Question

you throw a baseball straight up. compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down.
a) the work is positive on the way up and positive on the way down.
b) the work is negative on the way up and on the way down because gravity is always downward.
c) the work is positive on the way up and negative on the way down.
d) the work is negative on the way up and positive on the way down.

Explanation:

Step1: Recall work formula

Work \(W = F\cdot d\cdot\cos\theta\), where \(F\) is force, \(d\) is displacement, \(\theta\) is angle between \(F\) and \(d\).

Step2: Analyze upward motion

Gravity \(F = mg\) (downward). Displacement \(d\) is upward. \(\theta = 180^{\circ}\), \(\cos\theta=- 1\). So \(W=-mgd\) (negative).

Step3: Analyze downward motion

Gravity \(F = mg\) (downward). Displacement \(d\) is downward. \(\theta = 0^{\circ}\), \(\cos\theta = 1\). So \(W = mgd\) (positive).

Answer:

d) The work is negative on the way up and positive on the way down.