A cyclist coasts down a 7.2 degree hill at a steady speed of 10km/h. If the total mass of the bike and rider is 75kg, what power output must the rider have to climb up the hill at the same speed?

Question

anonymous · Answer

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anonymous · Answer

The first thing to do is to determine the forces acting on the cyclist as he or she coasts downhill.  With that in hand you should be able to calculate the forces that need to be acting on the cyclist for he or she to pedal uphill at 10kph.  With forces in hand, power is given by:$$P=Fv$$where P is power; F is the sum of the forces on the cyclist pedaling uphill; and v is the cyclist's velocity.

anonymous · Answer

The fact that he coasts at a constant speed downhill means the wind and other frictional resistance at this speed is just equal to the component of gravitational force parallel to the ramp. The same forces will operate uphill along with the need to overcome gravity.

gebooors · Answer

Weight G has two components.
Because downhill speed is constant, there
Exist friction.

anonymous · Answer

@douglaswinslowcooper @Gebooors I think we also need to consider the level at which this problem is operating on. It may or may not be concerning friction.

anonymous · Answer

Agreed. Somehow there needs to be a force balance to produce constant velocity, however.

gebooors · Answer

That's true. We did quite a lot work with previous problem,
Problem was easier than we thought.

Friction should be ignored?

gebooors · Answer

I suggest we let nikkii work with this herself,
Now she has much hints to start.

shamim · Answer

p=mgv*sin7.2

anonymous · Answer

Don't forget to add frictional forces opposing uphill motion, too.