Question

At the gym, a woman lifts 40 kilograms of weights on the leg press machine. It takes her 0.5 seconds to raise the weights a vertical distance of 0.4 meters.

How much power does the woman generate when lifting the weights?
A) 180 watts
B) 200 watts
C) 320 watts
D) 500 watts

Answer 1

The power generated by the woman lifting 40 kilograms on a leg press machine is calculated using the formula for power in terms of work over time, resulting in approximately 320 watts.(Option C)

Step-by-step explanation:

To calculate the power generated by the woman lifting weights at the gym, we need to use the formula for power in terms of work done over time, which is P = W/t, where P is power in watts, W is work in joules, and t is time in seconds. The work done, in this case, is equal to the force applied to the weight times the distance it is moved, or W = F × d. Since the force applied is equal to the weight of the object caused by gravity, we use F = m × g where m is mass in kilograms and g is the acceleration due to gravity, approximately 9.8 m/s2. Therefore, W = m × g × d.

First, we calculate the work done:

W = 40 kg × 9.8 m/s2 × 0.4 m = 156.8 J (joules)

Now, we calculate the power:

P = 156.8 J / 0.5 s = 313.6 W

The woman generates a power of approximately 320 watts when lifting the weights, which aligns with option C.

Answer 2

In this problem, the work is equal to the increase of the potential energy of the weights.

∆ PE = 40 * 9.8 * 0.4 = 156.8J
Power = 156.8 / 0.5 = 313.6 watts
If use 10 m/s^2 for g, the power will be 320 watts.

I hope this helps!