Multiple-Concept Example 13 presents useful background for this problem. The cheetah is one of the fastest accelerating animals, for it can go from rest to 34.7 m/s in 3.03 s. If its mass is 102 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in (a) watts and (b) horsepower.
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To determine the average power developed by the cheetah during its acceleration phase, we need to use the formula:
Power = Force x Velocity
First, we need to find the force exerted by the cheetah during its acceleration. We can use Newton's second law of motion, which states:
Force = Mass x Acceleration
Given that the mass of the cheetah is 102 kg, and the acceleration is the change in velocity divided by the time taken, we can calculate the force:
Acceleration = (final velocity - initial velocity) / time
Acceleration = (34.7 m/s - 0 m/s) / 3.03 s
Acceleration = 11.43 m/s²
Force = Mass x Acceleration
Force = 102 kg * 11.43 m/s²
Force = 1168.86 N
Now that we have the force and the velocity (34.7 m/s), we can calculate the power:
Power = Force x Velocity
Power = 1168.86 N * 34.7 m/s
(a) To express the power in watts, we will use the SI unit for power:
1 watt = 1 joule/second
So, the power in watts is:
Power (watts) = 1168.86 N * 34.7 m/s
(b) To convert the power to horsepower, we can use the conversion factor:
1 horsepower = 745.7 watts
So, the power in horsepower is:
Power (horsepower) = Power (watts) / 745.7
Now you can substitute the values and calculate the power in both watts and horsepower.