Question

in which situations is work being done?
hannah leans against her locker, but it doesn’t move.
andy’s car rolls down a hill with the engine off.
a wind turbine stands still on a sunny, windless day.
a balloon expands as it is heated by the sun.
jamie pedals a stationary exercise cycle that doesn’t move.

Explanation:

To determine when work is done, we use the physics definition of work: \( W = F \cdot d \cdot \cos(\theta) \), where \( F \) is force, \( d \) is displacement, and \( \theta \) is the angle between force and displacement. Work is done only when a force causes displacement.

Analyzing each situation:

1. Hannah leans against her locker, but it doesn’t move.

• Force is applied (Hannah pushes the locker), but displacement \( d = 0 \).
• Since \( d = 0 \), \( W = 0 \) (no work done).

1. Andy’s car rolls down a hill with the engine off.

• Gravity exerts a force on the car, causing it to displace (roll down the hill).
• Force (gravity) and displacement are in the same direction (\( \theta = 0^\circ \), \( \cos(0^\circ) = 1 \)), so work is done by gravity.

1. A wind turbine stands still on a sunny, windless day.

• No force causes displacement (wind is absent, so no force from wind; turbine doesn’t move).
• \( d = 0 \), so no work done.

1. A balloon expands as it is heated by the Sun.

• The Sun’s heat increases the balloon’s internal pressure, which exerts a force on the balloon’s walls, causing displacement (expansion).
• Force (from pressure) and displacement (expansion) are in the same direction, so work is done by the expanding gas.

1. Jamie pedals a stationary exercise cycle that doesn’t move.

• Jamie applies force to the pedals, but the cycle has no displacement (\( d = 0 \)).
• Since \( d = 0 \), \( W = 0 \) (no work done).

Answer:

The situations where work is being done are:

• Andy’s car rolls down a hill with the engine off.
• A balloon expands as it is heated by the Sun.