Question

In the figure above, a block is suspended from two ropes, so that it hangs motionless in the air. If the magnitude of $T_2$ is 10.0 N, what is the magnitude of $T_1$ ? Note that $sin{30}^o$ = $cos{60}^o$ = 0.500, and $sin{60}^o$ = $cos{30}^o$ = 0.866.

• A. 0.433 N
• B. 0.500 N
• C. 0.866 N
• D. 10.0 N
• E. 17.3 N

Answer 1

The correct option is E 17.3 N

Since the block is motionless, the net force acting on it must be zero. That means that the component of $T_1$ that pulls the block to the left must be equal and opposite to the component of $T_2$ that pulls the block to the right. The component pulling the block to the right is $T_2$ sin 60 = (0.866)(10.0 N). The component pulling the block to the left is $T_1$ sin 30 = 0.500 $T_1$. With these components, we can solve for $T_1$

i.e. $T_{1}sin30=T_{2}sin60⟹T_1=\frac{10\times \sqrt{3}\times 2}{2}=17.3N$