A car (m = 690.0 kg) accelerates uniformly from rest up an inclined road which rises uniformly, to a height, h = 49.0 m. Find the average power the engine must deliver to reach a speed of 24.9 m/s at the top of the hill in 15.7 s(NEGLECT frictional losses: air and rolling, ...)
yeah the only thing you did wrong was the final answer it should be 34.72E3 W
I did the MgH term wrong, and agree with your answer.
Divide the energy acquired at the top of the hill (kinetic PLUS potential) buy the leapsed time (15.7 s). Energy divided by time equals power.
P = [(1/2)MV^2 + M g H]/15.7 s
g = 9.8 m/s^2
H = 49.0 m
To find the average power the engine must deliver to reach a speed of 24.9 m/s at the top of the hill, we can use the work-energy principle. The work-energy principle states that the work done on an object equals the change in its kinetic energy.
First, let's find the initial potential energy of the car at the bottom of the hill. The potential energy is given by the formula:
PE = m * g * h
where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the hill.
PE = 690.0 kg * 9.8 m/s^2 * 49.0 m
= 328,396 J
Next, let's find the final kinetic energy of the car at the top of the hill. The kinetic energy is given by the formula:
KE = (1/2) * m * v^2
where m is the mass of the car and v is the final velocity of the car.
KE = (1/2) * 690.0 kg * (24.9 m/s)^2
= 205,032.675 J
Now, let's find the work done on the car. The work done is the difference between the final kinetic energy and the initial potential energy:
Work = KE - PE
= 205,032.675 J - 328,396 J
= -123,363.325 J
Since the work done is negative, it means that work is done on the car. This work is done by the engine, and the magnitude of this work is equal to the average power delivered by the engine multiplied by the time it takes to reach the top of the hill.
Work = (Average Power) * (Time)
Since we're looking for average power, we can rearrange the equation:
(Average Power) = Work / Time
Average Power = (-123,363.325 J) / (15.7 s)
= -7858.67 W
The negative sign indicates that the power is being delivered by the car engine. However, it is important to note that this negative sign is not physically meaningful in this context, as power cannot be negative. Therefore, the average power the engine must deliver to reach a speed of 24.9 m/s at the top of the hill is approximately 7858.67 W.
Divide the energy acquired at the top of the hill (kinetic PLUS potential) by the elapsed time (15.7 s). Energy divided by time equals power.
P = [(1/2)MV^2 + M g H]/15.7 s
g = 9.8 m/s^2
H = 49.0 m
M = 690 kg
V = 24.9 m/s
P = (213,900 + 34,290)/15.7 = 18,808 W = 21 horsepower
Check my thinking and numnbers.