2015: Problem 4

Topic: Dynamics
Concepts: Forces in mechanics, Newton’s laws

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Solution:

For small $P$, the force of static friction $f=P$ balances the external force so $a=0$. This occurs up to the maximum force supplied by static friction $f_{\text{max}}=\mu_smg$. Once $P \geq \mu_smg$, we apply Newton’s 2nd law to obtain

$$P-f=ma$$

Since we have kinetic friction, $f=\mu_kmg$ so

$$P-\mu_kmg=ma$$

$$a=\frac{P}{m}-\mu_kg$$

which in an $a$–$P$ plot is a line with slope $1/m$ and intercept $-\mu_kg$.

Thus, the answer is A.

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