A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.0

Question

A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes without slippage over a frictionless pulley (the figure (Figure 1) ). The pulley has the shape of a uniform solid disk of mass 2.10kgand diameter 0.440m .

After the system is released, find the horizontal tension in the wire.

After the system is released, find the vertical tension in the wire.

After the system is released, find the acceleration of the box.

A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes without slippage over a frictionless pulley (the figure (Figure 1) ). The pulley has the shape of a uniform solid disk of mass 2.10kgand diameter 0.440m . After the system is released, find the horizontal tension in the wire. After the system is released, find the vertical tension in the wire. After the system is released, find the acceleration of the box. After the system is released, find magnitude of the horizontal and vertical components of the force that the axle exerts on the pulley.

Explanation / Answer

Here , let the acceleration of blocks is a

A)

Using second law of motion ,

a = effective Force / net force

a = 5g/(5 + 12 + 0.5 * 2.10 * r^2/r^2)

a = 2.71 m/s^2

Now , for block 12 Kg

Th = ma

Th = 12 * 2.71

Th = 32.6 N

the tension in the horizontal rope is 32.6 N

B)

For Block 5 kg

5g - Tv = 5 * 2.71

Tv = 35.45 N

the tension in the vertical rope is 35.45 N

c)

Here , acceleration of box is 2.71 m/s^2

d)

For pulley ,

Fx = Th

Fx = 32.6 N

Fy = Tv

Fy = 35.45 N

the axle exerts force (32.6 , 35.45 ) N

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