A 4.80kg cat leaps from the floor to the top of a 94.0-cm-high table.
If the cat pushes against the floor for 0.230s to accomplish this feat, what was her average power output in hp during the pushoff period?
To find the average power output of the cat during the pushoff period, we need to use the formula:
Power = Work / Time
First, let's calculate the work done by the cat. The work done is equal to the change in potential energy of the cat.
Potential energy (PE) = mass * gravity * height
Given:
Mass of the cat (m) = 4.80 kg
Height of the table (h) = 94.0 cm = 0.94 m
Acceleration due to gravity (g) = 9.8 m/s^2
Potential Energy (PE) = m * g * h
Next, let's calculate the time (t) taken by the cat during the pushoff period, which is given as 0.230s.
Now, we can calculate the work done by the cat using the formula:
Work = PE = mgh
Next, plug in the values we have:
Work = (4.80 kg) * (9.8 m/s^2) * (0.94 m)
Finally, we can calculate the average power output using the formula:
Power = Work / Time
Substitute the values we have:
Power = (4.80 kg * 9.8 m/s^2 * 0.94 m) / 0.230 s
Now, we can simplify and convert the unit to horsepower (hp):
Power (in watt) = (4.80 kg * 9.8 m/s^2 * 0.94 m) / 0.230 s
Power (in hp) = (4.80 * 9.8 * 0.94) / (0.230 * 745.7)
Hence, the average power output of the cat during the pushoff period is the calculated value in horsepower.
To find the average power output, we need to calculate the work done by the cat during the pushoff period and then divide it by the time.
1. First, calculate the work done by the cat during the pushoff period using the formula:
work = force * distance
The force can be calculated using Newton's second law of motion:
force = mass * acceleration
The acceleration can be calculated using the formula:
acceleration = change in velocity / time
The change in velocity can be calculated using the formula:
change in velocity = final velocity - initial velocity
Since the cat starts from rest, the initial velocity is 0 m/s.
To find the final velocity, use the formula:
final velocity = distance / time
Substituting the given values:
distance = 94.0 cm = 0.94 m
time = 0.230 s
final velocity = 0.94 m / 0.230 s = 4.087 m/s
change in velocity = final velocity - initial velocity = 4.087 m/s - 0 m/s = 4.087 m/s
acceleration = change in velocity / time = 4.087 m/s / 0.230 s = 17.78 m/s^2
force = mass * acceleration = 4.80 kg * 17.78 m/s^2 = 85.39 N
work = force * distance = 85.39 N * 0.94 m = 80.25 J
2. Convert the work done from Joules to horsepower.
1 horsepower (hp) is approximately equal to 745.7 Joules per second.
power (in hp) = work / time = 80.25 J / 0.230 s / 745.7 J/hp = 0.463 hp
Therefore, the cat's average power output during the pushoff period is approximately 0.463 horsepower.