A 2.0-kg mass is attached to the end of a 5.0-m rope. The mass moves in a circular path on a horizontal frictionless surface. If the breaking strength of the rope is 40 N, the maximum translational speed with which you can swing the mass without breaking the rope is approximately
A) 3.2 m/s
B) 4.0 m/s
C) 10 m/s
D) 20 m/s
E) 0.20 km/s

Question

A 2.0-kg mass is attached to the end of a 5.0-m rope. The mass moves in a circular path on a horizontal frictionless surface. If the breaking strength of the rope is 40 N, the maximum translational speed with which you can swing the mass without breaking the rope is approximately   
A) 3.2 m/s 
B) 4.0 m/s 
C) 10 m/s 
D) 20 m/s 
E) 0.20 km/s

Quizplus · Accepted Answer

The tension in the rope must supply the centripetal force required to keep the mass moving in a circle. 
The centripetal force can be calculated using: Fc = mv²/r, where Fc is the centripetal force, m is the mass of the object, v is the speed, and r is the radius of the circle. In this case, r = 5 m.

The tension in the rope (which is equal to the centripetal force) must not exceed the breaking strength of the rope, which is 40 N. Therefore:

Fc <= 40 N
mv²/r <= 40 N
v <= √(40 N × r/m)

Plugging in the given values, we get:

v <= √(40 N × 5 m /2.0 kg)
v <= √(100 N)
v <= 10 m/s

Therefore, the maximum translational speed with which you can swing the mass without breaking the rope is approximately 10 m/s, which corresponds to choice C.

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