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Two rectangular boxes $A$ and $B$ are of identical size. The boxes are at rest on a rough horizontal floor with $A$ on top of $B$. Box $A$ has mass $200{\text{ }}kg$ and box $B$ has mass $250{\text{ }}kg$. A horizontal force of magnitude $P{\text{ }}N$ is applied to $B$ (see diagram). The boxes remain at rest if $P \leqslant 3150$ and start to move if $P \gt 3150$.

a) Find the coefficient of friction between $B$ and the floor.

The coefficient of friction between the two boxes is 0.2. Given that $P \gt 3150$ and that no sliding takes place between the boxes,

b) show that the acceleration of the boxes is not greater than $2{\text{ }}m{\text{ }}{s^{ - 2}}$,

c) find the maximum possible value of $P$.

پاسخ تشریحی :
نمایش پاسخ

a) $R = 4500{\text{ }}N$

$3150 = \mu 4500$

Coefficient is 0.7

b) $0.2 \times 200g = 200a$

No sliding $ \to a \leqslant 2$

c) $\left[ {P - F = 450a;{\text{ }}P - F - {F_2} = 250a} \right]$

${P_{max}} = 3150 + 450 \times 2$

${P_{max}} = 3150 + 0.2 \times 2000 + 250 \times 2$

${P_{max}} = 4050{\text{ }}N$

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