Physics homework help regarding energy and friction

[Dan_321]

Homework Statement

The maximum power output of a car of mass 500kg is 75kW. Up a hill of angle 11.534, its maximum (constant) speed achievable with this power is 30m/s.

What is the energy dissipated by frictional forces every second, and what must the frictional force be?

Homework Equations

mgh=loss/gain of GPE, KE=(mv^2)/2=Kinetic energy gained/lost

The Attempt at a Solution

As this is a right angle triangle, we know that 30sin(11.534) will equal the vertical velocity going up (approx 6m/s). From there we know what mgh is: 6m/s*10*500=30000J gained per second. Since GPE-(KE+Frictional forces) must equal 0, 30000-((500*30^2)/2+F) should give F, but it turns out to be negative. How does this work?

 

[RPinPA]

its maximum (constant) speed

The assumption is that the speed is constant. Review the terms in your calculation given that information.

 

[Dan_321]

The assumption is that the speed is constant. Review the terms in your calculation given that information.

Yes, but surely the vertical velocity is going to be different from the diagonal velocity?

 

[RPinPA]

Yes. I agree with your calculation that the vertical velocity is a constant 6 m/s. Now look at your definitions in "relevant equations".

 

[haruspex]

GPE-(KE+Frictional forces)

Why, in this context? As @RPinPA notes, there is no change in KE.