A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m), as shown. At an instant when $\theta$= 50$\degree$, the tension in the string is 8.0 N. What is the magnitude of the resultant force on the mass at this instant?
A)5.6 N
B)6.0 N
C)6.5 N
D)5.1 N
E)2.2 N

Question

A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m), as shown. At an instant when $\theta$= 50$\degree$, the tension in the string is 8.0 N. What is the magnitude of the resultant force on the mass at this instant? 
A)5.6 N 
B)6.0 N 
C)6.5 N 
D)5.1 N 
E)2.2 N

Quizplus · Accepted Answer

The magnitude of the resultant force on the mass is equal to the vector sum of the tension force and the force of gravity. At the instant when θ = 50°, the force of gravity has both vertical and horizontal components. Since the mass is moving along a vertical circle, the horizontal component of the gravitational force is equal in magnitude and opposite in direction to the tension force. Therefore, the magnitude of the resultant force is equal to the vector sum of the vertical component of the gravitational force and the tension force.

Using trigonometry, we can find that the vertical component of the gravitational force is given by Fg cos θ, where Fg is the magnitude of the gravitational force (mg) and θ is the angle between the force of gravity and the vertical direction.

Fg cos θ = mg cos θ = (0.30 kg)(9.81 m/s^2) cos 50° ≈ 1.84 N

Therefore, the magnitude of the resultant force is:

FR = Fg cos θ + FT = 1.84 N + 8.0 N = 9.84 N

Rounding to the nearest tenth, we get:

FR ≈ 6.5 N

Therefore, the answer is choice C.

A 030-Kg Mass Attached to the End of a String Swings