a particle is subject to a force fx that varies with a position shown in figure P 7.15.find the work done by the force on the particle as it moves (a)from x=0 to x=5.00,(b)from 5.00m to 10.0 m,(c)from x=10.0 to x=15.0 m.(d) what is the total work done by the force over the distance x=0 to x=15.0 m?

To calculate the work done by a force, we need to use the formula:

Work = ∫F(x)dx

where F(x) represents the force at a given position x, and dx represents a small change in position.

Since the force varies with position, we cannot directly integrate it to find the work. However, we can estimate the work done by dividing the distance into small intervals and calculating the work done in each interval. Then, we can sum up all these small work values to find the total work done. Let's go step by step:

(a) To calculate the work done from x=0 to x=5.00, we need to calculate ∫F(x)dx in that range.

(b) To calculate the work done from x=5.00 to x=10.0, we need to calculate ∫F(x)dx in that range.

(c) To calculate the work done from x=10.0 to x=15.0, we need to calculate ∫F(x)dx in that range.

(d) To calculate the total work done over the distance x=0 to x=15.0, we need to calculate the sum of the work done in each range.

However, you mentioned that there is a figure P 7.15 showing the force variation with position. Without this figure or any specific information about the force function, it is not possible to proceed with the calculations. Please provide additional information or the figure to continue with the step-by-step solution.

To find the work done by the force on the particle as it moves from one position to another, you need to calculate the area under the force vs. position graph.

Since you mentioned a Figure P 7.15, it seems likely that you have a graph showing the force (F) as a function of position (x). Please refer to that graph to follow along with the explanation.

(a) The work done by the force on the particle as it moves from x = 0 to x = 5.00 is equal to the area under the graph between these two positions. To calculate this, you need to find the area of the triangle formed by the force vs. position graph between x = 0 and x = 5.00. The formula to find the area of a triangle is (1/2) * base * height. In this case, the base is 5.00 (the x-distance) and the height is the force value at x = 5.00. Multiply these values together and divide by 2 to get the work done.

(b) To find the work done as the particle moves from x = 5.00 m to x = 10.0 m, you need to calculate the area under the graph between these two positions. For this region, it appears to be a rectangle. The formula to find the area of a rectangle is length * width. In this case, the length is 5.00 m (the x-distance) and the width is the force value at x = 5.00 m. Multiply these values together to get the work done.

(c) Similar to the previous case, to find the work done as the particle moves from x = 10.0 m to x = 15.0 m, you need to calculate the area under the graph. This region seems to be a triangle. Use the formula for the area of a triangle — (1/2) * base * height — where the base is 5.0 m and the height is the force value at x = 15.0 m. Multiply these values together and divide by 2 to get the work done.

(d) The total work done by the force over the distance x = 0 to x = 15.0 m can be obtained by adding the work done in parts (a), (b), and (c) together.

Remember, these calculations are specific to the graph you mentioned in Figure P 7.15. Ensure you have the correct force vs. position graph and use the corresponding values to compute the work done.

dds