A 0.50 kg mass attached to the end of a string swings in a vertical circle (radius = 2.0 m). When the mass is at the highest point of the circle the speed of the mass is 8.0 m/s. What is the magnitude of the force of the string on the mass at this position?
A) 21 N
B) 11 N
C) 16 N
D) 26 N
E) 36 N

Question

Quizplus · Accepted Answer

At the highest point of the circle, the tension force of the string is equal to the weight of the mass. We can use the equation T=mg to find the tension force, where T is tension force, m is the mass of the object, and g is the acceleration due to gravity (9.8 m/s^2). Thus, T= (0.50 kg)(9.8 m/s^2)= 4.9 N. However, this is not the magnitude of the force of the string on the mass since there is also a centripetal force acting on the mass. We can use the equation Fc=mv^2/r to find the centripetal force, where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circle. Thus, Fc= (0.50 kg)(8.0 m/s)^2/2.0 m= 16 N. Therefore, the magnitude of the force of the string on the mass is the sum of the tension force and the centripetal force, which is 4.9 N + 16 N= 20.9 N, or approximately 21 N. Therefore, the best answer is choice B.

A 050 Kg Mass Attached to the End of a String