Brutus, a champion weightlifter, raises 243 kg of weights a distance of 2.65 m.
(b) How much work is done by Brutus holding the weights above his head?
Enter an exact number.2 J
(e) If Brutus completes the lift in 2.7 s, how much power is developed?
Enter a number.5 kW
Show that 480 W of power is expended by a weightlifter
when lifting a 60-kg barbell a vertical distance of 1.2 m
in a time interval of 1.5 s.
To find the work done by Brutus holding the weights above his head, we use the formula:
Work (W) = Force (F) * Distance (d)
Brutus raises 243 kg of weights, so the force exerted by him is equal to the weight of the weights:
Force (F) = Mass (m) * Acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
Therefore:
Force (F) = 243 kg * 9.8 m/s^2 = 2381.4 N
The distance (d) is given as 2.65 m.
Now we can calculate the work done:
Work (W) = Force (F) * Distance (d) = 2381.4 N * 2.65 m = 6310.01 J
The work done by Brutus holding the weights above his head is 6310.01 Joules.
To find the power developed by Brutus, we use the formula:
Power (P) = Work (W) / Time (t)
The time taken by Brutus to complete the lift is given as 2.7 s.
Now we can calculate the power:
Power (P) = Work (W) / Time (t) = 6310.01 J / 2.7 s = 2337.41 W
The power developed by Brutus is 2337.41 Watts, which is equivalent to 2.33741 kW (kiloWatts).
To calculate the work done by Brutus holding the weights above his head, we can use the formula:
work = force * distance
In this case, the force is equal to the weight being lifted, which is given as 243 kg. The distance is given as 2.65 m.
So, the work done is:
work = 243 kg * 2.65 m
= 642.45 J
Therefore, the work done by Brutus holding the weights above his head is 642.45 J.
Now, to calculate the power developed by Brutus, we can use the formula:
power = work / time
In this case, the work is 642.45 J and the time is given as 2.7 s.
So, the power developed is:
power = 642.45 J / 2.7 s
≈ 237.94 W
However, the answer is requested in kilowatts (kW). To convert watts to kilowatts, divide the power by 1000:
power = 237.94 W / 1000
= 0.23794 kW
Therefore, the power developed by Brutus is approximately 0.23794 kW.