The magnitudes of the applied force F and the frictional force f of a wheel

In summary, the conversation discusses the calculation of angular acceleration using moments and applying horizontal forces on a solid wheel with mass M, radius R, and rotational inertia MR^2/2. The correct answer is determined to be F = 3/2 Ma and f = Ma/2. It is also mentioned that taking moments about the mass centre or a fixed point is the safest approach for calculating angular acceleration.
  • #1
hidemi
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Homework Statement
A solid wheel with mass M, radius R, and rotational inertia MR^2/2, rolls without sliding on a horizontial surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

a. F = Ma, f = 0
b. F = Ma, f = Ma/2
c. F = 2Ma, f = Ma
d. F = 2Ma, f = Ma/2
e. F = 3Ma/2, f = Ma/2

Ans: E
Relevant Equations
F R = (1/2 MR^2 + MR^2 ) a/R
I calculate in this way as follows and get a correct answer. Howere I am not sure if I am using the right way.

F R = (½ MR^2 + MR^2 ) a/R
F = 3/2 Ma
F - f = Ma
f = 3/2 Ma - Ma = Ma/2
 
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  • #2
hidemi said:
Homework Statement:: A solid wheel with mass M, radius R, and rotational inertia MR^2/2, rolls without sliding on a horizontial surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

a. F = Ma, f = 0
b. F = Ma, f = Ma/2
c. F = 2Ma, f = Ma
d. F = 2Ma, f = Ma/2
e. F = 3Ma/2, f = Ma/2

Ans: E
Relevant Equations:: F R = (1/2 MR^2 + MR^2 ) a/R

I calculate in this way as follows and get a correct answer. Howere I am not sure if I am using the right way.

F R = (½ MR^2 + MR^2 ) a/R
F = 3/2 Ma
F - f = Ma
f = 3/2 Ma - Ma = Ma/2
The safest way with angular acceleration is to take moments about either the mass centre or a fixed point.
You have effectively taken the second option.
 
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  • #3
haruspex said:
The safest way with angular acceleration is to take moments about either the mass centre or a fixed point.
You have effectively taken the second option.
Thanks for commenting.
 
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Related to The magnitudes of the applied force F and the frictional force f of a wheel

1. What is the relationship between the applied force and the frictional force of a wheel?

The applied force and the frictional force of a wheel are directly proportional to each other. This means that as the applied force increases, the frictional force also increases.

2. How does the magnitude of the applied force affect the motion of a wheel?

The magnitude of the applied force determines the acceleration of the wheel. A larger applied force will result in a greater acceleration, while a smaller applied force will result in a slower acceleration.

3. Is there a maximum amount of frictional force that can be applied to a wheel?

Yes, there is a maximum amount of frictional force that can be applied to a wheel. This maximum value is known as the static frictional force and it is dependent on the coefficient of friction between the wheel and the surface it is rolling on.

4. How does the surface of the wheel and the surface it is rolling on affect the frictional force?

The coefficient of friction between the wheel and the surface it is rolling on is affected by the type of materials and their surface textures. A rougher surface will result in a higher coefficient of friction and thus a greater frictional force.

5. Can the frictional force of a wheel be greater than the applied force?

No, the frictional force of a wheel cannot be greater than the applied force. The maximum frictional force that can be applied is equal to the applied force, and any excess force will result in the wheel slipping or skidding.

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