Answer:
Force, F = 17.82 N
T = 32.72 N
Explanation:
The mass of the sphere, m = 2.8 kg
Angle made by the string with the vertical, θ = 33°
The force, F, is said to act horizontally on the sphere, and the string makes angle 33° with the vertical. Check the free body diagram for the representation of the situation that is described.
Weight of the sphere, W = mg
W = 2.8 * 9.8
W = 27.44 N
Sin θ = F/T
sin 33 = F/T............(1)
cos θ = W/T
cos 33 = 27.44/T
T = 27.44/cos 33
T = 32.72 N
Put the value of T into equation (1)
sin 33 = F/32.72
F = 32.72 sin 33
F = 17.82 N
Answer:
The magnitude of the Tension in the string = 32.72 N
The magnitude of the electric force on the ball = 17.82 N
Explanation:
The sketch of the free body diagram for the question is presented in the attached image to this solution.
Doing a force balance on the charged ball of sphere,
- T represents the tension in the string which acts away from the ball at angle 33° to the vertical. The tension can be split into a horizontal and a vertical component (Tₓ and Tᵧ respectively).
- Electric force, F, on the charged ball of sphere which acts horizontally to balance the the horizontal component of the tension in the string.
- The weight of the ball, W, which acts vertically downwards and balances the vertical component of the Tension.
Resolving the tension into the horizontal and vertical component
Tₓ = T sin 33° = (0.5446T) N
Tᵧ = T cos 33° = (0.8387T) N
W = mg = 2.8 × 9.8 = 27.44 N
(g = acceleration due to gravity = 9.8 m/s²)
Tᵧ = W
0.8387T = 27.44
T = (27.44/0.8387) = 32.72 N
F = Tₓ
F = 0.5446T = 0.5446 × 32.72 = 17.82 N
The magnitude of the Tension in the string = 32.72 N
The magnitude of the electric force on the ball = 17.82 N
Hope this Helps!!!
