Question

A block of steel is pulled with constant velocity of 0.3ms^-1 on a horizontal surface as shown above. The mass of the steel block is 225 kg and the mass of the weight is 75 kg i) show the free body diagram of the steel block ii) Find the coefficient of dynamic friction between the surfaces of the steel block and the desk (assume the pulley is frictionless). iii) If the rope breaks, how long does it take for the block to come to rest?

Answer 1

I)

pulley 75kg

II)

Applying Newton's second law on both bodies:

block of steel:

$N-Wb=0 \Rightarrow N=Wb$

$T-\mu N=ma=0$ since the velocity is constant there is no acceleration

$T=\mu W_b$ (A)

For the weight:

$T-W=0\Rightarrow T=W=75\cdot 9.8=735\, N$ (B)

B in A

$\mu =\frac{T}{W_b}=\frac{735}{225\cdot 9.8}=0.333$

III)

Now if the rope breaks, T is zero

$\mu N=ma\Rightarrow \mu mg=ma\Rightarrow a=\mu g=3.266\, m/s^2$

The time i'll take to stop would be:

$t=\frac{v_f-v_o}{a}=\frac{0.3}{3.266}=0.091\, s$