Physics Problems & Solutions: Classical Mechanics

Two wedges, each of mass m, are placed next to each other on a flat floor. A cube of mass M is balanced on the wedges as shown above. Assume no friction between the cube and the wedges, but a coefficient of static friction $\mu<1$ between the wedges and the floor. What is the largest M that can be balanced as shown without motion of the wedges?

A. $\frac{m}{\sqrt2}$

B. $\frac{\mu m}{\sqrt2}$

C. $\frac{\mu m}{1-\mu}$

D. $\frac{2\mu m}{1-\mu}$

E. All M will balance

(GR9277 #06)

Solution:

$2N_w=2mg+Mg\rightarrow N_w=mg+\frac{Mg}{2}$

$\begin{aligned} \\F_x&=f \\N_c \cos 45&=\mu N_w \\Mg (\cos 45)^2&=\mu \left (mg+\frac{Mg}{2} \right ) \\M \left (\frac{\sqrt{2}}{2} \right )^2&=\mu m+\frac{\mu M}{2} \\\frac{M}{2} &=\mu m+\frac{\mu M}{2} \\M &=2\mu m+2\mu M \\M &=\frac{2\mu m}{1-\mu} \end{aligned}$

Answer: D

Physics Problems & Solutions

Classical Mechanics - Friction Force

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