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Q. 59

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 259

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Short Answer

A particle experiences the one-dimensional, conservative force Fx shown in FIGURE .

a. Let the zero of potential energy be at .

What is the potential energy at ? Hint: Use the definition of potential energy and the geometric interpretation of work.

b. Suppose the particle is shot to the right from with a speed of . Where is its turning point?

(a) The potential energy at respectively.

(b) The turning point occurs at

See the step by step solution

Step by Step Solution

Step 1: Given information (part a) 

Given the graph which shows the variation of the conservative force FX with x.

Step 2: Explanation (part a) 

Force acting on the particle is conservative. So the work done by this conservative force is stored as the potential energy of the particle.

The work done by the conservative is calculated by measuring the area under the curve in the graph. this work done is equal to the potential energy of the particle that position.

hence;

Potential energy = Area under graph

potential energy at the following position is given by.

Step 3: Given information (part b) 

Given the graph which shows the variation of the conservative force FX with x.

Step 4: Explanation (part b)

The turning point occurs where the total energy line crosses the potential energy curve.

Here, the potential energy at the, is found to be .

Total energy = Kinetic energy + potential energy

The graph can be drawn showing the total energy (TE) and the variation of potential energy.

The turning point occurs where the total energy line crosses the potential energy curve. We can see from the graph this is at approximately . For a more accurate value, the potential energy function is

The TE line crosses at the point where

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