Using energy considerations, calculate the average force a 60.0 kg sprinter exerts backward on the track to accelerate from 2.00 to 6.00 m/s in a distance of 25.0 m, if he encounters a headwind that exerts an average force of 30.0 N against him.
f=ma=60g*(6-2)/time
what is the time? avg velocity is 4, distance 25, time=25/4 seconds
force applied=30+60*g*4*4/24 N
5.77
To calculate the average force exerted by the sprinter, we need to consider the change in kinetic energy. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
The change in kinetic energy can be calculated using the following formula:
ΔKE = 1/2 mv²f - 1/2 mv²i
Where:
ΔKE = Change in kinetic energy
m = Mass of the sprinter (60.0 kg)
v²f = Final velocity squared (6.00 m/s)²
v²i = Initial velocity squared (2.00 m/s)²
Let's calculate the change in kinetic energy:
ΔKE = 1/2 × 60.0 kg × (6.00 m/s)² - 1/2 × 60.0 kg × (2.00 m/s)²
= 1/2 × 60.0 kg × 36.0 m²/s² - 1/2 × 60.0 kg × 4.0 m²/s²
= 1/2 × 60.0 kg × 32.0 m²/s²
= 960.0 kg·m²/s²
Now, let's consider the work done against the headwind. The work done is defined as the force exerted multiplied by the distance over which it is exerted:
Work = Force × Distance
The headwind exerts a force of 30.0 N against the sprinter, and the distance over which this force acts is 25.0 m. The work done against the headwind can be calculated as:
Work = 30.0 N × 25.0 m
= 750.0 N·m
Since the work done against the headwind is negative (as it opposes the motion), we need to subtract it from the change in kinetic energy to find the net work done:
Net Work = ΔKE - Work
= 960.0 kg·m²/s² - 750.0 N·m
= 210.0 N·m
Finally, we can now calculate the average force exerted by the sprinter:
Force = Net Work / Distance
= 210.0 N·m / 25.0 m
= 8.40 N
Therefore, the average force exerted by the sprinter on the track to accelerate from 2.00 to 6.00 m/s is 8.40 N.