A force F is applied to a 2.0-kg radio-controlled model car parallel to the x-ax

Question

A force F is applied to a 2.0-kg radio-controlled model car parallel to the x-axis as it moves along a straight track. The x-component of the force varies with the x-coordinate of the car as shown in the figure (Figure 1) .

Part A

Calculate the work done by the force F?  when the car moves from x=0 to x=3.0m.

Express your answer using two significant figures.

Part B

Calculate the work done by the force F?  when the car moves from x=3.0m to x=4.0m.

Part C

Calculate the work done by the force F?  when the car moves from x=4.0m to x=7.0m.

Part D

Calculate the work done by the force F?  when the car moves from x=0 to x=7.0m.

Part E

Calculate the work done by the force F?  when the car moves from x=7.0m to x=2.0m.

Explanation / Answer

a) Work done from 0 to 3 = area under the F v/s x curve from (0 to 3)

= 1/2*2*2 + 1*2 = 2 + 2 = 4 units

b) Work done from 3 to 4 = area under the F v/s x curve from (3 to 4)

= 0 units

c) Work done from 4 to 7 = area under the F v/s x curve from (4 to 7)

= -1/2*2*1 = -1 units

d) Work done from 0 to 7 = area under the F v/s x curve from (0 to 7)

1/2*2*2 + 1*2 -1/2*2*1 = 4 -1 = 3 units

e) Work done from 7 to 2 = area under the F v/s x curve from (7 to 2)

1*2 -1/2*2*1 = -2 + 1 = -1 units

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