AP Physics 1 Question 296: Answer and Explanation
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4. A block of known mass M is connected to a horizontal spring that is sliding along a flat, frictionless surface. There is an additional block of known mass m resting on top of the first block. Which of the following quantities would NOT be needed to determine whether the top block will slide off the bottom block?
- A. The maximum coefficient of static friction between the blocks
- B. The amplitude of the system's motion
- C. The spring constant
- D. The average speed of the blocks
Correct Answer: D
It's easiest to consider both blocks as one system, calculate the maximum acceleration of the pair of blocks caused by the spring (which occurs at maximum displacement from equilibrium), and determine whether friction between the two block is strong enough to give the top block the necessary acceleration to keep up with the bottom block. Applying Newton's Second Law to the system of blocks, Fspring = (combined mass) * a → kA = (M + m)a. In order for the top block to accelerate at this rate, static friction must be strong enough that Fsf = ma → µsFN = ma. You don't need to do any math to see that µs (coefficient of static friction), A (amplitude), and k (spring constant) appear, but average speed doesn't.