Review. A 60.0-kg person running at an initial speed of 4.00 m/s jumps onto a 120-kg cart initially at rest (Fig. P9.37). The person slides on the cart’s top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.400. Friction between the cart and ground can be ignored. (a) Find the final velocity of the person and cart relative to the ground. (b) Find the friction force acting on the person while he is sliding across the top surface of the cart. (c) How long does the friction force act on the person? (d) Find the change in momentum of the person and the change in momentum of the cart. (c) Determine the displacement of the person relative to the ground while he is sliding on the cart. (f) Determine the displacement of the cart relative to the ground while the person is sliding. (g) Find the change in kinetic energy of the person. (h) Find the change in kinetic energy of the cart. (i) Explain why the answers to (g) and (h) differ. (What kind of collision is this one, and what accounts for the loss of mechanical energy)
Figure P9.37
(a)

The final velocity of the person and cart relative to the ground.
Answer to Problem 37AP
The final velocity of the person and cart relative to the ground is
Explanation of Solution
The mass of the person is
Write the expression of conservation of momentum.
Here,
Substitute
Conclusion:
Therefore, the final velocity of the person and cart relative to the ground is
(b)

The frictional force acting on the person while he is sliding.
Answer to Problem 37AP
The frictional force acting on the person while he is sliding is
Explanation of Solution
Write the expression to calculate the frictional force.
Here,
Substitute
The negative sign indicates that the frictional force is acting toward negative x axis.
Conclusion:
Therefore, the frictional force acting on the person while he is sliding is
(c)

The time duration in which the frictional force is acting on the person.
Answer to Problem 37AP
The time duration in which the frictional force is acting on the person is
Explanation of Solution
Write the expression of Impulse-momentum equation.
Here,
Substitute
Conclusion:
Therefore, the time duration in which the frictional force is acting on the person is
(d)

The change in momentum of the person and cart.
Answer to Problem 37AP
The change in momentum of the person and cart is
Explanation of Solution
Write the expression to calculate the change in momentum of the person.
Substitute
Write the expression to calculate the change in momentum of the cart.
Substitute
Conclusion:
Therefore, the change in momentum of the person and cart is
(e)

The displacement of the person relative to the ground during sliding on the cart.
Answer to Problem 37AP
The displacement of the person relative to the ground during sliding on the cart is
Explanation of Solution
Write the expression to calculate the displacement of the person.
Substitute
Conclusion:
Therefore, the displacement of the person relative to the ground during sliding on the cart is
(f)

The displacement of the cart relative to the ground during the person sliding on the cart.
Answer to Problem 37AP
The displacement of the cart relative to the ground during the person sliding on the cart is
Explanation of Solution
Write the expression to calculate the displacement of the cart.
Substitute
Conclusion:
Therefore, the displacement of the cart relative to the ground during the person sliding on the cart is
(g)

The change in kinetic energy of the person.
Answer to Problem 37AP
The change in kinetic energy of the person is
Explanation of Solution
Write the expression to calculate the change in kinetic energy of the person.
Substitute
`
Conclusion:
Therefore, the change in kinetic energy of the person is
(h)

The change in kinetic energy of the cart.
Answer to Problem 37AP
The change in kinetic energy of the cart is
Explanation of Solution
Write the expression to calculate the change in kinetic energy of the cart.
Substitute
`
Conclusion:
Therefore, the change in kinetic energy of the cart is
(i)

The reason due to which the answer in part (g) and (h) are different.
Answer to Problem 37AP
The collision between the person and the cart is perfectly inelastic collision and the loss of energy is due to frictional force.
Explanation of Solution
The force acting on the person must be equal in magnitude and opposite in direction to the force exerted by the cart on the person.
According to the conservation of linear momentum, the change in momentum of the person and the cart must be equal in magnitude and must add to zero. The change in kinetic energy of the person and cart must be equal for elastic collision but in this case change in kinetic energy of the person and cart is not equal, which shows that this is inelastic collision.
The reason of change in kinetic energy of both object of not being same is, the displacement of person and the cart is not same due to frictional force acting on the person.
Due to the frictional force the loss of energy in form of heat is the internal energy.
Write the expression to calculate the internal energy.
Substitute
Thus, the collision between the person and the cart is perfectly inelastic collision due to the loss of energy.
Conclusion:
Therefore, the collision between the person and the cart is perfectly inelastic collision and the loss of energy is due to frictional force.
Want to see more full solutions like this?
Chapter 9 Solutions
PHYSICS FOR SCI.AND ENGR W/WEBASSIGN
- You are standing a distance x = 1.75 m away from this mirror. The object you are looking at is y = 0.29 m from the mirror. The angle of incidence is θ = 30°. What is the exact distance from you to the image?arrow_forwardFor each of the actions depicted below, a magnet and/or metal loop moves with velocity v→ (v→ is constant and has the same magnitude in all parts). Determine whether a current is induced in the metal loop. If so, indicate the direction of the current in the loop, either clockwise or counterclockwise when seen from the right of the loop. The axis of the magnet is lined up with the center of the loop. For the action depicted in (Figure 5), indicate the direction of the induced current in the loop (clockwise, counterclockwise or zero, when seen from the right of the loop). I know that the current is clockwise, I just dont understand why. Please fully explain why it's clockwise, Thank youarrow_forwardA planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).arrow_forward
- What are the expected readings of the ammeter and voltmeter for the circuit in the figure below? (R = 5.60 Ω, ΔV = 6.30 V) ammeter I =arrow_forwardsimple diagram to illustrate the setup for each law- coulombs law and biot savart lawarrow_forwardA circular coil with 100 turns and a radius of 0.05 m is placed in a magnetic field that changes at auniform rate from 0.2 T to 0.8 T in 0.1 seconds. The plane of the coil is perpendicular to the field.• Calculate the induced electric field in the coil.• Calculate the current density in the coil given its conductivity σ.arrow_forward
- An L-C circuit has an inductance of 0.410 H and a capacitance of 0.250 nF . During the current oscillations, the maximum current in the inductor is 1.80 A . What is the maximum energy Emax stored in the capacitor at any time during the current oscillations? How many times per second does the capacitor contain the amount of energy found in part A? Please show all steps.arrow_forwardA long, straight wire carries a current of 10 A along what we’ll define to the be x-axis. A square loopin the x-y plane with side length 0.1 m is placed near the wire such that its closest side is parallel tothe wire and 0.05 m away.• Calculate the magnetic flux through the loop using Ampere’s law.arrow_forwardDescribe the motion of a charged particle entering a uniform magnetic field at an angle to the fieldlines. Include a diagram showing the velocity vector, magnetic field lines, and the path of the particle.arrow_forward
- Discuss the differences between the Biot-Savart law and Coulomb’s law in terms of their applicationsand the physical quantities they describe.arrow_forwardExplain why Ampere’s law can be used to find the magnetic field inside a solenoid but not outside.arrow_forward3. An Atwood machine consists of two masses, mA and m B, which are connected by an inelastic cord of negligible mass that passes over a pulley. If the pulley has radius RO and moment of inertia I about its axle, determine the acceleration of the masses mA and m B, and compare to the situation where the moment of inertia of the pulley is ignored. Ignore friction at the axle O. Use angular momentum and torque in this solutionarrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning





