Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

A particle $P$ with mass $0.8\,\text{kg}$ rests on a rough horizontal table. The coefficient of friction between $P$ and the table is $\mu$. A force of magnitude $5\,\text{N}$, directed upwards at an angle $\alpha$ above the horizontal, where $\tan\alpha = \frac{3}{4}$, acts on $P$. The particle is just about to slide across the table.
(i)[4]

Find the numerical value of $\mu$.

(ii)[3]

The force on $P$ is then raised to $10\,\text{N}$, while its direction stays unchanged. Find the acceleration of $P$.

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