]
Hydraulic Lift - After change
[tex]P + \Delta P = \frac{F + \Delta F}{A}[/tex]
Where:
[tex]P[/tex] - Hydrostatic pressure, measured in pascals.
[tex]\Delta P[/tex] - Change in hydrostatic pressure, measured in pascals.
[tex]A[/tex] - Cross sectional area of the hydraulic lift, measured in square meters.
[tex]F[/tex] - Hydrostatic force, measured in newtons.
[tex]\Delta F[/tex] - Change in hydrostatic force, measured in newtons.
The additional weight is obtained after some algebraic handling and the replacing of all inputs:
[tex]\frac{F}{A} + \Delta P = \frac{F}{A} + \frac{\Delta F}{A}[/tex]
[tex]\Delta P = \frac{\Delta F}{A}[/tex]
[tex]\Delta F = A\cdot \Delta P[/tex]
Given that [tex]\Delta P = 100\,Pa[/tex] and [tex]A = 25\,m^{2}[/tex], the additional weight is:
[tex]\Delta F = (25\,m^{2})\cdot (100\,Pa)[/tex]
[tex]\Delta F = 2500\,N[/tex]
The additional mass needed for the additional weight is:
[tex]\Delta m = \frac{\Delta F}{g}[/tex]
Where:
[tex]\Delta F[/tex] - Additional weight, measured in newtons.
[tex]\Delta m[/tex] - Additional mass, measured in kilograms.
[tex]g[/tex] - Gravitational constant, measured in meters per square second.
If [tex]\Delta F = 2500\,N[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], then:
[tex]\Delta m = \frac{2500\,N}{9.807\,\frac{m}{s^{2}} }[/tex]
[tex]\Delta m = 254.92\,kg[/tex]
The additional weight and mass needed for lifting the other piston slowly is 2500 N and 254.92 kg, respectively.
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
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
What do behaviorism and cognitive psychology have in common?
O Both rely on the scientific method.
Both attempt to explain human behavior.
Both note the differences between human and animal behavior
Behaviorism focuses on actions only.
Answer:
Both attempt to explain human behavior
Explanation:
Psychology is generally regarded as the science of human behavior. Behaviourism is the psychological theory which holds that behaviour can be fully understood in terms of conditioning, without actually considering thoughts or feelings. The theory holds that psychological disorders can be aptly handled by simply altering the behavioural patterns of the individual. It involves the study of stimulus and responses.
Cognitive psychology attempts to decipher what is going on in people's minds. That is, it looks at the mind as a processor of information. Hence we can define cognitive psychology as the study of the internal mental processes. This according to behaviorists, cannot be studied in measurable terms as in behaviourism (stimulus response approach) even though mental processes are known to influence human behavior significantly.
Hence, both behaviourism and cognitive psychology attempt to study human behavior from different perspectives.
A cat’s crinkle ball toy of mass 15g is thrown straight up with an initial speed of 3m/s. Assume in this problem that air drag is negligible. If the gravitational potential energy is taken to be zero at the point where it leaves your hand, what is the gravitational potential energy when the ball is at its peak height?
Answer:
P.E = 0.068 J = 68 mJ
Explanation:
First we need to find the height attained by the ball toy. For this purpose, we will be using 3rd equation of motion:
2gh = Vf² - Vi²
where,
g = -9.8 m/s² (negative sign due to upward motion)
h = height attained by the ball toy = ?
Vf = Final Velocity = 0 m/s (since it momentarily stops at the highest point)
Vi = Initial Velocity = 3 m/s
Therefore,
2(-9.8 m/s²)h = (0 m/s)² - (3 m/s)²
h = (9 m²/s²)/(19.6 m/s²)
h = 0.46 m
Now, the gravitational potential energy of ball at its peak is given by the following formula:
P.E = mgh
P.E = (0.015 kg)(9.8 m/s²)(0.46 m)
P.E = 0.068 J = 68 mJ
what is a push or a pull on an object known as
Answer:
Force
Explanation:
Force is simply known as pull or push of an object
If vector C is added to vector D, the result is a third vector that is perpendicular to D and has a magnitude equal to 3D. What is the ratio of the magnitude of C to that of D?
a) 1.3
b) 1.6
c) 1.8
d) 2.2
e) 3.2
Answer:
(e) 3.2
Explanation:
We are given that vector C and D.
Let R be the magnitude of C+D.
According to question
R=3D
We have to find the ratio of the magnitude of C to that of D.
By using right triangle property
[tex]C^2=R^2+D^2[/tex]
[tex]C^2=(3D)^2+D^2[/tex]
[tex]C^2=9D^2+D^2[/tex]
[tex]C^2=10D^2[/tex]
[tex]C=\sqrt{10D^2}=3.2D[/tex]
[tex]\frac{C}{D}=3.2[/tex]
Hence, the ratio of the magnitude of C to that of D=3.2
(e) 3.2
The electric potential of a charge distribution is given by the equation V(x) = 3x2y2 + yz3 - 2z3x, where x, y, z are measured in meters and V is measured in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0)
Answer:
The magnitude of the electric field is [tex]|E| = 8.602 \ V/m[/tex]
Explanation:
From the question we are told that
The electric potential is [tex]V = 3x^2y^2 + yz^3 - 2z^3x[/tex]
Generally electric filed is mathematically represented as
[tex]E = - [\frac{dV }{dx} i + \frac{dV}{dy} j + \frac{dV}{dz} \ k][/tex]
So
[tex]E =- ( [6xy^2 - 2z^3] i + [6x^2y+ z^3]j + [3yz^2 -6xz^2])[/tex]
at (x,y,z) = (1.0, 1.0, 1.0)
[tex]E = [6(1)(1)^2 - 2(1)^3] i + [6(1)^2(1)+ (1)^3]j + [6(1)(1)^2 -6(1)(1)^2][/tex]
[tex]E =- ([4] i + [7]j + [-3])[/tex]
[tex]E =-4i -7j + 3 k[/tex]
The magnitude of the electric field is
[tex]|E| = \sqrt{(-4)^2 + (-7)^2 + (3^2)}[/tex]
[tex]|E| = 8.602 \ V/m[/tex]
A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof 1.0 s later. You may ignore air resistance. If the height of the building is 20 m, what must the initial speed be of the first ball if both balls are to hit the ground at the same time
Answer:
4.9 m/s
Hope this helps! ;)
Explanation:
The magnet has an unchanging magnetic field: very strong near the magnet, and weak far from the magnet. How did the magnetic field through the coil change as the magnet fell toward it? How did the magnetic flux through the coil change as the magnet fell toward it?
Answer:
The magnetic field through the coil at first increases steadily up to its maximum value, and then decreases gradually to its minimum value.
Explanation:
At first, the magnet fall towards the coils; inducing a gradually increasing magnetic field through the coil as it falls into the coil. At the instance when half the magnet coincides with the coil, the magnetic field magnitude on the coil is at its maximum value. When the magnet falls pass the coil towards the floor, the magnetic field then starts to decrease gradually from a strong magnitude to a weak magnitude.
This action creates a changing magnetic flux around the coil. The result is that an induced current is induced in the coil, and the induced current in the coil will flow in such a way as to oppose the action of the falling magnet. This is based on lenz law that states that the induced current acts in such a way as to oppose the motion or the action that produces it.
A 300-W computer (including the monitor) is turned on for 8.0 hours per day. If electricity costs 15¢ per kWh, how much does it cost to run the computer annually for a typical 365-day year? (Choose the closest answer)
Answer:
Cost per year = $131.4
Explanation:
We are given;
Power rating of computer with monitor;P = 300 W = 0.3 KW
Cost of power per KWh = 15 cents = $0.15
Time used per day by the computer with monitor = 8 hours
Thus; amount of power consumed per 8 hours each day = 0.3 × 8 = 2.4 KWh per day
Thus, for 365 days in a year, total amount amount of power = 2.4 × 365 = 876 KWh
Now, since cost of power per KWh is $0.15, then cost for 365 days would be;
876 × 0.15 = $131.4
A long horizontal hose of diameter 3.4 cm is connected to a faucet. At the other end, there is a nozzle of diameter 1.8 cm. Water squirts from the nozzle at velocity 14 m/sec. Assume that the water has no viscosity or other form of energy dissipation.
A) What is the velocity of the water in the hose ?
B) What is the pressure differential between the water in the hose and water in the nozzle ?
C) How long will it take to fill a tub of volume 120 liters with the hose ?
Answer:
a) v₁ = 3.92 m / s , b) ΔP = = 9.0 10⁴ Pa, c) t = 0.0297 s
Explanation:
This is a fluid mechanics exercise
a) let's use the continuity equation
let's use index 1 for the hose and index 2 for the nozzle
A₁ v₁ = A₂v₂
in area of a circle is
A = π r² = π d² / 4
we substitute in the continuity equation
π d₁² / 4 v₁ = π d₂² / 4 v₂
d₁² v₁ = d₂² v₂
the speed of the water in the hose is v1
v₁ = v₂ d₂² / d₁²
v₁ = 14 (1.8 / 3.4)²
v₁ = 3.92 m / s
b) they ask us for the pressure difference, for this we use Bernoulli's equation
P₁ + ½ ρ v₁² + m g y₁ = P₂ + ½ ρ v₂² + mg y2
as the hose is horizontal y₁ = y₂
P₁ - P₂ = ½ ρ (v₂² - v₁²)
ΔP = ½ 1000 (14² - 3.92²)
ΔP = 90316.8 Pa = 9.0 10⁴ Pa
c) how long does a tub take to flat
the continuity equation is equal to the system flow
Q = A₁v₁
Q = V t
where V is the volume, let's equalize the equations
V t = A₁ v₁
t = A₁ v₁ / V
A₁ = π d₁² / 4
let's reduce it to SI units
V = 120 l (1 m³ / 1000 l) = 0.120 m³
d1 = 3.4 cm (1 m / 100cm) = 3.4 10⁻² m
let's substitute and calculate
t = π d₁²/4 v1 / V
t = π (3.4 10⁻²)²/4 3.92 / 0.120
t = 0.0297 s
g The Trans-Alaskan pipeline is 1,300 km long, reaching from Prudhoe Bay to the port of Valdez, and is subject to temperatures ranging from -71°C to +35°C. How much does the steel pipeline expand due to the difference in temperature?
Answer:
ΔL = 1.653 km
Explanation:
The linear expansion of any object due to change in temperature is given by the following formula:
ΔL = αLΔT
where,
ΔL = Change in length or expansion of steel pipe line = ?
α = coefficient of linear expansion of steel = 12 x 10⁻⁶ /°C
L = Original Length of the steel pipe = 1300 km
ΔT = Change in temperature = 35°C - (- 71°C) = 35°C + 71°C = 106°C
Therefore,
ΔL = (12 x 10⁻⁶ /°C)(1300 km)(106°C)
ΔL = 1.653 km
As you know, a common example of a harmonic oscillator is a mass attached to a spring. In this problem, we will consider a horizontally moving block attached to a spring. Note that, since the gravitational potential energy is not changing in this case, it can be excluded from the calculations. For such a system, the potential energy is stored in the spring and is given by
U = 12k x 2
where k is the force constant of the spring and x is the distance from the equilibrium position. The kinetic energy of the system is, as always,
K = 12mv2
where m is the mass of the block and v is the speed of the block.
A) Find the total energy of the object at any point in its motion.
B) Find the amplitude of the motion.
C) Find the maximum speed attained by the object during its motion.
Answer:
a) [tex]E = \frac{1}{2} \cdot k \cdot x^{2} + \frac{1}{2} \cdot m \cdot v^{2}[/tex], b) Amplitude of the motion is [tex]A = \sqrt{\frac{2\cdot E}{k} }[/tex], c) The maximum speed attained by the object during its motion is [tex]v_{max} = \sqrt{\frac{2\cdot E}{m} }[/tex].
Explanation:
a) The total energy of the object is equal to the sum of potential and kinetic energies. That is:
[tex]E = K + U[/tex]
Where:
[tex]K[/tex] - Kinetic energy, dimensionless.
[tex]U[/tex] - Potential energy, dimensionless.
After replacing each term, the total energy of the object at any point in its motion is:
[tex]E = \frac{1}{2} \cdot k \cdot x^{2} + \frac{1}{2} \cdot m \cdot v^{2}[/tex]
b) The amplitude of the motion occurs when total energy is equal to potential energy, that is, when objects reaches maximum or minimum position with respect to position of equilibrium. That is:
[tex]E = U[/tex]
[tex]E = \frac{1}{2} \cdot k \cdot A^{2}[/tex]
Amplitude is finally cleared:
[tex]A = \sqrt{\frac{2\cdot E}{k} }[/tex]
Amplitude of the motion is [tex]A = \sqrt{\frac{2\cdot E}{k} }[/tex].
c) The maximum speed of the motion when total energy is equal to kinetic energy. That is to say:
[tex]E = K[/tex]
[tex]E = \frac{1}{2}\cdot m \cdot v_{max}^{2}[/tex]
Maximum speed is now cleared:
[tex]v_{max} = \sqrt{\frac{2\cdot E}{m} }[/tex]
The maximum speed attained by the object during its motion is [tex]v_{max} = \sqrt{\frac{2\cdot E}{m} }[/tex].
A positively charged particle Q1 = +45 nC is held fixed at the origin. A second charge Q2 of mass m = 4.5 μg is floating a distance d = 25 cm above charge The net force on Q2 is equal to zero. You may assume this system is close to the surface of the Earth.
|Q2| = m g d2/( k Q1 )
Calculate the magnitude of Q2 in units of nanocoulombs.
Answer:
( About ) 6.8nC
Explanation:
We are given the equation |Q2| = mgd^2 / kQ1. Let us substitute known values into this equation, but first list the given,
Charge Q2 = +45nC = (45 × 10⁻⁹) C
mass of charge Q2 = 4.5 μg, force of gravity = 4.5 μg × 9.8 m/s² = ( 4.41 × 10^-5 ) N,
Distance between charges = 25 cm = 0.25 m,
k = Coulomb's constant = 9 × 10^9
_______________________________________________________
And of course, we have to solve for the magnitude of Q2, represented by the charge magnitude of the charge on Q2 -
(4.41 × 10^-5) = [(9.0 × 10⁹) × (45 × 10⁻⁹) × Q₂] / 0.25²
_______________________________________________________
Solution = ( About ) 6.8nC
Suppose two children push horizontally, but in exactly opposite directions, on a third child in a sled. The first child exerts a force of 79 N, the second a force of 92 N, kinetic friction is 5.5 N, and the mass of the third child plus sled is 24 kg.
1. Using a coordinate system where the second child is pushing in the positive direction, calculate the acceleration in m/s2.
2. What is the system of interest if the accelaration of the child in the wagon is to be calculated?
3. Draw a free body diagram including all bodies acting on the system
4. What would be the acceleration if friction were 150 N?
Answer:
Please, read the anser below
Explanation:
1. In order to calculate the acceleration of the children you use the Newton second law for the summation of the implied forces:
[tex]F_2-F_1-F_f=Ma[/tex] (1)
Where is has been used that the motion is in the direction of the applied force by the second child
F2: force of the second child = 92N
F1: force of the first child = 79N
Ff: friction force = 5.5N
M: mass of the third child = 24kg
a: acceleration of the third child = ?
You solve the equation (1) for a, and you replace the values of the other parameters:
[tex]a=\frac{F_2-F_1.F_f}{M}=\frac{96N-79N-5.5N}{24kg}=0.48\frac{m}{s^2}[/tex]
The acceleration is 0.48m/s^2
2. The system of interest is the same as before, the acceleration calculated is about the motion of the third child.
3. An image with the diagram forces is attached below.
4. If the friction would be 150N, the acceleration would be zero, because the friction force is higher than the higher force between children, which is 92N.
Then, the acceleration is zero
Suppose you are chatting with your friend, who lives on the moon. He tells you he has just won a Newton of gold in a contest. Excitedly, you tell him that you entered the Earth version of the same contest and also won a Newton of gold. Who is richer
Answer:
The friend on moon is richer.
Explanation:
The value of acceleration due to gravity changes from planet to planet. So the weight of 1 Newton of gold carries different mass on different places. So we need to calculate the mass of gold that both persons have.
FRIEND ON MOON:
W₁ = m₁g₁
where,
W₁ = Weight of Gold won by friend on moon = 1 N
m₁ = mass of gold won by friend on moon = ?
g₁ = acceleration due to gravity on moon = 1.625 m/s²
Therefore,
1 N = m₁(1.625 m/s²)
m₁ = 0.62 kg
ON EARTH:
W₂ = m₂g₂
where,
W₂ = Weight of Gold won by me on Earth = 1 N
m₂ = mass of gold won by me on Earth = ?
g₂ = acceleration due to gravity on Earth = 9.8 m/s²
Therefore,
1 N = m₁(9.8 m/s²)
m₁ = 0.1 kg
Since, the friend on moon has greater mass of gold than me.
Therefore, the friend on moon is richer.
You throw a ball straight up into the air from the top of a building. The building has a height of 15.0 m. The ball reaches a height (measured from the ground) of 25.0 m and then it starts to fall back down.
a) Determine the initial velocity of the ball.
b) What is the velocity of the ball when it comes back down and is at the same height from which it was thrown?
c) How long will it take the ball to come back down to this height from the time at which it was first thrown?
d) Let’s say that you missed catching the ball on the way back down and it fell to the ground. How long did it take to hit the ground from the moment you threw it up?
e) What was the ball’s final velocity the moment before it hit the ground?
Answer:
a) vo = 14m/s
b) v = 14m/s
c) t = 2.85s
d) t = 0.829s
e) v = 22.12 m/s
Explanation:
a) To find the initial velocity of the ball yo use the following formula:
[tex]h_{max}=\frac{v_o^2}{2g}[/tex] (1)
hmax: maximum height reached by the ball but measured from the point at which the ball is thrown = 25.0m - 15.0m = 10.0m
vo: initial velocity of the ball = ?
g: gravitational acceleration = 9.8m/s^2
You solve the equation (1) for vo and replace the values of the other parameters:
[tex]v_o=\sqrt{2gh_{max}}}=\sqrt{2(9.8m/s^2)(10.0m)}=14\frac{m}{s}[/tex]
The initial velocity of the ball is 14m/s
b) To find the velocity of the ball when it is at the same position as the initial point where it was thrown, you can use the following formula:
[tex]v^2=2gh_{max}\\\\v=\sqrt{2gh_{max}}[/tex]
as you can notice, v = vo = 14m/s
The velocity of the ball is 14 m/s
c) The flight time of the ball is given by twice the time the ball takes to reach the maximum height. You use the following formula:
[tex]t=2\frac{v_o}{g}=2\frac{14m/s}{9.8m/s^2}=2.85s[/tex] (3)
The time is 2.85s
d) To find the time the ball takes to arrive to the ground after the ball passes the same height at which is was thrown, you can use the following formula:
[tex]y=y_o-v_ot-\frac{1}{2}gt^2[/tex] (4)
y: 0 m (ball just after it impact the ground)
yo: initial position = 15.0 m
vo: in)itial velocity of the ball = 14m/s
t: time
You replace the values of the parameters in the equation (4) and obtain a quadratic formula:
[tex]0=15.0-14t-\frac{1}{2}(9.8)t^2\\\\[/tex]
You use the quadratic formula to find the roots t:
[tex]t_{1,2}=\frac{-(-14)\pm\sqrt{(-14)^2-4(4.9)(15)}}{2(-4.9)}\\\\t_{1,2}=\frac{14\pm22.13}{-9.8}\\\\t_1=0.829s\\\\t_2=-2.19s[/tex]
you choose the positive values because is has physical meaning
The time the ball takes to arrive to the ground is 0.829s
e) The final velocity is:
[tex]v=v_o+gt[/tex]
[tex]v=14m/s+(9.8m/s^2)(0.829s)=22.12\frac{m}{s}[/tex]
The final velocity is 22.14 m/s
Water molecules are made of slightly positively charged hydrogen atoms and slightly negatively charged oxygen atoms. Which force keeps water molecules stuck to one another? strong nuclear gravitational weak nuclear electromagnetic
Answer:
The answer is electromagnetic
Answer:
electromagnetic
Explanation:
edge 2021
A 26 kg child is coasting at 2.0 m/s over flat ground in a 5.0 kg wagon. The child drops a 1.5 kg ball from the side of the wagon. What is the final speed (in m/s) of the child and wagon
Answer:
Final speed = 2.067 m/s
Explanation:
We are told that the child weighs 26 kg.
Also, that the wagon weighs 5kg.
Thus,initial mass of the child and wagon with ball is;
m_i = 26 + 5 = 31 kg.
Also, we are told that the child now dropped 1.5 kg ball from the wagon. So,
Final mass is;
m_f = 26 + 5 - 1 = 30 kg
Now, from conservation of linear momentum, we know that;
Initial momentum = final momentum
Thus;
m_i * v_i = m_f * v_f
Where v_i is initial velocity and v_f is final velocity.
Making v_f the subject, we have;
v_f = (m_i * v_i)/m_f
We are given that initial velocity v_i = 2 m/s
Plugging in the relevant values, we have;
v_f = (31 * 2)/30
v_f = 2.067 m/s
In the slap shot video, and the professor said that the puck experienced "an average force of 100 pounds" which we now know is 445 Newtons of average force. The duration of this collision is .02 seconds. Calculate the Impulse in this puck/stick collision. The mass of the puck is .175 kg.
Answer:
I = 89 N s
Explanation:
Momentum is a concept that tells us how much the amount of movement of a system changes, it is described by the expression
I = ∫ F dt = F_average t
where F is the force and t is the time
let's calculate
I = 445 0.2
I = 89 N s