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

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

Step-by-step 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 = (MV_m_a_x^(2) )/(r)\\\\V_m_a_x^(2) = (Tr)/(M)\\\\V_m_a_x = \sqrt{(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.