A Physics question?

Question

A 520 g block is suspended by a string that is wrapped around a rotating disk. The block is released from rest and accerlates at 2.1 m/s^2 downward. (a) find the tension in the string. (b) calculate the mas of the disk

Answer 1

(a)

The mass of the block is 520 g = 0.52 kg.

Accerlation = 2.1m/sec²

The tension in the string in moving the object downward T = mg - ma.

Garvitational Force Fg

Fg = mg

Fg = 0.52 * 9.8

Fg = 5.096 N

We know that force F = ma

F = 0.52*2.1

F = 1.092 N

Then Tension in the String

T = mg - ma

T = 5.096 - 1.092

T = 4.004 N.

Tension in the string is 4.004 N.

Answer 2

(b)

The mass of the block is 520 g = 0.52 kg.

Accerlation = 2.1m/sec²

The tension in the string in moving the object downward T = mg - ma.

Garvitational Force Fg

Fg = mg

Fg = 0.52 * 9.8

Fg = 5.096 N

We know that force F = ma

F = 0.52*2.1

F = 1.092 N

Then Tension in the String

T = mg - ma

T = 5.096 - 1.092

T = 4.004 N.

Now the Torque in the solid disk

Torque = T*r where T is the tension in the string.

We also know that

Torque  = I * α.

Where I is the moment of inertia = (1/2) mr².

And α = a/r

Torque  = (1/2) Mr² * (a / r).

Torque  = (1/2) M * a * r.

T * r = (1/2) M * a * r

T = (1/2) M * a

M = 2T / a

M = (2 * 4.004) / 2.1

M = 3.81 kg.

Therefore the mass of the Disk is 3.81 kg.