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?
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?