how to find acceleration of a box sliding on a rough horizontal table?

Question

how to find acceleration of a box sliding on a rough horizontal table?

in term of mu_k , mu_s , m , g

I need an expression for the acceleration of the box in those terms

Answer 1

F=ma, Ff=mu_s*m*g, F_applied=Ff, Ff'=mu_k*m*g
Fnet=F_applied-Ff'=Ff-Ff',
Fnet=mu_s*m*g-mu_k*m*g
Fnet=mu_s-mu_k*m*g=ma
(mu_s-mu_k)m*g=ma
a=(mu_s-mu_k)*g

You know that the box will start moving when the applied force equals the force of static friction (Ff). then the new friction force equals Ff' or mu_k(mg). So the net force is equal to the difference of the coefficient of frictions times mg. then set that equal to F=ma. the masses cancel out so the acceleration is equal to the difference in coefficient of frictions times g.