A woman uses a pulley and a rope to raise a 20 kg weight to a height of 2 m. If it takes 4 s to do this, about how much power is she supplying? Use g = 10 m/s².

Understand the Problem

The question is asking to calculate the power supplied by a woman who raises a 20 kg weight to a height of 2 m in 4 seconds, using the acceleration due to gravity. The formula for power can be derived from work done over time, where work is the product of force and distance.

Answer

The power supplied is $100 \, \text{W}$.

Steps to Solve

Calculate the Weight Force

First, we need to calculate the force exerted to lift the weight. This is done using the formula:

$$ F = m \cdot g $$

where ( m ) is the mass (20 kg) and ( g ) is the acceleration due to gravity (10 m/s²). Therefore,

$$ F = 20 , \text{kg} \cdot 10 , \text{m/s}^2 = 200 , \text{N} $$

Calculate the Work Done

Next, determine the work done against gravity to raise the weight to a height of 2 m, using the formula:

$$ W = F \cdot d $$

where ( d ) is the distance (2 m). Substituting the values we have:

$$ W = 200 , \text{N} \cdot 2 , \text{m} = 400 , \text{J} $$

Calculate the Power Supplied

Finally, we can find the power supplied using the formula:

$$ P = \frac{W}{t} $$

where ( t ) is the time taken (4 s). Thus,

$$ P = \frac{400 , \text{J}}{4 , \text{s}} = 100 , \text{W} $$

The power supplied by the woman is ( P = 100 , \text{W} ).

More Information

In this problem, we used the basic formulas for force, work, and power in a physics context. Power is a measure of how quickly work is done, and in this case, it demonstrates the effort exerted in lifting the weight.

Tips

Failing to use the correct value for ( g ). Ensure that ( g = 10 , \text{m/s}^2 ) is used consistently.
Not calculating the force correctly. Remember to multiply mass by gravity to find the weight.
Forgetting to convert work (in Joules) to power (in Watts) by dividing by time taken.

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