Solved: Forces on a Bike: Calculating Friction and Total Force

In summary, A biology student rides her bike around a corner of radius 30 meters at a steady speed of 8.1 m/sec. The combined mass of the student and the bike is 89 kg. The coefficient of static friction between the bike and the road is ìs = 0.32. To find the magnitude of the force of friction on her bike from the road, the student used the formula F=m*a to calculate a value of 194.643 Newtons. To determine the minimum value the coefficient of static friction can have before the bike tire will skid, the student used Newton's second law and found the value to be 0.223. However, when trying to find the magnitude of the total
  • #1
Rockdog
23
0
A biology student rides her bike around a corner of radius 30 meter at a steady speed of 8.1 m/sec. The combined mass of the student and the bike is 89 kg. The coefficent of static friction between the bike and the road is ìs = 0.32.

a) If she is not skidding, what is the magnitude of the force of friction on her bike from the road?
b) What is the minimum value the coefficient of static friction can have before the bike tire will skid?
c) What is the magnitude of the total force between the bike tire and the road?
----------------------------------------------------
I'm stuck on part c, but maybe doing part a and b can help out also.

a) A=v^2/R
so A=8.1^2/30=2.187m/s/s
Then I used F=m*a => 89kg*2.187m/sec/sec => 194.643 Newtons

b) Well, I used Newton's second law for the x axis, and figured out that
-fs= -m(v^2/R)
where fs is static friction force, m is mass, v is velocity, R is radius
and I know that fs(max)=Us*N
where Us=static coefficient of friction
N=normal
so I plug in for fs and solve for Us.
Us=(m*v^2)/(N*R)
since N=m*g
Us=(m*v^2)/(m*g*R) or Us= (v^2)/(g*R)
plug in my numbers, and I get minimum Us to be .223. That is when the bike is on the verge of skidding.

c) Here is where I get stuck. I want the total force between bike tire and the road. I did a force diagram of the bike, with a mg force pointing down, a Normal force pointing up, and a frictional force to the left.
So I tried adding weight of the bike/girl to the frictional force, but that doesn't work. I'm pretty sure I need to add the normal force of the girl into there, but to what other force, if any, I'm stuck on.
 
Physics news on Phys.org
  • #2
You are correct so far.

Consider the forces from the ground on the bike:

THe normal force, pointing up, and the static friction, pointing to the left. THat's it. Find the resultant of these two perpendicular components.
 
  • #3


Great job on parts a and b! To solve part c, we need to consider the forces acting on the bike in the horizontal direction. These forces include the force of friction, the force of normal reaction (from the ground), and the force of inertia (centripetal force).

First, let's find the centripetal force using the formula Fc = mv^2/R. Plugging in the values, we get Fc = 89kg * (8.1m/s)^2 / 30m = 194.43 Newtons.

Next, we can use Newton's second law to find the total force in the horizontal direction. This is given by the formula F = ma, where a is the acceleration in the horizontal direction. We can calculate the acceleration using the centripetal force and the mass of the bike and rider. So, F = (89kg * 2.187m/s^2) = 194.643 Newtons.

Now, we can set up an equation for the forces in the horizontal direction:

F - fs = ma

Where fs is the force of friction, and a is the acceleration we just calculated. We can rearrange this equation to solve for fs:

fs = ma - F

Plugging in the values, we get fs = (89kg * 2.187m/s^2) - 194.43 Newtons = 0 Newtons.

This means that the force of friction is equal to the force of inertia (centripetal force), so there is no net force in the horizontal direction. Therefore, the magnitude of the total force between the bike tire and the road is equal to the centripetal force, which we calculated to be 194.43 Newtons.

Hope this helps! Keep up the good work.
 

1. What is the purpose of calculating friction and total force on a bike?

The purpose of calculating these forces is to understand how they affect the movement and stability of a bike. By calculating friction, we can determine how much resistance is acting against the bike's motion, which is crucial for riders to maintain control and balance. Total force takes into account all the forces acting on the bike, such as gravity, air resistance, and the rider's pedaling force, providing a comprehensive understanding of the bike's motion.

2. How is friction calculated on a bike?

Friction on a bike is calculated by multiplying the coefficient of friction, a measure of the surface's roughness, by the normal force, which is the force acting perpendicular to the surface. This calculation helps determine the maximum friction force that can act against the bike's motion.

3. What factors affect the total force on a bike?

The total force on a bike is affected by several factors, including the rider's weight and pedaling force, the bike's weight and aerodynamics, and external forces such as wind resistance and gravity. The terrain and surface conditions also play a role in the total force acting on the bike.

4. How does understanding forces on a bike impact bike design and performance?

Understanding forces on a bike is crucial for designing a bike that is safe, efficient, and performs well. By considering the forces acting on the bike, engineers can design bikes with optimal weight distribution, aerodynamics, and materials, resulting in better performance and stability.

5. Can these calculations be used for other modes of transportation?

Yes, the principles of calculating friction and total force can be applied to other modes of transportation, such as cars, trains, and airplanes. These calculations are essential for ensuring the safety and efficiency of various transportation methods and can also be used to improve their design and performance.

Similar threads

  • Introductory Physics Homework Help
Replies
11
Views
3K
  • Introductory Physics Homework Help
Replies
29
Views
3K
  • Introductory Physics Homework Help
Replies
20
Views
2K
Replies
27
Views
3K
  • Introductory Physics Homework Help
3
Replies
97
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
780
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
518
  • Introductory Physics Homework Help
Replies
8
Views
856
  • Introductory Physics Homework Help
Replies
5
Views
1K
Back
Top