What Forces Affect a Cyclist Coasting and Climbing a Slope?

[Min_Shin]

A man of mass 85kg, on a bicycle of mass 15kg, coasts down a slope inclined at 4.5* to the horizontal, at a constant speed of 4.7m/s.
a)what is the force of friction on the man and his bicycle?
b)if the man wanted to ride up the same slope at the same speed, what force would he have to exert?
c)if the man exerted a force of 150N up the hill, at what rate would he accelerate?

a)I thought the force of friction would be equal to the sine angle componenet of the force of gravity on the mass. 100g*sin 4.5* = 77N

b) Since going up the hill, i thought he needs a force that could counterbalance both slide force of the mass and friction force (since the movement is up the hill now), so i doubled the magnitude of the friction force i got at a) 77N * 2 = 154N

c) But now i was wondering if he only exerts 150 N up he wouldn't even be able to climb the hill.. which i don't think is the answer to the question

Where did i go wrong?

btw thanks in advance!

 

[OlderDan]

I assume part c) is the only thing bothering you. Suppose the man starts up the hill with some velocity. You can still calculate an acceleration. He might even make it to the top of the hill.

 

[kyle8921]

It seems like you have a good understanding of the concepts involved in this problem. However, there are a few things you may want to consider in your approach. First, the force of friction is not equal to the sine component of the force of gravity on the mass. Friction is a separate force that opposes motion and is dependent on factors such as surface materials and the normal force. In this case, the normal force would be equal to the weight of the man and the bicycle, which would be (85kg + 15kg) * 9.8m/s^2 = 980N. The force of friction would then be equal to the coefficient of friction (µ) multiplied by the normal force. So the equation would be: Friction = µ * Normal force = µ * (85kg + 15kg) * 9.8m/s^2 = µ * 1000N.

Secondly, when going up the hill, the man would need to exert a force that is equal to the sum of the forces acting against him, which includes the force of gravity pulling him down the hill, the force of friction, and the force required to overcome the incline of the slope. So the equation would be: Force needed = Force of gravity + Force of friction + Force to overcome incline = (85kg + 15kg) * 9.8m/s^2 + µ * (85kg + 15kg) * 9.8m/s^2 + (85kg + 15kg) * 4.7m/s^2 * sin 4.5* = 1000N + µ * 1000N + 80N.

Lastly, if the man exerts a force of 150N up the hill, he would not be able to accelerate up the hill at a constant speed. The acceleration would depend on the net force acting on the man and the bicycle. The equation for acceleration is: Acceleration = Net force / Mass = (Force exerted by man - Force of gravity - Force of friction - Force to overcome incline) / (85kg + 15kg). So in this case, the acceleration would be: (150N - 1000N - µ * 1000N - 80N) / 100kg = -930N / 100kg = -9.3m/s^2. This means that the man and