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AP Physics B : Understanding Work

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Example Question #1 : Conservation Of Energy

A 2.7kg $\displaystyle 2.7kg$ ball starts rolling up a 38^o $\displaystyle 38^o$ incline at speed of $17\frac{m}{s}$ $\displaystyle 17\frac{m}{s}$. Using conservation of energy, find out how much work gravity does on the ball when it travels from the bottom to the maximum height.

38_deg._incline

Possible Answers:

$W=-736\ \text{J}$ $\displaystyle W=-736\ \text{J}$

$W=-239\ \text{J}$ $\displaystyle W=-239\ \text{J}$

$W=-846\ \text{J}$ $\displaystyle W=-846\ \text{J}$

$W=-73\ \text{J}$ $\displaystyle W=-73\ \text{J}$

$W=-389\ \text{J}$ $\displaystyle W=-389\ \text{J}$

Correct answer:

$W=-389\ \text{J}$ $\displaystyle W=-389\ \text{J}$

Explanation:

The energies involved in this problem are kinetic and potential energy. Conservation of energy shows that the initial energies will be equal to the final energies.

$mgh_i+\frac{1}{2}mv_i^2=mgh_f+\frac{1}{2}mv_f^2$ $\displaystyle mgh_i+\frac{1}{2}mv_i^2=mgh_f+\frac{1}{2}mv_f^2$

Choosing the bottom of the incline to be the zero height, the ball starts out with kinetic energy and zero potential energy. When the ball reaches maximum height, its velocity is zero (zero kinetic energy). This simplifies our energy equation.

$0+\frac{1}{2}mv_i^2=mgh_f+0$ $\displaystyle 0+\frac{1}{2}mv_i^2=mgh_f+0$

Isolate the height variable and use the given values to solve for the maximum height.

$h_f=\frac{v_i^2}{2g}$ $\displaystyle h_f=\frac{v_i^2}{2g}$

$h_f=\frac{(17\frac{m}{s})^2}{2(9.8\frac{m}{s^2})}$ $\displaystyle h_f=\frac{(17\frac{m}{s})^2}{2(9.8\frac{m}{s^2})}$

$h_f=14.7\ \text{m}$ $\displaystyle h_f=14.7\ \text{m}$

This is the vertical height. The work done by gravity is calculated as the product for force and distance.

$W=F_{gravity}h_f=-mgh_f$ $\displaystyle W=F_{gravity}h_f=-mgh_f$

The minus sign indicates that the force of gravity acts downward (negative direction).

$W=-(2.7kg)(9.8\frac{m}{s^2})(14.7m)$ $\displaystyle W=-(2.7kg)(9.8\frac{m}{s^2})(14.7m)$

$W=-389\ \text{J}$ $\displaystyle W=-389\ \text{J}$

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AP Physics B : Understanding Work

Study concepts, example questions & explanations for AP Physics B

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Example Question #1 : Conservation Of Energy

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