Question

physics students study a piano being pulled across a room on a rug. they know that when it is at rest, it experiences a gravitational force of 2200 n. when it is being pulled with 1200 n it is sliding across the room in equilibrium, but the students feel like they had to pull harder than 1200 n at first to begin motion.
which best describes the friction acting on the piano?
the static and kinetic frictional forces are equal, so the static frictional force is equal to 1200 n.
the kinetic frictional force is greater than the static frictional force, so the kinetic frictional force is greater than 1200 n.
the static frictional force is greater than the kinetic frictional force, so the static frictional force is greater than 1200 n.
the static and kinetic friction are both equal to the gravitational force of 2200 n.

Explanation:

1. Recall friction concepts: Static friction opposes the start of motion, kinetic friction opposes sliding motion. Static friction can vary up to a maximum, and kinetic friction is generally less than maximum static friction.
2. Analyze the scenario: The piano slides at equilibrium with 1200 N pull, so kinetic friction ($F_k$) = 1200 N (since net force is zero). To start motion, they pulled harder than 1200 N, meaning the maximum static friction ($F_{s,max}$) > 1200 N. And since $F_{s,max}$ > $F_k$, static frictional force (at start) is greater than kinetic frictional force (1200 N).
3. Evaluate options:

• First option: Static and kinetic friction equal? No, as starting required more force than 1200 N.
• Second option: Kinetic > static? No, kinetic is 1200 N, static was more to start.
• Third option: Static > kinetic, so static > 1200 N. This matches the analysis.
• Fourth option: Friction equal to gravitational force? No, friction depends on normal force (here equal to gravitational force, but friction is $\mu N$, not equal to $N$ directly).

Answer:

The static frictional force is greater than the kinetic frictional force, so the static frictional force is greater than 1200 N.