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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Definitions:

Slope

The measure of the steepness or incline of a line, indicating the rate at which y values change with respect to x values.

Budget Line

A chart that displays every possible mix of two commodities that could be bought, given a particular financial plan, with unchanging prices.

Price Ratio

The ratio expressing the relative prices of two goods or services, indicating how much of one is needed to trade for one unit of the other.

Marginal Rate

Refers to the rate at which one quantity changes with respect to a change in another quantity, commonly used in the context of taxes and interest rates.