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Solved: A force is applied to a 2.0-kg, radio-controlled
Chapter 6, Problem 41E(choose chapter or problem)
A force \(\overrightarrow{\boldsymbol{F}}\) 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 Fig. E6.41. Calculate the work done by the force \(\overrightarrow{\boldsymbol{F}}\) when the car moves from
(a) x = 0 to x = 3.0 m;
(b) x = 3.0 m to x = 4.0 m;
(c) x = 4.0 m to x = 7.0 m;
(d) x = 0 to x = 7.0 m;
(e) x = 7.0 m to x = 2.0 m.
Questions & Answers
QUESTION:
A force \(\overrightarrow{\boldsymbol{F}}\) 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 Fig. E6.41. Calculate the work done by the force \(\overrightarrow{\boldsymbol{F}}\) when the car moves from
(a) x = 0 to x = 3.0 m;
(b) x = 3.0 m to x = 4.0 m;
(c) x = 4.0 m to x = 7.0 m;
(d) x = 0 to x = 7.0 m;
(e) x = 7.0 m to x = 2.0 m.
ANSWER:
Solution 41E
Step 1 of 6:
The magnitude of the work done by equals the area under the
versus x curve. The work is positive when
and the displacement are in the same direction; it is negative when they are in opposite directions.