Question

in which case is positive work done?
a. 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.
b. a cart is moving at a constant velocity of 10 m/s w when a 0.5 n e force is applied.
c. earth applies a force on the moon as the moon travels one completion rotation in orbit around earth.
d. the work done by air resistance as a baseball is thrown horizontally towards the catcher.
e. the work done by air resistance on a ball as the ball, which was initially at rest, falls 3.0 m down towards earth.

a

b

c

d

question 4 (1 point)

according to the law of conservation of energy,
a. the amount of energy present before an energy transformation is the same as the amount of energy present after the transformation.
b. energy is conserved only when the device is 100% efficient.
c. the amount of energy present before and after an energy transformation is not equal.
d. energy is conserved in all cases where the efficiency of the device is 50% or above.
e. energy cannot change from one form to another.

Explanation:

First Question (Positive Work)

To determine positive work, we use the formula \( W = Fd\cos\theta \), where \( \theta \) is the angle between force (\( F \)) and displacement (\( d \)). Positive work occurs when \( \cos\theta>0 \) (i.e., \( \theta < 90^\circ \), force and displacement in the same general direction).

• Option a: Force (eastward) and displacement (eastward, as the ball moves east to increase speed) are in the same direction. \( \theta = 0^\circ \), \( \cos\theta = 1 \), so work is positive.
• Option b: Force (east) and displacement (west, since cart moves west) are opposite. \( \theta = 180^\circ \), \( \cos\theta=- 1 \), work is negative.
• Option c: Earth’s force on the Moon is centripetal (toward Earth), while displacement is tangential (perpendicular to force). \( \theta = 90^\circ \), \( \cos\theta = 0 \), work is zero.
• Option d: Air resistance opposes the baseball’s horizontal motion (force opposite to displacement). \( \theta = 180^\circ \), work is negative.
• Option e: Air resistance opposes the ball’s downward motion (force upward, displacement downward). \( \theta = 180^\circ \), work is negative.

The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another, and the total energy of a closed system remains constant.

• Option a: Correct. Total energy before and after a transformation (in a closed system) is equal.
• Option b: Energy is conserved regardless of efficiency (efficiency relates to useful energy, not total energy).
• Option c: Contradicts the law (total energy is conserved).
• Option d: Energy is conserved in all cases, not just when efficiency is ≥50%.
• Option e: Energy can change forms (e.g., kinetic to potential).

Answer:

a. 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.

Second Question (Law of Conservation of Energy)