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PhysicsPhysics for Scientists and Engineers: Foundations and Connections1st Edition
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A particle of mass m = 2.50 kg moving along the x axis from x = 0 to x = 10.0 m experiences a net conservative force in an isolated system given by F = 3 x – 5, where F is in newtons and x is in meters. a. What is the work done on the particle by the force F ? b. What is the change in the potential energy of the system during this motion? c. If the speed of the particle at the origin is 1.25 m/s, what is its kinetic energy at x = 10.0 m?

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Physics for Scientists and Enginee...

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Publisher: Cengage Learning
ISBN: 9781133939146

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Physics for Scientists and Enginee...

1st Edition
Katz + 1 other
Publisher: Cengage Learning
ISBN: 9781133939146
Chapter 9, Problem 75PQ
Textbook Problem
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A particle of mass m = 2.50 kg moving along the x axis from x = 0 to x = 10.0 m experiences a net conservative force in an isolated system given by F = 3x – 5, where F is in newtons and x is in meters. a. What is the work done on the particle by the force F? b. What is the change in the potential energy of the system during this motion? c. If the speed of the particle at the origin is 1.25 m/s, what is its kinetic energy at x = 10.0 m?

(a)

To determine

The work done on the particle by the force F.

Explanation of Solution

Given that the force in the system is F=3x−5, the particle move from x=0 to x=10.

Write the expression for the work done by the force.

  W=∫xixfFdx (I)

Here, W is the work done, F is the force, xi is the initial position, and xf is the final position.

Conclusion:

Substitute (3x−5) for F and perform the integration (I) with limits 0 to 10

(b)

To determine

The change in potential energy of the system during this motion.

(c)

To determine

The kinetic energy of the particle at x=10.0 m.

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