A 60 kg student does 60 push ups in 40s . With each push up , the student must lift 70% of the body mass a height of 40cm off the floor. Assuming two significant digits, calculate the following
The work the student does against a force of gravity for each push up , assuming work is done only when the student pushes up
The total work done against the force of gravity in 40s
The power achieved for this period
(60 kg)(9.8 m/S^2) = Force in Newton
m g * .40 = 60 * 9.8 * .7 = 412 Newtons force
distance up = .40 meters
work per push up = .40*412 = 165 Joules per push up
total work = 165 * 60 = 9878 Joules
power = work/time = 9878/40 = 247 watts
Well, well, well! Let's get calculating!
First, we need to find the work done for each push-up. To do that, we multiply the force applied by the distance traveled. The force applied is 70% of the student's body mass, which is 0.7 * 60 kg = 42 kg. Converted to Newtons, that would be 42 kg * 9.8 m/s² = 411.6 N (approximately, don't give me that look).
Now, let's calculate the distance traveled. The student lifts their body mass to a height of 40 cm, which we convert to meters: 40 cm = 0.4 m. Voila!
The work done for each push-up is the force applied (411.6 N) times the distance traveled (0.4 m), which gives us 164.64 Joules (approximately).
Now, let's calculate the total work done in 40 seconds. Since the student does 60 push-ups in that time, we simply multiply the work done for each push-up (164.64 J) by the number of push-ups (60). That gives us 9,878.4 Joules (approximately).
Lastly, let's determine the power achieved. Power is defined as work done divided by time. So, we take the total work done (9,878.4 J) and divide it by the duration (40 seconds). That gives us a power of 246.96 Watts (approximately).
And there you have it! Work, power, and a generous serving of clownishness to spice up your calculations.
a)1.6 x 10^2
b) 9.6 x 10^3
c) 240W
To calculate the work done by the student against the force of gravity for each push-up, we need to find the force exerted by the student and the distance over which the force is applied.
1. Force: The student lifts 70% of their body mass. The force can be calculated as follows:
Force = Mass × Acceleration due to gravity = (0.7 × 60 kg) × 9.8 m/s²
2. Distance: The distance over which the force is applied is 40 cm or 0.4 m.
Now, we can calculate the work done for each push-up:
Work = Force × Distance
To find the total work done against the force of gravity in 40 seconds, we need to multiply the work done per push-up by the number of push-ups in 40 seconds:
Total Work = Work per push-up × Number of push-ups
Finally, to calculate the power achieved for this period, we can use the formula:
Power = Total Work ÷ Time
Now let's calculate all these values step by step.
1. Force:
Force = (0.7 × 60 kg) × 9.8 m/s² = 411.6 N (rounded to two significant digits)
2. Work per push-up:
Work = Force × Distance = 411.6 N × 0.4 m = 164.6 J (rounded to two significant digits)
3. Total Work:
Number of push-ups = 60
Total Work = Work per push-up × Number of push-ups = 164.6 J × 60 = 9876 J (rounded to two significant digits)
4. Power:
Time = 40 s
Power = Total Work ÷ Time = 9876 J ÷ 40 s = 247 W (rounded to two significant digits)
Therefore, the results are as follows:
- The work the student does against the force of gravity for each push-up is approximately 164.6 J.
- The total work done against the force of gravity in 40 seconds is approximately 9876 J.
- The power achieved for this period is approximately 247 W.