Question

A pulley is in the form of a uniform solid cylinder of radius 7cm and mass 2kg. One end of a very light rope is fixed to wind the pulley and the other end is

free. When we pull the free end of the rope the pulley starts rotating from rest and accelerates uniformly. If the angular acceleration is 100rad/s2 so the
constant force that we exert on the pulley through the rope is:
Chọn một:
a.
200 N
b.
7N
C
0.49 N
d.
49 N

Answer 1

correct is b 7N

Step-by-step explanation:

The torque is

Στ = I α

torque

τ = F x R

bold, indicate vectors. The magnitude of torque is

τ = F R sin θ

in this case the angle is 90º so sin 90 = 1

τ = F R

The moment of inertia of a cylinder

I = ½ M R²

substitute

F R = ½ M R² α

F = ½ M R α

reduce to the SI system

R = 7 cm (1m / 100cm) = 0.07 m

calculate

F = ½ 2 0.07 100

F = 7 N