Bicyclist coasting down hill (Newton's Laws)

In summary: So, mass is required in order to solve the problem.In summary, the problem involves a bicyclist coasting down a 5° hill at a constant speed of 7.0 km/h. The force of friction is proportional to the speed, and the value of the constant c can be calculated using Newton's Laws. In order to descend the hill at 22 km/h, the average force that must be applied is calculated using the mass of 79 kg, which is given in part B. Both parts of the problem require the use of mass in order to be solved.
  • #1
ndifabio
6
0

Homework Statement


"A bicyclist can coast down a 5° hill at a constant 7.0 km/h. Assume the force of friction (air resistance) is proportional to the speed v so that Fair = cv."

(a) Calculate the value of the constant c.
(b) Calculate the average force that must be applied in order to descend the hill at 22 km/h. The mass of the cyclist plus bicycle is 79 kg.


Homework Equations



Newton's Laws

The Attempt at a Solution



Since a=0, Ʃforce must=0.

Fair=Fg

Fg=mgsin(5°)=Fair

c=mgsin(5°)/v

I just can't figure out how to work around not having mass in this problem.

Any help would be greatly appreciated :)
 
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  • #2
What do you mean not having mass? You say the mass of the cyclist + bike is 79kg!
 
  • #3
your equation is correct...the mass is given in part b. Now try part b.
 
  • #4
I understand that the mass is given in part B. But not having the mass in the initial problem implies that mass is not needed to solve part A. I was hoping that someone could tell me how to solve part A without mass. Sorry for the confusion
 
  • #5
The mass applies to both parts. You can't solve part 'a' numerically without knowing the mass, and you can't solve part 'b' numerically without knowing the numerical result of part 'a'.
 

Related to Bicyclist coasting down hill (Newton's Laws)

1. How does Newton's First Law apply to a bicyclist coasting down a hill?

According to Newton's First Law of Motion, an object in motion will stay in motion unless acted upon by an external force. In the case of a bicyclist coasting down a hill, the initial force of pedaling has already been applied and the cyclist will continue to move at a constant velocity unless a force, such as friction or air resistance, slows them down.

2. Does Newton's Second Law apply to a bicyclist coasting down a hill?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. While the bicyclist is coasting down the hill, the net force acting on them is equal to zero, so there is no acceleration. However, if the cyclist were to pedal or brake, the net force would change and Newton's Second Law would apply.

3. How does Newton's Third Law apply to a bicyclist coasting down a hill?

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. In the case of a bicyclist coasting down a hill, the action is the force of gravity pulling the cyclist and the bike down the hill. The reaction is the force of the bike and cyclist pushing against the ground, which allows them to move forward.

4. What role does friction play in a bicyclist coasting down a hill?

Friction is the force that opposes the motion of an object. It plays a crucial role in a bicyclist coasting down a hill as it acts in the opposite direction of the bike's motion, ultimately slowing it down. Friction between the tires and the road, as well as air resistance, contribute to the decrease in speed of the cyclist.

5. How does the mass of the cyclist and the bike affect their coasting speed?

According to Newton's Second Law, the mass of an object is directly proportional to the force needed to accelerate it. Therefore, a heavier cyclist and bike will require more force to accelerate and maintain a certain speed while coasting down a hill. However, other factors such as the slope of the hill and air resistance also play a role in determining the coasting speed of a cyclist.

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