Friction of an object on a moving board

In summary, a 2 kg body is placed on an 8 kg board with a friction coefficient of 0.2. A 30 N force is applied to the front edge of the board and the body starts moving towards the rear edge. The time it takes for the body to fall off the board can be calculated using Newton's laws and the equations of motion for both the board and the body. The horizontal forces acting on the board are the applied force and the weight of the body, while the forces on the body are the force exerted by the board and the friction force. By applying Newton's second law, the equations for the board and body can be determined and the friction force can be calculated.
  • #1
grusini
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Homework Statement



A body of mass [itex]m_A=2 kg[/itex] is placed on a long board of mass [itex]m_B=8 kg[/itex] at distance [itex]d=1 m[/itex] from the rear edge of the board. The friction coefficient between the body and the board is [itex]μ=0.2[/itex]. A force of magnitude [itex]30 N[/itex] is applied to the front edge of the board and the body start moving towards the rear edge. How much time will it take to fall off the board?


Homework Equations



The force of friction is given by [itex]F_f=F_n\cdot μ[/itex] where F_n is the normal force exerted by the object on the surface.


The Attempt at a Solution



I tried to write down Newton's equation of motion (on the x-axis) for the body and the board as follows:

Board: [itex]F=(m_A+m_B)a_1[/itex]

Body: [itex]F\frac{m_A}{m_A+m_B}-F_f=m_A a_2[/itex] where [itex]F_f=m_Agμ[/itex].

With these equations the problems doesn't come out right...
 
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  • #2
What forces act on the body? Apply Newton's 2nd law.
What forces act on the board? Apply Newton's 2nd law.

(Don't treat 'board + body' as a single system, since parts are in relative motion.)
 
  • #3
On the board: [itex]F[/itex] (and the weight of [itex]A[/itex] which is equilibrated by the board itself).

On the body: The force exerted by the board on the body, directed along the direction of [itex]F[/itex] and of a "certain" magnitude and the friction force.
 
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  • #4
All we care about are the horizontal forces, since vertical forces will cancel.
grusini said:
On the board: [itex]F[/itex] (and the weight of [itex]A[/itex] which is equilibrated by the board itself).
You are missing the horizontal force of the body on the board. (Newton's 3rd law.)
On the body: The force exerted by the board on the body, directed along the direction of [itex]F[/itex] and of a "certain" magnitude and the friction force.
The only horizontal force on the body is the friction force from the board.
 
  • #5
So the body exerts a horizontal force [itex]F_f[/itex] on the board in the opposite direction of [itex]F[/itex]? Then Newton's 2nd law for the board is
[itex]F-F_f=m_Ba_1[/itex]
and the Newton's law for the body would be:
[itex]F_f=m_Aa_2[/itex]?
 
  • #6
grusini said:
So the body exerts a horizontal force [itex]F_f[/itex] on the board in the opposite direction of [itex]F[/itex]? Then Newton's 2nd law for the board is
[itex]F-F_f=m_Ba_1[/itex]
and the Newton's law for the body would be:
[itex]F_f=m_Aa_2[/itex]?
Right. And you also know how to calculate the friction force.
 

FAQ: Friction of an object on a moving board

1. What causes friction between an object and a moving board?

Friction between an object and a moving board is caused by the microscopic irregularities on the surfaces of both the object and the board. These irregularities create resistance when the two surfaces come into contact, resulting in friction.

2. How does the weight of an object affect its friction on a moving board?

The weight of an object does not affect its friction on a moving board. Friction is determined by the surface properties and the force applied, not the weight of the object.

3. Can the type of material impact the friction between an object and a moving board?

Yes, the type of material can have a significant impact on the friction between an object and a moving board. Materials with rougher surfaces tend to have higher friction, while smoother materials have lower friction.

4. What factors can reduce the friction between an object and a moving board?

The amount of force applied, the smoothness and type of material of the surfaces, and the presence of lubricants or other substances can all reduce the friction between an object and a moving board.

5. How does friction affect the movement of an object on a moving board?

Friction can act as a resistance to the movement of an object on a moving board. This means that it can slow down the object or prevent it from moving altogether if the force of friction is greater than the force applied to the object.

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