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A disk with a mass of 30.0 kg and a radius of 40.0 cm is mounted on a friction- less horiz...

A disk with a mass of 30.0 kg and a radius of 40.0 cm is mounted on a friction- less horizontal axle. A string is wound many times around the disk and then attached to a 70.0-kg block, as shown in the figure. Find the acceleration of the block, assuming that the string does not slip.

Step-by-Step Solution

Solution 1
Step #1 of 7

THINK:

Step #2 of 7

Determine the acceleration of the block attached to a string.

SKETCH:

The figure shows a string is wound many times around the disk and then attached to a block.

Step #3 of 7

RESEARCH:

For rigid objects, the torque is given by,

…… (1)

Here, the moment of inertia of the object, and for the disk,

With no slipping, the linear accelerationis related to the angular acceleration through

…… (2)

For the block of mass:

According to Newton’s second law of motion, we have

Then, the tension in the string is given by

…… (3)

The torque produced by the tension in the string is,

…… (4)

Step #4 of 7

SIMPLIFY:

Step #5 of 7

From the above equations, we have

Step #6 of 7

GIVEN DATA:

Mass of the disk,

Radius of the disk,

Mass of the block,

Acceleration due to gravity,

Step #7 of 7

CALCULATE:

The acceleration of the block can be calculated as

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