Power Calculation for a Car Driving on a Hilly Road with a Given Slope

[LauraMorrison]

Homework Statement

A car of mass 850 kg is driven at a steady speed of 70 km/hr up a hilly road
with a slope of 30°. Using the macroscopic energy equation, determine the
power delivered by the engine of the car.

Homework Equations

E= KE + PE
E = (1/2)mC^(2) + mgz
Power = E/t

The Attempt at a Solution

My attempt at a solution was:
E = 1/2mC^(2) + mg(Ctsin(30))
E = 1/2(850)(19.44)^(2) + (850)(9.81)(19.44)tsin(30)

Therefore

Power = (1/2(850)(19.44)^(2))/t + (850)(9.81)(19.44)sin(30)

Why do I still have an unknown t? I am supposed to be able to solve it with the information given but I can't get it!
Please please help!

 

[DrClaude]

Your problem is with

Power = E/t

You should be considering variations...

 

[LauraMorrison]

Do you mean the variations in potential and kinetic energy as the car drives up the hill? I am not sure how to calculate that, would you be able to explain?

I am sorry, I know it is such a simple question.

 

[DrClaude]

If you write $P = E/t$, think what happens if the car is going at constant speed on a flat road.

The power is used to change the energy of the car, so you have to consider $P = \Delta E / \Delta t$ or, even better, the instantaneous power $P = dE / dt$.

Hope this helps. Don't hesitate with further questions if it doesn't!

 

[rezeew]

First of all, great job on using the macroscopic energy equation to solve for the power delivered by the engine of the car. Your equations and attempt at a solution are correct. However, you are correct in noticing that there is still an unknown variable, t, in your final equation. This is because the problem statement did not provide the time it takes for the car to travel up the hilly road, which is necessary in order to calculate power (Power = E/t).

In order to solve for t, we can use the fact that the car is traveling at a steady speed of 70 km/hr. We can convert this to m/s by multiplying by 1000/3600, which gives us a speed of 19.44 m/s. We can then use the equation v = d/t, where v is the speed, d is the distance, and t is the time. In this case, the distance traveled is the length of the hilly road, which we can calculate using the slope and the height of the road. Once we have the distance, we can solve for t and then plug that value into your final equation to solve for the power delivered by the engine.

In addition, I would like to mention that the units for power should be in watts (W) or horsepower (hp), not in joules (J). This is because power is the rate at which energy is being transferred, so it is measured in units of energy divided by time. In this case, the units should be in watts since the energy is in joules and the time is in seconds.

Overall, great job on your attempt at solving this problem. Just remember to always check for missing information and to use the correct units in your final answer. Keep up the good work!