Answer:
v = 61.09m/s
Explanation:
In order to calculate the speed of the electron when it is 3.00cm from the proton, you first calculate the acceleration of the electron, produced by the electric force between the electron and the proton. By using the second Newton law you have:
[tex]F=ma=k\frac{q^2}{r^2}[/tex] (1)
m: mass of the electron = 9.1*10^-31kg
q: charge of electron and proton = 1.6*10^-19C
r: distance between electron and proton = 9.00cm = 0.09m
k: Coulomb's constant = 8.98*10^9Nm2/C^2
You solve the equation (1) for a, and replace the values of the other parameters:
[tex]a=\frac{kq^2}{mr^2}=\frac{(8.98*10^9Nm^2/C^2)(1.6*10^{-19}C)^2}{(9.1*10^{-31}kg)(0.09m)^2}=3.11*10^4\frac{m}{s^2}[/tex]
Next, you use the following formula to calculate the final speed of the electron:
[tex]v^2=v_o^2+2ax[/tex] (2)
vo: initial speed of the electron = 0m/s
a: acceleration = 3.11*10^4m/s^2
x: distance traveled by the electron
When the electron is at 3.00cm from the proton the electron has traveled a distance of 9.00cm - 3.00cm = 6.00cm = 0.06m = x
You replace the values of the parameters in the equation (2):
[tex]v=\sqrt{2ax}=\sqrt{2(3.11*10^4m/s)(0.06m)}=61.09\frac{m}{s}[/tex]
The speed of the electron is 61.09m/s
A force of 175 N is exerted on the pedal cylinder of an automatic hydraulic system. The pedal cylinder has a diameter of 0.475 cm. How much pressure is transmitted in the hydraulic system
Answer:
this is the required pressure transmitted in the hydraulic system.
Dolphins of the open ocean are classified as Type II Odontocetes (toothed whales). These animals use ultrasonic "clicks" with a frequency of about 55 kHz to navigate and find prey. You may want to review (Pages 465 - 467) . Part A Suppose a dolphin sends out a series of clicks that are reflected back from the bottom of the ocean 75 m below. How much time elapses before the dolphin hears the echoes of the clicks
Answer:
0.1 sec
Explanation:
frequency of the clicks produced = 55 kHz = 55000 Hz
depth of the bottom of ocean from the dolphin = 75 m
we know that the speed of sound in water is generally accepted to be ≅ 1480 m/s.
the total distance traveled by the sound from the dolphin, to the bottom of the ocean, and then back to the dolphin = 2 x 75 = 150 m
time elapsed will then be
time = distance traveled ÷ speed of sound
time = 150/1480 ≅0.1 sec
A force in the negative x-direction is applied for 27 ms to a 0.4 kg mass initially moving at 14 m/s in the x-direction. The force varies in magnitude and delivers an impulse with a magnitude of 32.4 N-s. What is the mass's velocity in the x-direction
Answer:
-67 m/s
Explanation:
We are given that
Mass of ball,m=0.4 kg
Initial speed,u=14 m/s
Impulse,I=-32.4 N-s
Time,t=27 ms=[tex]27\times 10^{-3} s[/tex]
We have to find the mass's velocity in the x- direction.
We know that
[tex]Impulse=mv-mu[/tex]
Substitute the values
[tex]-32.4=0.4v-0.4(14)[/tex]
[tex]-32.4+0.4(14)=0.4 v[/tex]
[tex]-26.8=0.4v[/tex]
[tex]v=\frac{-26.8}{0.4}=-67m/s[/tex]
Explain how a refrigerator works to cool down warm objects that would otherwise be room temperature
Answer: evaporation
Explanation:
Refrigerators work by causing the refrigerant circulating inside them to change from a liquid into a gas. This process, called evaporation, cools the surrounding area and produces the desired effect.
In Young's double slit experiment, 427 nm light gives a fourth-order bright fringe at a certain location on a flat screen. What is the longest wavelength of visible light that would produce a dark fringe at the same location
Answer:
λ' = 379.22nm
Explanation:
In order to find the longest wavelength that allows one to dark fringe coincides with the bright fringe, you use the following formulas:
[tex]y_{bright}=\frac{m\lambda D}{d}[/tex] (1)
[tex]y_{dark}=(m+\frac{1}{2})\frac{\lambda' D}{d}[/tex] (2)
y-dark and y-bright are the positions of dark fringes and bright fringes respectively.
m: order of the fringe (dark or bright) = 4
D: distance to the screen
d: distance between slits
λ: light for y-bright= 427nm
λ': second light for y-dark = ?
By the information of the statement you know that y-bright = y-dark.
You divide equation (2) into the equation (1) and solve for λ':
[tex]\frac{y_{dark}}{y_{bright}}=1=\frac{(m+1/2)\lambda'}{m\lambda}\\\\\lambda'=\frac{m\lambda}{m+1/2}[/tex] (3)
Finally, you solve the equation (3) by replacing the values of m and the wavelength:
[tex]\lambda'=\frac{4(427nm)}{4+1/2}=379.55nm[/tex]
The longest wavelength which produces the fourth dark fringe in the same location for the fourth bright fringe of the first wavelength is 379.22nm
Assume you have a rocket in Earth orbit and want to go to Mars. The required change in velocity is ΔV≈9.6km/s . There are two options for the propulsion system --- chemical and electric --- each with a different specific impulse. Recall that the relationship between specific impulse and exhaust velocity is: Vex=g0Isp Using the Ideal Rocket Equation and setting g0=9.81m/s2 , calculate the propellant fraction required to achieve the necessary ΔV for each of propulsion system. Part 1: Cryogenic Chemical Propulsion First, consider a cryogenic chemical propulsion system with Isp≈450s . Enter the required propellant fraction as a proportion with at least 2 decimal places (i.e., enter 0.25 to represent 25%): incorrect Part 2: Electric Propulsion Next, consider an electric propulsion system with Isp≈2000s . Enter the required propellant fraction as a proportion with at least 2 decimal places (i.e., enter 0.25 to represent 25%):
Answer: Part 1: Propellant Fraction (MR) = 8.76
Part 2: Propellant Fraction (MR) = 1.63
Explanation: The Ideal Rocket Equation is given by:
Δv = [tex]v_{ex}.ln(\frac{m_{f}}{m_{e}} )[/tex]
Where:
[tex]v_{ex}[/tex] is relationship between exhaust velocity and specific impulse
[tex]\frac{m_{f}}{m_{e}}[/tex] is the porpellant fraction, also written as MR.
The relationship [tex]v_{ex}[/tex] is: [tex]v_{ex} = g_{0}.Isp[/tex]
To determine the fraction:
Δv = [tex]v_{ex}.ln(\frac{m_{f}}{m_{e}} )[/tex]
[tex]ln(MR) = \frac{v}{v_{ex}}[/tex]
Knowing that change in velocity is Δv = 9.6km/s and [tex]g_{0}[/tex] = 9.81m/s²
Note: Velocity and gravity have different measures, so to cancel them out, transform km in m by multiplying velocity by 10³.
Part 1: Isp = 450s
[tex]ln(MR) = \frac{v}{v_{ex}}[/tex]
ln(MR) = [tex]\frac{9.6.10^{3}}{9.81.450}[/tex]
ln (MR) = 2.17
MR = [tex]e^{2.17}[/tex]
MR = 8.76
Part 2: Isp = 2000s
[tex]ln(MR) = \frac{v}{v_{ex}}[/tex]
ln (MR) = [tex]\frac{9.6.10^{3}}{9.81.2.10^{3}}[/tex]
ln (MR) = 0.49
MR = [tex]e^{0.49}[/tex]
MR = 1.63
Robin is standing terrified at the end of a diving board, which is high above the water. If Robin has a mass of 76 kg and is standing 1.6 m from the board's pivot point, what torque is Robin exerting on the board
Answer:
Torque = 1191.68 N-m
Explanation:
Given data
mass m = 76 kg
standingdistance r = 1.6 m
Solution
we get here torque that si express as
torque = force × distance ................1
torque = r × F sin(theta)
and we know that
F = mg .........2
and g = 9.8 m/s²
put here value in equation 1 we get
Torque = 76 × 1.6 × 9.8 × sin(90)
Torque = 1191.68 N-m
When you lift a bowling ball with a force of 58.4 N, the ball accelerates upward with an acceleration a. If you lift with a force of 65.9 IN, the ball's acceleration is 2.01a. Calculate the weight of the bowling ball.
Answer :):):):):):):):):):):):):):):):):):):):):);):):):):):):):):)
Explanation:
Three particles are moving perpendicular to a uniform magnetic field and travel on circular paths (see the drawing). They have the same mass and speed. List the particles in order of their charge magnitude, largest to smallest.
Explanation:
Radius of a charged particle is given by
r=mv / Bq
= k/ q
where k = m v / B is a constant.
i.e. more is the magnitude of charge, less is the radius. (inversely proportional)
From the diagram r_3 > r_2 > r_1 (more the curvature, less is the radius)
( although drawing is not given i am assuming the above order, however, one can change the order as per the diagram. The concept used remains the same)
therefore, q_1 > q_2 > q_3 .
A high-jumper clears the bar and has a downward velocity of - 5.00 m/s just before landing on an air mattress and bouncing up at 1.0 m/s. The mass of the high-jumper is 60.0 kg. What is the magnitude and direction of the impulse that the air mattress exerts on her
-- As she lands on the air mattress, her momentum is (m v)
Momentum = (60 kg) (5 m/s down) = 300 kg-m/s down
-- As she leaves it after the bounce,
Momentum = (60 kg) (1 m/s up) = 60 kg-m/s up
-- The impulse (change in momentum) is
Change = (60 kg-m/s up) - (300 kg-m/s down)
Magnitude of the change = 360 km-m/s
The direction of the change is up /\ .
The direction of a body or object's movement is defined by its velocity.In its basic form, speed is a scalar quantity.In essence, velocity is a vector quantity.It is the speed at which distance changes.It is the displacement change rate.
Solve the problem ?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path.In other words, velocity is a vector, whereas speed is a scalar value. We discuss the conceptive impulse in this puzzle.A high jumper weighing 60.0 kg sprints on the matrix at minus 6 meters per second in the downhill direction before falling to the mattress.her admirer.Speed drops to 0 meters/second.We must determine the impulse's size and presumed direction, which is upward and positive.The change in momentum is then equal to the impulse.The impulse therefore equals m times.the end velocity less the starting velocity.60.0kg times 0 minus minus 6 meters per second is the impulse, therefore.The impulse is 360 kilogram meters per second, or 360 newtons, to put it another way.The second is upward, and the direction.To learn more about magnitude refer
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Which circuits are parallel circuits?
Answer:
The bottom two lines.
Explanation:
They need their own line of voltage quantity. A parallel circuit has the definition of 'two or more paths for current to flow through.' The voltage does stay the same in each line.
A 73 kg swimmer dives horizontally off a 462 kg raft initially at rest. If the diver's speed immediately after leaving the raft is 5.54 m/s, what is the corresponding raft speed
Answer:
Corresponding raft speed = -0.875 m/s (the minus sign indicates that the raft moves in the direction opposite to the diver)
Explanation:
Law of conservation of momentum gives that the momentum of the diver and the raft before the dive is equal to the momentum of the diver and the raft after the dive.
And since the raft and the diver are initially at rest, the momentum of the diver after the dive is equal and opposite to the momentum experienced by the raft after the dive.
(Final momentum of the diver) + (Final momentum of the raft) = 0
Final Momentum of the diver = (mass of the diver) × (diving velocity of the diver)
Mass of the diver = 73 kg
Diving velocity of the diver = 5.54 m/s
Momentum of the diver = 73 × 5.54 = 404.42 kgm/s
Momentum of the raft = (mass of the raft) × (velocity of the raft)
Mass of the raft = 462 kg
Velocity of the raft = v
Momentum of the raft = 462 × v = (462v) kgm/s
404.42 + 462v = 0
462v = -404.42
v = (-404.42/462) = -0.875 m/s (the minus sign indicates that the raft moves in the direction opposite to the diver)
Hope this Helps!!!
The exit nozzle in a jet engine receives air at 1200 K, 150 kPa with negligible kinetic energy. The exit pressure is 80 kPa, and the process is reversible and adiabatic. Use constant specific heat at 300 K to find the
Complete question:
The exit nozzle in a jet engine receives air at 1200 K, 150 kPa with negligible kinetic energy. The exit pressure is 80 kPa, and the process is reversible and adiabatic. Use constant specific heat at 300 K to find the exit velocity.
Answer:
The exit velocity is 629.41 m/s
Explanation:
Given;
initial temperature, T₁ = 1200K
initial pressure, P₁ = 150 kPa
final pressure, P₂ = 80 kPa
specific heat at 300 K, Cp = 1004 J/kgK
k = 1.4
Calculate final temperature;
[tex]T_2 = T_1(\frac{P_2}{P_1})^{\frac{k-1 }{k}[/tex]
k = 1.4
[tex]T_2 = T_1(\frac{P_2}{P_1})^{\frac{k-1 }{k}}\\\\T_2 = 1200(\frac{80}{150})^{\frac{1.4-1 }{1.4}}\\\\T_2 = 1002.714K[/tex]
Work done is given as;
[tex]W = \frac{1}{2} *m*(v_i^2 - v_e^2)[/tex]
inlet velocity is negligible;
[tex]v_e = \sqrt{\frac{2W}{m} } = \sqrt{2*C_p(T_1-T_2)} \\\\v_e = \sqrt{2*1004(1200-1002.714)}\\\\v_e = \sqrt{396150.288} \\\\v_e = 629.41 \ m/s[/tex]
Therefore, the exit velocity is 629.41 m/s
An Olympic track runner starts from rest and has an acceleration of 2.1 m/s2 for 3.5 s, then has zero acceleration for the remainder of the race. Find the runner's speed at the following times.
(a) at time t = 1.3 s
m/s
(b) the end of the race
m/s
Answer:
a) = 2.73 m/s
b) 7.35 m/s
Explanation:
runner starts from rest, initial velocity u = 0 m/s
acceleration a = 2.1 m/s^2
time = 3.5 s
after the 3.5 s, his acceleration = 0
a) the time t = 1.3 s falls within the time frame where he was accelerating.
using the equation
[tex]v = u + at[/tex]
v = 0 + (2.1 x 1.3)
v = 2.73 m/s
b) the end of the race fall outside the time frame in which the runner is accelerating.
This means that his speed at the end of the race will be equal to his speed at 3.5 s
we use the formula as before
[tex]v = u + at[/tex]
v = 0 + (2.1 x 3.5)
v = 7.35 m/s
In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima. You observe that this separation is greatest when you illuminate the double slit with In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima. You observe that this separation is greatest when you illuminate the double slit with:
1. yellow light.
2. red light.
3. blue light.
4. green light.
5. The separation is the same for all wavelengths.
Answer:
we see that the lights with the most extreme wavelength are blue and red
we see that the separation between the interference lines (y) increases linearly with the wavelength for which the phenomenon is best observed in the RED response 2
Explanation:
In Young's double-slit experiment, constructive interference is written by the equation
d sin θ = m λ
where you give the gap separation, lam the length of the donda used and m the order of interference
in many he uses trigonometry to express the synth in confusing the distances on a very distant screen
so θ = y / L
in this experiment the angles are generally very small, so
tan θ = sin θ / cos θ = sin θ
sint θ = y / L
let's replace
d y / L = mλ
y = (m L / d) λ
now let's examine the effect of changing the wavelength
1 yellow lam = 600 10⁻⁹ m
2) red lam = 750 10⁻⁹m
3) blue lam = 450 10⁻⁸ nm
4) green lam = 550 10⁻⁹ nm
we see that the lights with the most extreme wavelength are blue and red
we see that the separation between the interference lines (y) increases linearly with the wavelength for which the phenomenon is best observed in the RED response 2
An electron moves at a speed of 1.0 x 104 m/s in a circular path of radius 2 cm inside a solenoid. The magnetic field of the solenoid is perpendicular to the plane of the electron’s path. Calculate (a) the strength of the magnetic field inside the solenoid and (b) the current in the solenoid if it has 25 turns per centimeter.
Answer:
(a) B = 2.85 × [tex]10^{-6}[/tex] Tesla
(b) I = I = 0.285 A
Explanation:
a. The strength of magnetic field, B, in a solenoid is determined by;
r = [tex]\frac{mv}{qB}[/tex]
⇒ B = [tex]\frac{mv}{qr}[/tex]
Where: r is the radius, m is the mass of the electron, v is its velocity, q is the charge on the electron and B is the magnetic field
B = [tex]\frac{9.11*10^{-31*1.0*10^{4} } }{1.6*10^{-19}*0.02 }[/tex]
= [tex]\frac{9.11*10^{-27} }{3.2*10^{-21} }[/tex]
B = 2.85 × [tex]10^{-6}[/tex] Tesla
b. Given that; N/L = 25 turns per centimetre, then the current, I, can be determined by;
B = μ I N/L
⇒ I = B ÷ μN/L
where B is the magnetic field, μ is the permeability of free space = 4.0 ×[tex]10^{-7}[/tex]Tm/A, N/L is the number of turns per length.
I = B ÷ μN/L
= [tex]\frac{2.85*10^{-6} }{4*10^{-7} *25}[/tex]
I = 0.285 A
Question 9(Multiple Choice Worth 4 points) (05.03 LC) What most likely happens when water vapor cools? It changes into gas. It changes into liquid. Its temperature increases. Its temperature remains constant.
Answer:
it changes into liquid
Answer:
It changes in to liquids
Explanation:
This is because the water vapor cools down and condenses it attaches it self to dust forming water droplets. Those water droplets are water.
A hockey puck on a frozen pond is given an initial speed of 20.0 m/s. If the puck always remains on the ice and slides 115 m before coming to rest, determine the coefficient of kinetic friction between the puck and ice.
Answer:
μ_k = 0.1773
Explanation:
We are given;
Initial velocity;u = 20 m/s
Final velocity;v = 0 m/s (since it comes to rest)
Distance before coming to rest;s = 115 m
Let's find the acceleration using Newton's second law of motion;
v² = u² + 2as
Making a the subject, we have;
a = (v² - u²)/2s
Plugging relevant values;
a = (0² - 20²)/(2 × 115)
a = -400/230
a = -1.739 m/s²
From the question, the only force acting on the puck in the x direction is the force of friction. Since friction always opposes motion, we see that:
F_k = −ma - - - (1)
We also know that F_k is defined by;
F_k = μ_k•N
Where;
μ_k is coefficient of kinetic friction
N is normal force which is (mg)
Since gravity acts in the negative direction, the normal force will be positive.
Thus;
F_k = μ_k•mg - - - (2)
where g is acceleration due to gravity.
Thus,equating equation 1 and 2,we have;
−ma = μ_k•mg
m will cancel out to give;
-a = μ_k•g
μ_k = -a/g
g has a constant value of 9.81 m/s², so;
μ_k = - (-1.739/9.81)
μ_k = 0.1773
The coefficient of kinetic friction between the hockey puck and ice is equal to 0.178
Given the following data:
Initial speed = 20 m/sFinal velocity = 0 m/s (since it came to rest)Distance = 115 mScientific data:
Acceleration due to gravity = 9.8 [tex]m/s^2[/tex]To determine the coefficient of kinetic friction between the hockey puck and ice:
First of all, we would calculate the acceleration of the hockey puck by using the third equation of motion.
[tex]V^2 = U^2 + 2aS\\\\0^2 =20^2 + 2a(115)\\\\-400=230a\\\\a=\frac{-400}{230}[/tex]
Acceleration, a = -1.74 [tex]m/s^2[/tex]
Note: The negative signs indicates that the hockey puck is slowing down or decelerating.
From Newton's Second Law of Motion, we have:
[tex]\sum F_x = F_k + F_n =0\\\\F_k =- F_n\\\\\mu mg =-ma\\\\\mu = \frac{-a}{g}\\\\\mu = \frac{-(-1.74)}{9.8}\\\\\mu = \frac{1.74}{9.8}[/tex]
Coefficient of kinetic friction = 0.178
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Fiber optics are an important part of our modern internet. In these fibers, two different glasses are used to confine the light by total internal reflection at the critical angle for the interface between the core (ncore =1.497) and the cladding (ncladding =1.421)
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]\theta_{max} =18.38^o[/tex]
b
New [tex]n_{cladding} =1.491[/tex]
Explanation:
From the question we are told that
The refractive index of the core is [tex]n_{core} = 1.497[/tex]
The refractive index of the cladding is [tex]n_{cladding} = 1.421[/tex]
Generally according to Snell's law
[tex]n_{core} * sin(90- \theta) = n_{cladding} * sin (90)[/tex]
Where [tex]\theta_{max}[/tex] is the largest angle a largest angle a ray will make with respect to the interface of the fiber and experience total internal reflection
[tex]\theta_{max} = 90 - sin^{-1} [\frac{n_{cladding}}{n_{core}} ][/tex]
[tex]\theta_{max} = 90 - sin^{-1} [\frac{1.421}{1.497}} ][/tex]
[tex]\theta_{max} =18.38^o[/tex]
Given from the question the the largest angle is 5°
Generally the refraction index of the cladding is mathematically represented as
[tex]n_{cladding} = n_{core} * sin (90 - 5)[/tex]
[tex]n_{cladding} =1.491[/tex]
An electron moving in a direction perpendicular to a uniform magnetic field at a speed of 1.6 107 m/s undergoes an acceleration of 7.0 1016 m/s2 to the right (the positive x-direction) when its velocity is upward (the positive y-direction). Determine the magnitude and direction of the field.
Answer:
B = 0.024T positive z-direction
Explanation:
In this case you consider that the direction of the motion of the electron, and the direction of the magnetic field are perpendicular.
The magnitude of the magnetic force exerted on the electron is given by the following formula:
[tex]F=qvB[/tex] (1)
q: charge of the electron = 1.6*10^-19 C
v: speed of the electron = 1.6*10^7 m/s
B: magnitude of the magnetic field = ?
By the Newton second law you also have that the magnetic force is equal to:
[tex]F=qvB=ma[/tex] (2)
m: mass of the electron = 9.1*10^-31 kg
a: acceleration of the electron = 7.0*10^16 m/s^2
You solve for B from the equation (2):
[tex]B=\frac{ma}{qv}\\\\B=\frac{(9.1*10^{-31}kg)(7.0*10^{16}m/s^2)}{(1.6*10^{-19}C)(1.6*10^7m/s)}\\\\B=0.024T[/tex]
The direction of the magnetic field is found by using the right hand rule.
The electron moves upward (+^j). To obtain a magnetic forces points to the positive x-direction (+^i), the direction of the magnetic field has to be to the positive z-direction (^k). In fact, you have:
-^j X ^i = ^k
Where the minus sign of the ^j is because of the negative charge of the electron.
Then, the magnitude of the magnetic field is 0.024T and its direction is in the positive z-direction
A horizontal 790-N merry-go-round of radius 1.60 m is started from rest by a constant horizontal force of 45 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 4.0 s. (Assume it is a solid cylinder. Also assume the force is applied at the outside edge.)
Answer:
404.3 J
Explanation:
Given that
Weight of the merry go round = 790 N
Radius if the merry go round = 1.6 m
Horizontal force applied = 45 N
Time taken = 4 s
To find the mass of the merry go round, we divide the weight by acceleration due to gravity. Thus,
m = F/g
m = 790 / 9.8
m = 80.6 kg
We know that the moment of inertia is given as
I = ½mr², on substitution, we have
I = ½ * 80.6 * 1.6²
I = 103.17 kgm²
Torque = Force applied * radius, so
τ = 45 * 1.6
τ = 72 Nm
To get the angular acceleration, we have,
α = τ / I
α = 72 / 103.17
α = 0.70 rad/s²
Then, the angular velocity is
ω = α * t
ω = 0.7 * 4
ω = 2.8 rad/s
Finally, to get the Kinetic Energy, we have
K.E = ½ * Iω², on substituting, we get
K.E = ½ * 103.17 * 2.8²
K.E = 404.3 J
Therefore, the kinetic energy is 404.3 J
A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 21.6 m/s at an angle of 50.0° to the horizontal.
Required:
By how much does the ball clear or fall short (vertically) of clearing the crossbar?
Answer:
The difference is height is [tex]\Delta h =6.92 \ m[/tex]
Explanation:
From the question we are told that
The distance of ball from the goal is [tex]d = 36.0 \ m[/tex]
The height of the crossbar is [tex]h = 3.05 \ m[/tex]
The speed of the ball is [tex]v = 21.6 \ m/s[/tex]
The angle at which the ball was kicked is [tex]\theta = 50 ^o[/tex]
The height attained by the ball is mathematically represented as
[tex]H = v_v * t - \frac{1}{2} gt^2[/tex]
Where [tex]v_v[/tex] is the vertical component of velocity which is mathematically represented as
[tex]v_v = v * sin (\theta )[/tex]
substituting values
[tex]v_v = 21.6 * (sin (50 ))[/tex]
[tex]v_v = 16.55 \ m/s[/tex]
Now the time taken is evaluated as
[tex]t = \frac{d}{v * cos(\theta )}[/tex]
substituting value
[tex]t = \frac{36}{21.6 * cos(50 )}[/tex]
[tex]t = 2.593 \ s[/tex]
So
[tex]H = 16.55 * 2.593 - \frac{1}{2} * 9.8 * (2.593)^3[/tex]
[tex]H = 9.97 \ m[/tex]
The difference in height is mathematically evaluated as
[tex]\Delta h = H - h[/tex]
substituting value
[tex]\Delta h = 9.97 - 3.05[/tex]
[tex]\Delta h =6.92 \ m[/tex]
g A mass of 2 kg is attached to a spring whose constant is 7 N/m. The mass is initially released from a point 4 m above the equilibrium position with a downward velocity of 10 m/s, and the subsequent motion takes place in a medium that imparts a damping force numerically equal to 10 times the instantaneous velocity. What is the differential equation for the mass-spring system.
Answer:
mass 20 times of an amazing and all its motion
The gravity tractor, is a proposed spacecraft that will fly close to an asteroid whose trajectory threatens to impact the Earth. Due to the gravitational attraction between the two objects and a prolonged period of time over which it acts (several years), the asteroid's trajectory is changed slightly, thus hopefully diverting it from impacting the Earth. If the gravity tractor's weight on Earth is 20,000 lbs and it flies with a center of gravity 160ft from the surface of the asteroid, and the asteroid is homogenous pure iron with 1290 ft diameter spherical shape, detirmine the force of mutual attraction. Idealize the gravity tractor to be a particle.
Answer:
[tex]F_g=461lb_f[/tex]
Explanation:
First calculate the mass of the asteroid. To do so, you need to find the volume and know the density of iron.
If r = d/2 = 645ft, then:
[tex]V = \frac{4}{3} \pi r^3[/tex]
[tex]V = \frac{4}{3} \pi r^3\\V = 1.124\times10^{9}ft^3\delta_{iron}=m/V=491lb/ft^3m=V\times\delta=5.519\times10^{11}lb[/tex]
In order to find force, use Newton's universal law of gravitation:
[tex]F_g=G\frac{m_1m_2}{d^2}[/tex]
Where,
G= the gravitational constant:
[tex]G= 1.068846 \times10^{-9} ft^3 lb^{-1} s^{-2}[/tex]
[tex]F_g=461lb_f[/tex]
Your roommate is working on his bicycle and has the bike upside down. He spins the 68.0 cm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. A. What is the pebble's speed? B. What is the pebble's acceleration?
Answer:
a. 6.41 m/s
b. 120.85 m/s^2
Explanation:
The computation is shown below:
a. Pebble speed is
As we know that according to the tangential speed,
[tex]v = r \times \omega[/tex]
[tex]= \frac{0.68}{2} \times 18.84[/tex]
= 6.41 m/s
The 18.84 come from
[tex]= 2 \times 3.14 \times 3[/tex]
= 18.84
b. The pebble acceleration is
[tex]a = \frac{v^2}{r}[/tex]
[tex]= \frac{6.41^2}{0.34}[/tex]
= 120.85 m/s^2
We simply applied the above formulas so that the pebble speed and the pebble acceleration could come and the same is to be considered
An object is dropped from a tower, 576576 ft above the ground. The object's height above ground t seconds after the fall is s(t)equals=576 minus 16 t squared576−16t2. Determine the velocity and acceleration of the object the moment it reaches the ground.
Answer: 192 ft/s
Explanation:
The initial height of the object is:
576ft above the ground.
The position equation is:
p(t) = -16*t^2 + 576
in the position equation, we only can see the therm of the initial height and the term of the acceleration (that is equal to the gravitational acceleration g = 32 ft/s^2 over 2)
So we have no initial velocity, this means that at the beginning we only have potential energy:
U = m*g*h
where m is the mass of the object, g = 32m/s^2 and h = 576 ft.
Now, as the object starts to fall down, the potential energy is transformed into kinetic energy, and when the object is about to hit the ground, all the potential energy has become kinetic energy.
The kinetic energy equation is:
K = (m/2)*v^2
where v is the velocity of the object, then the maximum kinetic energy (when the object reaches the ground) is equal to the initial potential energy:
m*g*h = (m/2)*v^2
now we can solve this for v.
v = √(2*g*h) = √(2*32ft/s^2*576ft) = 192 ft/s
In cricket how bowler and batsman use acceleration?
The energy band gap of GaAs is 1.4ev. calculate the optimum wavelength of the light for photovoltaic generation in a GaAs solar cell
Answer:
The wavelength is [tex]\lambda = 886 \ nm[/tex]
Explanation:
From the question we are told that
The energy band gap is [tex]E = 1.4 eV[/tex]
Generally the energy of a single photon of light emitted for an electron jump in a GaAS solar cell is mathematically represented as
[tex]E = \frac{hc}{\lambda }[/tex]
Where h is the Planck's constant with values
[tex]h = 4.1357 * 10^{-15} eV[/tex]
and c is the speed of light with values [tex]c = 3*10^{8} \ m/s[/tex]
So
[tex]\lambda = \frac{hc}{E}[/tex]
substituting values
[tex]\lambda = \frac{4.1357 *10^{-15} * 3.0 *10^{8}}{1.4}[/tex]
[tex]\lambda = 886 \ nm[/tex]
An airplane is flying on a bearing of N 400 W at 500 mph. A strong jet-stream speed wind of 100 mph is blowing at S 500 W.
Required:
a. Find the vector representation of the plane and of the wind.
b. Find the resultant vector that represents the actual course of the plane.
c. Give the resulting speed and bearing of the plane.
Answer:
A. a (-321.393, 383.022) b (-76.40, -64.278)
B. (-397.991, 318.744)
C. a. resulting speed 509.9mph b. bearing of the plane = 51.6°
Explanation:
Complete the following sentences to see if you can apply these ideas.
If a car is moving to the left with constantvelocity, one can conclude that:_______.
a) there mustbe no forces applied to the car.
b) the netforce applied to the car is directed to the left.
c) the netforce applied to the car is zero.
d) there isexactly one force applied to the car.
Answer:
THE ANSWER IS C
Explanation:
the net force applied to the car is zero