A 66 kg human sprinter can accelerate from rest to 11 m/s in 3.4s. During the same interval, a 35 kg greyhound can accelerate from rest to 20 m/s. Compute
(a) the change in kinetic energy of the sprinter.
(b) the change in kinetic energy of the greyhound.
(c) the average power output of the sprinter.
(d) the average power output of the greyhound.
a
(1/2)(66)(11)^2
b
(1/2)(35)(20)^2
c
power = work/time = Ke/time = answer a/3.4
d
answer b / 3.4
To solve this problem, we need to use the formulas for kinetic energy and power.
(a) The change in kinetic energy (ΔKE) of an object can be calculated using the formula:
ΔKE = 0.5 * mass * (final velocity^2 - initial velocity^2)
In this case, the mass of the sprinter is 66 kg and the final velocity is 11 m/s, but since the sprinter starts from rest, the initial velocity is 0 m/s. Substituting these values into the formula, we have:
ΔKE = 0.5 * 66 kg * (11 m/s)^2
= 0.5 * 66 * 121
= 0.5 * 7986
= 3993 Joules
Therefore, the change in kinetic energy of the sprinter is 3993 Joules.
(b) Following the same approach, we can calculate the change in kinetic energy of the greyhound. The mass of the greyhound is 35 kg and the final velocity is 20 m/s, with an initial velocity of 0 m/s. Thus, the calculation becomes:
ΔKE = 0.5 * 35 kg * (20 m/s)^2
= 0.5 * 35 * 400
= 0.5 * 14000
= 7000 Joules
Therefore, the change in kinetic energy of the greyhound is 7000 Joules.
(c) The average power output can be computed using the formula:
Average Power = ΔKE / Time
In this case, we already know the change in kinetic energy of the sprinter (ΔKE = 3993 Joules), but we need the time taken to accelerate. The time given in the question is 3.4 seconds.
Substituting these values into the formula, we have:
Average Power = 3993 Joules / 3.4 seconds
≈ 1174.41 Watts
Therefore, the average power output of the sprinter is approximately 1174.41 Watts.
(d) Similarly, we can find the average power output of the greyhound. The change in kinetic energy for the greyhound is 7000 Joules, and the time taken to accelerate is also 3.4 seconds.
Substituting these values into the formula, we have:
Average Power = 7000 Joules / 3.4 seconds
≈ 2058.82 Watts
Therefore, the average power output of the greyhound is approximately 2058.82 Watts.