# 1st and 3rd laws

## Main Question or Discussion Point

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) im a little confused???

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.