In a race, a 54 kg athlete runs from rest to a speed of 11 m/s on a flat surface. The athlete’s body has
an efficiency of 85% during the run. How much input energy did the athlete provide?
To calculate the input energy provided by the athlete, we need to consider the work done to accelerate the athlete from rest to a speed of 11 m/s on a flat surface. The work done can be calculated using the formula:
Work = force × distance
The force applied to the athlete can be calculated using Newton's second law of motion:
force = mass × acceleration
The acceleration can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
As the athlete starts from rest, the initial velocity is 0 m/s. The final velocity is 11 m/s. Let's assume it takes t seconds for the athlete to reach this speed.
acceleration = (11 m/s - 0 m/s) / t
acceleration = 11 m/s / t
Using Newton's second law, we can calculate the force:
force = mass × acceleration
force = 54 kg × (11 m/s / t)
Now, let's calculate the work done:
Work = force × distance
As the athlete is running on a flat surface, the distance traveled is irrelevant. However, we should consider the body's efficiency during the run. The efficiency is given as 85%, which means only 85% of the input energy is converted into useful work. Therefore, we need to multiply the work done by the inverse of the efficiency to get the input energy provided by the athlete:
Input energy = Work / Efficiency
Input energy = (force × distance) / Efficiency
Now, let's substitute the values:
Input energy = [54 kg × (11 m/s / t)] / 0.85
Therefore, the input energy provided by the athlete is given by [54 kg × (11 m/s / t)] / 0.85.