Physics of Everyday Phenomena
Physics of Everyday Phenomena
9th Edition
ISBN: 9781259894008
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
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Chapter 6, Problem 16E

A roller-coaster car with a mass of 900 kg starts at rest from a point 22 m above the ground. At point B, it is 8 m above the ground. [Express your answers in kilojoules (kJ).]

  1. a. What is the initial potential energy of the car?
  2. b. What is the potential energy at point B?
  3. c. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 30,000 J (30 kJ), what is the kinetic energy of the car at point B?

(a)

Expert Solution
Check Mark
To determine

The initial potential energy of the car in kilojoules.

Answer to Problem 16E

The initial potential energy of the car is 194kJ.

Explanation of Solution

Given info: The mass of the car is 900kg and the position of the car above the ground is at 22m.

Write the expression for the gravitational potential energy at a given height.

PE=mgh

Here,

PE is the gravitational potential energy

m is the mass

g is the acceleration due to gravity

h is the height

Substitute 900kg for m, 9.8m/s2 for g and 22m for h to find the initial potential energy of the car.

PE=(900kg)(9.8m/s2)(22m)=194040J=194040J×103kJ1J194kJ

Conclusion:

Therefore, the initial potential energy of the car is 194kJ.

(b)

Expert Solution
Check Mark
To determine

The potential energy of the car at point B.

Answer to Problem 16E

The potential energy of the car at point B is 70.6kJ.

Explanation of Solution

Given info: The mass of the car is 900kg and the height of the point B is 8m.

Write the expression for the gravitational potential energy at a given height.

PE=mgh

Substitute 900kg for m, 9.8m/s2 for g and 8m for h to find the initial potential energy of the car.

PE=(900kg)(9.8m/s2)(8m)=70560J=70560J×103kJ1J70.6kJ

Conclusion:

Therefore, the potential energy of the car at point B is 70.6kJ.

(c)

Expert Solution
Check Mark
To determine

The kinetic energy of the car at point B.

Answer to Problem 16E

The kinetic energy of the car at point B is 93.5kJ.

Explanation of Solution

Given info: The initial potential energy of the car is 194040J, the potential energy of the car at point B is 70560J and the work done against the friction is 30000J.

During the motion of the car, the loss in potential energy is converted to the gain in kinetic energy. As well as the work done against the friction causes the dissipation of the kinetic energy.

The gain in kinetic energy during the motion from the initial point A to the final point B, is obtained as,

KEAB=PEAPEB

Here,

KEAB is the kinetic energy gained during the motion from A to B

PEA is the potential energy at the point A

PEB is the potential energy at the point B

Substitute 194040J for PEA and 70560J PEB to find KEAB.

KEAB=194040J70560J=123480J

The some of the kinetic energy gained is dissipated for the work done against the friction. Thus, the kinetic energy at the point B is given by,

KEB=KEABW

Here,

KEB is the kinetic energy at point B

W is the work done against the friction

Substitute 123480J for KEAB and 30000J for W to find the kinetic energy at point B.

KEB=123480J30000J=93480J=93480J×103kJ1J93.5kJ

Conclusion:

Therefore, the kinetic energy of the car at point B is 93.5kJ.

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Chapter 6 Solutions

Physics of Everyday Phenomena

Ch. 6 - A boy pushes his friend across a skating rink....Ch. 6 - A child pulls a block across the floor with force...Ch. 6 - If there is just one force acting on an object,...Ch. 6 - Prob. 14CQCh. 6 - A box is moved from the floor up to a tabletop but...Ch. 6 - Prob. 16CQCh. 6 - Is it possible for a system to have energy if...Ch. 6 - Prob. 18CQCh. 6 - Which has the greater potential energy: a ball...Ch. 6 - Prob. 20CQCh. 6 - Suppose the physics instructor pictured in figure...Ch. 6 - A pendulum is pulled back from its equilibrium...Ch. 6 - For the pendulum in question 22when the pendulum...Ch. 6 - Is the total mechanical energy conserved in the...Ch. 6 - Prob. 25CQCh. 6 - Prob. 26CQCh. 6 - Prob. 27CQCh. 6 - Prob. 28CQCh. 6 - Prob. 29CQCh. 6 - If one pole-vaulter can run faster than another,...Ch. 6 - Prob. 31CQCh. 6 - Suppose that the mass in question 31 is halfway...Ch. 6 - A spring gun is loaded with a rubber dart. The gun...Ch. 6 - Prob. 34CQCh. 6 - A sled is given a push at the top of a hill. Is it...Ch. 6 - Prob. 36CQCh. 6 - Prob. 37CQCh. 6 - A horizontally directed force of 40 N is used to...Ch. 6 - A woman does 210 J of work to move a table 1.4 m...Ch. 6 - A force of 80 N used to push a chair across a room...Ch. 6 - Prob. 4ECh. 6 - Prob. 5ECh. 6 - Prob. 6ECh. 6 - Prob. 7ECh. 6 - Prob. 8ECh. 6 - A leaf spring in an off-road truck with a spring...Ch. 6 - To stretch a spring a distance of 0.30 m from the...Ch. 6 - Prob. 11ECh. 6 - Prob. 12ECh. 6 - A 0.40-kg mass attached to a spring is pulled back...Ch. 6 - Prob. 14ECh. 6 - A roller-coaster car has a potential energy of...Ch. 6 - A roller-coaster car with a mass of 900 kg starts...Ch. 6 - A 300-g mass lying on a frictionless table is...Ch. 6 - The time required for one complete cycle of a mass...Ch. 6 - The frequency of oscillation of a pendulum is 16...Ch. 6 - Prob. 1SPCh. 6 - As described in example box 6.2, a 120-kg crate is...Ch. 6 - Prob. 3SPCh. 6 - Suppose that a 300-g mass (0.30 kg) is oscillating...Ch. 6 - A sled and rider with a total mass of 50 kg are...Ch. 6 - Suppose you wish to compare the work done by...
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