2. A 7.0 kg box, which is initially at rest at the bottom of a frictionless ramp, is pulled up the ramp by a string When it reaches a height of 2.0 m, the box is moving at 6.0 m/s. It takes 2.0 seconds for the box to reach this height.
a) Calculate the work done by the string in pulling the box
up
the
ramp.
b) Calculate the power exerted by the string in pulling the box up the ramp.

a) The work done in raising the block up to 2.0 m is 137.2 joules

b) The power exerted by the string in pulling the box up the ramp is 68.6 watts

Explanation:

The question examines the relationship between work energy and power

The parameters of the pulled box are;

The mass of the box, m = 7.0 kg

The height to which the box is pulled, h = 2.0 m

The velocity at which the box is moving at the 2.0 m height = 6.0 m/s

The time if takes the box to reach the height of 2.0 m = 2.0 seconds

The acceleration due to gravity, 'g' is taken as approximately 9.8 m/s²

a) The work done in raising the block up to 2.0 m = The potential energy gained by the block

The potential energy gained by the block, P.E. = m·g·h

Therefore, we have;

The work done in raising the block up to 2.0 m = P.E. = m·g·h

By substituting the given values, we get;

The work done in raising the block up to 2.0 m = 7.0 kg × 9.8 m/s² × 2.0 m =  137.2 joules

b) Power = The rate of doing work

∴ Power, P = Work done/(Time takes for the work)

The work done in raising the block up to 2.0 m = 137.2 joules

The time if takes the box to reach the height of 2.0 m = 2.0 seconds

∴ The power exerted by the string in pulling the box up the ramp, 'P' is given as follows;

P = 137.2 joules/(2.0 seconds) = 68.6 watts

The power exerted by the string in pulling the box up the ramp, P = 68.6 watts.

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