Horsepower/friction problem, find Ff

[aelarz]

Homework Statement

A 900 kg car whose motor delivers a maximum power of 40.0 hp to its wheels can maintain a steady speed of 130 km/h on a horizontal roadway. How large is the friction force that impedes its motion at this speed?

Homework Equations

Power = work done by a force/time taken or force*speed
work = change in KE + change in PE
work = cosQsF where s = distance and F = Force
1 hp = 746 Watts
KE = 1/2mv^s
PE = mgh, g = 9.81 m/s^2

The Attempt at a Solution

first must convert to SI units :
130 km/hr = 1083.3 m/s ^2 , therefore takes .000923 sec for 1 meter
40 hp = 29840 Watts

to use or not to use:
If power = force*speed, 29840 watts = F - Ff (1083), F - Ff = 27.6 N
Fx = max, Fx = 900(1083) = 974,970
974,970 - x = 27.6 , Ff = 974997.6
WRONG

if Power = work/ time
.5(900)(1083^2) = change KE = 527800050
cos0(Ff)1083 = 527800050, Ff = 487350
WRONG

the correct answer is 826 N. I'd appreciate if you could explain how to arrive at this answer!

 

[Fewmet]

I haven't worked all the the way through this yet, but I see you have a conversion error:
130 km/hr is not 1083.3 m/s ^2. Correct both the value and units and see if that gives the expected answer.

 

[aelarz]

Ah! simple. it really is not the 'dog ate my homework' type excuse... but there are sticky keys on my calculator. thank you fewmet!

 

[nlerma2]

Hi, I know you did this a long time ago but I am having trouble with the same problem.
How did you get 826N?
I was trying to work it out like you had posted an for conversion factor I got 36.1m/s and I used that but it didn't work. Could you help please?

 

[rwisz]

To solve this problem, we need to use the equation Power = force * speed. We know that the power of the car's motor is 40 hp, which is equivalent to 29840 watts. We also know that the car is traveling at a steady speed of 130 km/h, which is equivalent to 1083.3 m/s.

Using the equation Power = force * speed, we can rearrange it to solve for force: force = power/speed. Plugging in the values, we get force = 29840/1083.3 = 27.55 N. This is the total force acting on the car, which includes both the force from the motor and the friction force.

To find the friction force, we need to subtract the force from the motor from the total force. So, Ff = 27.55 N - 27.55 N = 0 N.

But wait, how can the friction force be 0 N when we know that there must be some friction acting on the car to maintain its steady speed? This is where we need to consider the work-energy principle.

The work-energy principle states that the work done by all forces acting on an object is equal to the change in kinetic energy of the object. In this case, the car is moving at a constant speed, so its kinetic energy is not changing. Therefore, the work done by all forces must be 0.

In other words, the work done by the motor (29840 watts) must be equal and opposite to the work done by the friction force (Ff). So, 29840 watts = Ff * 1083.3 m/s. Solving for Ff, we get Ff = 29840/1083.3 = 27.55 N. This is the same value we found earlier, but this time it represents only the friction force.

Therefore, the friction force acting on the car is 27.55 N, which is equivalent to 826 N. This is the force that is impeding the car's motion at a speed of 130 km/h.