Question

Two blocks, with masses m and 3m, are attached to the ends of a string with negligible mass that passes over a pulley,as shown above. The pulley has negligible mass and friction and is attached to the ceiling by a bracket. The blocks are simultaneously released from rest.

(b) Determine the work done by the string on the two-block system as each block moves a distance d.

Answer 1

The work done by the string on the two-block system as each block moves a distance is: W = 2 m g d

How to determine the work done?

Work, being a scalar quantity, is additive in nature

Given:

Light block (mass = m):

`\[ W_1 = -W \cdot d = -mgd \]`

Heavy block (mass = 3m):

`\[ W_2 = W \cdot d = 3mgd \]`

The total work is the sum of
`\( W_1 \)` and
`\( W_2 \)`:

`\[ W = W_1 + W_2 \]`

`\[ W = -mgd + 3mgd \]`

`\[ W = 2mgd \]`

Therefore, the total work done is
`\( 2mgd \)`.

Work done is a measure of the energy transferred to or from an object via the application of force along a displacement.

In physics, work done on an object is calculated by multiplying the force applied to the object by the displacement of the object in the direction of the force.

See attached image for missing part of the question.

Answer 2

Step-by-step explanation:

b )

T = 2m₁m₂g / (m₂ + m₁)

= 2 x m x 3m g / 4m

= 14.7 m

Work done by tension on both the masses in moving by distance d

= 2 x 14.7 m x d ( 2 x force x displacement )

= 29.4 md .