A Variable Force of Magnitude $F ( x )$ Moves a Body of Mass

question 27

Multiple Choice

A variable force of magnitude $F ( x )$ moves a body of mass $m$ along the $x$ -axis from $x _ { 1 }$ to $x _ { 2 }$ . The net work done by the force in moving the body from $x _ { 1 }$ to $x _ { 2 }$ is $W = \int _ { x _ { 1 } } ^ { x _ { 2 } } F ( x ) d x = \frac { 1 } { 2 } m _ { 2 } { } ^ { 2 } - \frac { 1 } { 2 } m v _ { 1 } ^ { 2 }$ , where $v _ { 1 }$ and $v _ { 2 }$ are the body's velocities at $x _ { 1 }$ and $x _ { 2 }$ . Knowing that the work done by the force equals the change in the body's kinetic energy, solve the problem.
-A 2-oz tennis ball was served at $140 \mathrm { ft } / \mathrm { sec }$ about ( $95 \mathrm { mph }$ ) . How much work was done on the ball to make it go this fast? (To find the ball's mass from its weight, express the weight in pounds and divide by $32 \mathrm { ft } / \mathrm { sec } ^ { 2 }$ , the acceleration of gravity.)

• A) 36 ft-lb
• B) 38 ft-lb
• C) 18 ft-lb
• D) 77 ft-lb

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