Question

A rope can withstand a maximum tension of 75 N before snapping . What maximum speed can you spin a 6.0 kg rock in a vertical circle of radius 1.5 m without breaking the rope?

Answer 1

Answer:

The maximum speed of the stone without breaking the rope is 4.33 m/s.

Explanation:

Given;

maximum tension the rope can withstand, T = 75 N

mass of the rock, m = 6 kg

radius of the circle, r = 1.5 m

As the stone spin in a vertical circle, it performs circular motion with centripetal acceleration directed inwards. The maximum centripetal force during this motion will be equal to maximum tension on the rope.

$F_c,_m_a_x = T = \frac{MV_m_a_x^{2} }{r}\\\\V_m_a_x^{2} = \frac{Tr}{M}\\\\V_m_a_x = \sqrt{\frac{75*1.5}{6}}\\\\V_m_a_x = 4.33 \ m/s$

Therefore, the maximum speed of the stone without breaking the rope is 4.33 m/s.