question 10 (1 point)\nin which case is negative work done?\na. the work done by earth on a ball as the…

question 10 (1 point)\nin which case is negative work done?\na. the work done by earth on a ball as the ball, which was initially at rest, falls 3.0 m down towards earth.\nb. 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.\nc. a cart is moving at a constant velocity of 10 m/s w when a 0.5 n downward force is applied.\nd. the work done by earth on an arrow as it is fired 200 m straight up into the air.\ne. earth applies a force on the moon as the moon travels one completion rotation in orbit around earth.\n\na\n\nb\n\nc\n\nd\n\ne

question 10 (1 point)\nin which case is negative work done?\na. the work done by earth on a ball as the ball, which was initially at rest, falls 3.0 m down towards earth.\nb. 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.\nc. a cart is moving at a constant velocity of 10 m/s w when a 0.5 n downward force is applied.\nd. the work done by earth on an arrow as it is fired 200 m straight up into the air.\ne. earth applies a force on the moon as the moon travels one completion rotation in orbit around earth.\n\na\n\nb\n\nc\n\nd\n\ne

Answer

Brief Explanations:

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.