A car (mass 920 kg) drives up a hill (height 328 m) in 143 seconds. At the bottom of the hill, it has a speed of 24 m/s, but at the top, it has slowed down to 14 m/s. Neglecting friction, what is the average engine power
To find the average engine power, we need to calculate the work done by the car's engine in driving up the hill and then divide it by the time taken.
First, let's calculate the work done by the car in driving up the hill. The work done can be calculated using the formula:
Work = Force x Distance x cos(theta)
Where:
- Force is the net force acting on the car
- Distance is the displacement
- theta is the angle between the direction of force and displacement
In this case, the net force acting on the car is the gravitational force pulling it down the hill. The gravitational force can be calculated using the formula:
Force = Mass x Gravitational Acceleration
So, the work done becomes:
Work = Mass x Gravitational Acceleration x Distance x cos(theta)
Since we neglect friction, the net force acting on the car is the component of gravity that acts parallel to the displacement, which is given by:
Force = Mass x Gravitational Acceleration x sin(theta)
Now, we need to calculate the displacement. Since the car is driving up the hill, the displacement is equal to the height of the hill, which is 328 m.
Plugging in the values, the work done becomes:
Work = Mass x Gravitational Acceleration x Distance x cos(theta)
= Mass x Gravitational Acceleration x 328 x cos(theta)
Next, we need to calculate the time taken. In the question, it is mentioned that the car takes 143 seconds to drive up the hill.
Finally, we can calculate the average engine power (P) using the formula:
P = Work / Time taken
Substituting the values, we have:
P = Mass x Gravitational Acceleration x 328 x cos(theta) / 143
Remember to convert the mass of the car into kilograms and the gravitational acceleration to m/s^2.
It's important to note that we need the angle between the direction of force and displacement (theta) to calculate the actual average engine power. However, if the angle is not provided, we can assume that the force and displacement are parallel, and therefore, theta is 0 degrees. In this case, the average engine power can be calculated without knowing the angle.