Calculating Force Applied to Wall with 1st & 3rd Laws

[Alem2000]

I had a question about a particle with mass $$m=3.0kg$$ if you take

this mass and push it up against a wall how much force would you have to

apply to keep it from falling if you had $$\mu_s = .7$$? where $$\eta$$ is the normal force and $$P$$ is the push force what I did was apply the first and 3rd laws my

equations came out to be

$$\eta=mg$$ and $$f_k=P$$ now after I calculate this I know I have to do something next b/c of the 3rd law. Do I draw in vector form the push exherted on the wall and the the push that the wall exherts back and add the (by taking the negative vector and reversing it to make it posative) I am a little confused?

 

[tomkeus]

What keeps particle from falling is the friction force $$F_{f}$$ which is equal to $$F_{f}=\mu_{s}\eta$$. On the other side, from 3rd law you know that $$P=\eta$$ and that in order for particle not to fall must be $$F_{g}=F_{f}$$, where $$F_{f}=mg$$. When you push the body pushes the wall with force $$P$$, so vector $$P$$ "attacks" wall. What Sir Isaac Newton says in his 3rd law is tha walls makes a "counter attack" on particle with force of the same intensity and direction as $$P$$, only in different way and this reactive force acts on a particle, and not on a wall. I hope this is what you wanted to know.

 

[GSXR750]

To calculate the force applied to the wall in this scenario, you can use the first and third laws of motion. The first law states that an object at rest will remain at rest or an object in motion will continue to move at a constant velocity unless acted upon by an external force. In this case, the particle is at rest against the wall and the external force acting on it is the push force (P) that you apply.

The third law states that for every action, there is an equal and opposite reaction. In this case, the action is the push force (P) exerted on the wall by the particle, and the reaction is the force exerted by the wall on the particle.

To find the force applied to the wall, you can use the equation F = ma, where F is the force applied, m is the mass of the particle, and a is the acceleration. In this case, the particle is not moving, so the acceleration is 0. Therefore, the force applied to the wall is also 0.

To find the force exerted by the wall on the particle, you can use the equation F = \mu_s\eta, where \mu_s is the coefficient of static friction and \eta is the normal force. The normal force is equal to the weight of the particle, which can be calculated using the equation \eta = mg. So, the force exerted by the wall on the particle is \mu_smg.

Now, to find the total force applied to the wall, you can add the force applied by the particle (P) and the force exerted by the wall on the particle (\mu_smg). This is because of the third law, which states that these two forces are equal and opposite. So, the total force applied to the wall is P + \mu_smg.

In vector form, you can draw the push force exerted by the particle on the wall and the push force exerted by the wall on the particle, both pointing in opposite directions. The magnitude of these forces will be equal, and you can add them to find the total force applied to the wall.

I hope this helps clarify the process for calculating the force applied to the wall in this scenario using the first and third laws of motion. Remember to always consider both forces in action and reaction pairs when using the third law.