Pulley question about a mass on a string

• slain4ever

Homework Statement

i'm having a lot of trouble with this question.

A pulley, consisting of a 0.40 m diameter wheel mounted on a horizontal frictionless axle, is firmly attached to the ceiling. A light rope wrapped around the pulley supports a 0.50 kg object, as shown in the diagram below. Any motion of the rope causes the pulley to turn, with no slipping between the rope and pulley. When released from rest, the object accelerates downward at 5.0 m/s2.

1) find the tension in the rope.
2) the torque on the pulley from the rope
3) the angular acceleration of the pulley
4) the moment of inertia of the pulley.

F=T+ma = 0

The Attempt at a Solution

I'm stuck on the first part i keep getting 2.5N since the tension = ma it should be T=5m/s^2 * 0.5 kg but the answers say 2.4N and I can't figure out why. I am assuming it has something to do with the pulley but since it is frictionless i don't see how it adds tension.

Relevant equations

F=T+ma = 0

The Attempt at a Solution

I'm stuck on the first part i keep getting 2.5N since the tension = ma it should be T=5m/s^2 * 0.5 kg but the answers say 2.4N and I can't figure out why. I am assuming it has something to do with the pulley but since it is frictionless i don't see how it adds tension.
Look at your relevant equation again,T does not = ma. Use your relevant equation by first identifying the value of F acting on the object.

f= ma
0.5 kg * 5 m/s^2
=2.5 N

looking at the forces acting on the object, its weight acts down and the tension acts up. Since the object is falling and accelerating down, the weight force must be greater than the tension force, thus, from Newton 2,
F_net = ma
mg -T =ma
Solve for T.
Note that tension forces always pull away from the objects on which they act, and that acceleration is always in the direction of the net force.