Suppose you try to move a carate by tying a rope qround it and pulling on the rope at angle of $30^0$ above the horizontal. What is the tension required to keep the crate moving with constant velocity? Assume weight of the crate $W = 500N$ and coefficient of dynamic fraction $\mu_k = 0.40$.

Given,

Let $W$ be the weight of the crate, and $R$ be the normal reaction, $T$ be the tension and $f_s$ be the frictional force. 

Let $\theta = 30^0$ be the angle between $T$ and horizontal. Then,

W = R

In horizontal direction, $F = T\;cos\theta \; - \; F_s$

For constant velocity, $a = 0$

$T\cos\theta = F_s$

$T$ = $\frac{\mu_k\;*\;R}{cos\theta}$ = $\frac{0.4 \;*\; 500}{cos(30^0)}$ = $230.94 \; N$

Return to Main Menu