Mechanics (general motion of a rigid body)

In summary, the bicyclist applies brakes as he descends a track, but the front wheel locks and starts to slip. If the decleration a were to become dangerous, the combined center of mass of the rider and bicycle would tip. The coefficient of friction between the wheel and the track is μ, and the bicyclist's weight and the normal force on the front wheel would not be enough to decelerate the bike.
  • #1
Incontro
4
0

Homework Statement



The bicyclist applies brakes as he descends a track making an angle β with a horizontal direction. The front wheel of the bike locks and starts to slip along the incline. Find the magnitude of the decleration a that would cause a dangerous condition of tipping about the front wheel. The combined center of mass of the rider and bicycle is at G and the total moment of inertia of the bicyclist and the bicycle about the axis perpendicular to the plane of the paper throufg G is Ig. The coefficient of frictions between the wheel and the track is μ.

2a7stpy.jpg


2. The attempt at a solution

There's no friction in the front wheel, right?
And when there's a tipping of the front wheel the friction on the back wheel and the normal force on the back wheel is zero? But now I'm only left with the weight of the bicycle and the bicyclist and the normal force on the front wheel, and these forces can't make the deceleration...?
 
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  • #2
There is friction in the front wheel. Why not? It is slipping.
 
  • #3
ahh, thanks!

So how do I continue?

I've got the weight, and the normal and the friction force at the front wheel.

mag=F-mgsinβ
Ma=mah=mghsinβ-mgbcosβ
N=mgcosβ ??
 
  • #4
Incontro said:
Ma=mah=mghsinβ-mgbcosβ

What is this? Are you equating mass with torque. about which point are you taking torque
 
  • #5
Oh, my fault. I'm taking torque and around the point where the front wheel meet the ground. I'm then equating mah (the total force on the body times the length h between mass centre and A) with the torque on A.
 
  • #6
What is your next attempt?
 
  • #7
Mg=Igtheta(doubledot)=Fh-Nb=N((Mu)h-b)

I want theta(doubledot)

B is where the back wheel meet the ground.

aB=aex-theta(doubledot)(b+c)ey ?
 

1. What is the difference between translational and rotational motion?

Translational motion refers to the movement of an object in a straight line, while rotational motion refers to the movement of an object around an axis or point. In translational motion, all points on the object move the same distance in the same direction, whereas in rotational motion, different points on the object move different distances and in different directions.

2. What is a rigid body?

A rigid body is an idealized model of an object that does not deform or change shape when subjected to external forces. In other words, all points on a rigid body maintain a fixed distance from each other, and the object as a whole can only translate or rotate.

3. What are the three laws of motion?

The three laws of motion, also known as Newton's laws, are fundamental principles that govern the motion of objects. The first law states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

4. How do you calculate the center of mass of a rigid body?

The center of mass of a rigid body is the point at which the entire mass of the object can be considered to be concentrated. It can be calculated by finding the weighted average of the positions of all the individual mass elements in the object. This can be done using the formula xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn), where m is the mass of each element and x is its position.

5. What is the difference between linear and angular momentum?

Linear momentum refers to the quantity of motion an object has in a straight line, and is calculated by multiplying its mass by its velocity. Angular momentum, on the other hand, refers to the quantity of rotational motion an object has around an axis, and is calculated by multiplying its moment of inertia by its angular velocity. Both linear and angular momentum are conserved quantities, meaning they remain constant unless acted upon by an external force.

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