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?