Calculate the energy in kcal used by a
53-kg
woman who does 55 deep knee bends in which her center of mass is lowered and raised
0.400 m.
(She does work in both directions.) You may assume her efficiency is 20%.
To calculate the energy used by the woman, we can use the following formula:
Energy = Work * Efficiency
First, let's calculate the work done by the woman during one deep knee bend:
Work = Force * Distance
The force can be calculated using Newton's second law:
Force = Mass * Acceleration
Acceleration can be calculated using the change in velocity and the time it takes to perform the knee bend:
Acceleration = Change in Velocity / Time
We can assume the time taken to perform a deep knee bend is negligible, so the change in velocity is zero. Therefore, the acceleration is also zero.
This means the force required is equal to the weight of the woman:
Force = Mass * Gravity
Using the given mass of the woman (53 kg) and assuming a gravity of 9.8 m/s^2, we can calculate the force:
Force = 53 kg * 9.8 m/s^2 = 519.4 N
Now, let's calculate the work:
Work = Force * Distance = 519.4 N * 0.400 m = 207.76 J (joules)
Next, we'll calculate the energy used by multiplying the work by the efficiency:
Energy = Work * Efficiency = 207.76 J * 0.20 = 41.552 J
To convert this energy from joules to kilocalories (kcal), we can use the following conversion factor:
1 kcal = 4184 J
Energy (in kcal) = Energy (in J) / 4184 = 41.552 J / 4184 = 0.0099 kcal
Therefore, the energy used by the woman in kcal for 55 deep knee bends is approximately 0.0099 kcal.