Question

in which case is work being done?
stargazing
walking home
sitting in a hot tub
lifting a bag of ice

Explanation:

To determine when work is being 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 them. Work is done when a force causes displacement in the direction of the force (or a component of it).

Analyzing each option:

1. Stargazing: No force is applied to cause displacement (you’re stationary, observing stars). So, \( d = 0 \), and \( W = 0 \).
2. Walking home: While you exert force to walk, the primary force here is friction (or muscle force), but the question is simpler. However, the clearest case of work is when a force lifts an object (displacement against gravity).
3. Sitting in a hot tub: You’re stationary, so \( d = 0 \). No work is done (the buoyant force balances gravity, but no displacement).
4. Lifting a bag of ice: When lifting, you apply an upward force (\( F \)) to move the bag upward (displacement \( d \) in the same direction as \( F \)). Thus, \( W = F \cdot d \) (since \( \theta = 0^\circ \), \( \cos(0^\circ) = 1 \)), so work is done.

Answer:

D. lifting a bag of ice