# Friction problem involving 2 blocks sliding in 2 directions with 2 frictions

by 2FAST4U8
Tags: force, friction, newtons law
 P: 1 1. The problem statement, all variables and given/known data A 1-kg block is pushed against a 4-kg block on a horizontal surface of coefficient of friction 0.25, as shown in the figure. Determine the minimum force needed to ensure that the 1-kg block does not slip down. Assume that the coefficient of friction at the interface between the block is 0.4. Hint: The two blocks exert equal and opposite forces on each other. 2. Relevant equations F=(A+B)a Ag=fs N=Ba Ag=$$\mu$$Ba 3. The attempt at a solution In class we have done similiar problems, only with a frictionless horizontal surface. I don't know how to account for the horizontal coefficient of friction of .25 in this problem. Using the above equations and ignoring the horizontal coefficient of friction, I get this: a=(Ag)/($$\mu$$B F=(((A+B)Ag)/($$\mu$$B)) F=(((4+1)(1)(9.8))/((.4)(4))) F=30.62N Now how do I account for the horizontal coefficient of friction of .25? Thanks in advance for any help you can provide.
 Quote by 2FAST4U8 1. The problem statement, all variables and given/known data A 1-kg block is pushed against a 4-kg block on a horizontal surface of coefficient of friction 0.25, as shown in the figure. Determine the minimum force needed to ensure that the 1-kg block does not slip down. Assume that the coefficient of friction at the interface between the block is 0.4. Hint: The two blocks exert equal and opposite forces on each other. 2. Relevant equations F=(A+B)a Ag=fs N=Ba Ag=$$\mu$$Ba 3. The attempt at a solution In class we have done similiar problems, only with a frictionless horizontal surface. I don't know how to account for the horizontal coefficient of friction of .25 in this problem. Using the above equations and ignoring the horizontal coefficient of friction, I get this: a=(Ag)/($$\mu$$B F=(((A+B)Ag)/($$\mu$$B)) F=(((4+1)(1)(9.8))/((.4)(4))) F=30.62N Now how do I account for the horizontal coefficient of friction of .25? Thanks in advance for any help you can provide.
Well, examining block one, we notice that we want $$\sum\vec{F}=m\vec{a}=0=\vec{F}_f+\vec{F}_g\rightarrow\vec{F}_f=-\vec{F}_g$$. From this, we can examine the frictional force, specifically:
$$\vec{F}_f=\mu_i\vec{N}\rightarrow m\vec{g}/\mu_i=\vec{N}$$.