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Chapter 10: Q.30 (page 257)

A system in which only one particle can move has the potential energy shown in FIGUREEX10.30. What is the x-component of the force on the particle at x=5,15,and 25cm?

Short Answer

Expert verified

x-component of force atx=5cm=100N.

x-component of force atx=15cm=0N.

x-component of force atx=25cm=-50N.

Step by step solution

01

Force : 

The force exerted on a mass item that causes it to alter velocity.

02

Explanation : 

The equation gives the x-component of force on the potential energy diagram.

Fx=-dUdx

Particle's potential energy diagram,

The slope of the potential energy diagram is the x-component of force.

At x=5cm, the x-component of force(slope) is,

Fx=15=-10-0J0-10cm=1J/cm=100N1J/cm=1N-m0.01m=100N

At x=15cm,the x-component of force(slope) is,

Fx=15=-0-0J10-20cm=0J/cm=0N1J/cm=1N-m0.01m=100N

Atx=25cm,the x-component of force(slope) is,

Fx=15=-0-10J20-40cm=-0.5J/cm=-50N0.5J/cm=0.5N-m0.01m=50N

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A clever engineer designs a 鈥渟prong鈥� that obey the force law Fx=-qx-xeq3,where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we鈥檒l let xeq=0m. Then Fx=-qx3.

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