Question

question 10 (1 point)
in which case is negative work done?
a. the work done by earth on a ball as the ball, which was initially at rest, falls 3.0 m down towards earth.
b. a eastward force is applied to an eastward moving soccer ball that is already moving at a constant velocity to increase its speed in that direction.
c. a cart is moving at a constant velocity of 10 m/s w when a 0.5 n downward force is applied.
d. the work done by earth on an arrow as it is fired 200 m straight up into the air.
e. earth applies a force on the moon as the moon travels one completion rotation in orbit around earth.

a

b

c

d

e

Explanation:

To determine when negative work is done, we use the formula for work \( W = Fd\cos\theta \), where \( \theta \) is the angle between the force \( F \) and displacement \( d \). Negative work occurs when \( \cos\theta < 0 \), i.e., \( \theta > 90^\circ \) (force and displacement are in opposite directions).

• Option a: The force of gravity (Earth on the ball) and displacement (downward) are in the same direction (\( \theta = 0^\circ \), \( \cos\theta = 1 \)). Work is positive.
• Option b: The applied force (eastward) and displacement (eastward) are in the same direction (\( \theta = 0^\circ \), \( \cos\theta = 1 \)). Work is positive.
• Option c: The applied force (downward) and displacement (westward) are perpendicular (\( \theta = 90^\circ \), \( \cos\theta = 0 \)). Work is zero.
• Option d: The force of gravity (Earth on the arrow) is downward, but the displacement is upward (opposite direction, \( \theta = 180^\circ \), \( \cos\theta = -1 \)). Thus, \( W = Fd(-1) \), so work is negative.
• Option e: The gravitational force on the Moon is centripetal (toward Earth), and the Moon’s displacement in orbit is tangential (perpendicular to the force, \( \theta = 90^\circ \), \( \cos\theta = 0 \)). Work is zero.

Answer:

d. The work done by Earth on an arrow as it is fired 200 m straight up into the air.