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

[2FAST4U8]

Homework Statement

http://streetrodjohn.home.comcast.net/~streetrodjohn/physics.jpg

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.

Homework Equations

F=(A+B)a
Ag=f_s
N=Ba
Ag=$$\mu$$Ba

The Attempt at a Solution

In class we have done similar 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=(A_g)/($$\mu$$_B

F=(((A+B)A_g)/($$\mu$$_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.

 

[asleight]

Homework Statement

http://streetrodjohn.home.comcast.net/~streetrodjohn/physics.jpg

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.

Homework Equations

F=(A+B)a
Ag=f_s
N=Ba
Ag=$$\mu$$Ba

The Attempt at a Solution

In class we have done similar 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=(A_g)/($$\mu$$_B

F=(((A+B)A_g)/($$\mu$$_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:

$$\vec{F}_f=\mu_i\vec{N}\rightarrow m\vec{g}/\mu_i=\vec{N}$$.

What next? :)

 

[thomate1]

I would approach this problem by first understanding the physical principles involved. In this case, we are dealing with two blocks on a horizontal surface, where friction is present in both the horizontal and vertical directions. The key to solving this problem is to recognize that the two blocks are exerting equal and opposite forces on each other, and that these forces must be balanced in order for the 1-kg block to not slip down.

To account for the horizontal coefficient of friction, we need to consider the forces acting on the 1-kg block in the horizontal direction. These include the force of friction from the 4-kg block pushing against it, as well as any external forces pushing or pulling on the block. Let's call this external force F_ext.

In order for the 1-kg block to not slip down, the net force in the horizontal direction must be zero. This means that the force of friction from the 4-kg block (0.25*4*g) must be balanced by the external force, F_ext. In other words:

F_ext = 0.25*4*g = 9.8N

So, the minimum force needed to ensure that the 1-kg block does not slip down is 9.8N. This means that any external force greater than 9.8N will be enough to prevent the block from slipping down. We can also use this information to calculate the minimum force needed to overcome the horizontal coefficient of friction and move the block horizontally. This would simply be the force of friction (0.25*4*g) plus the minimum force needed to prevent slipping (9.8N), giving us a total of 19.6N.

In summary, to solve this problem we need to consider the forces acting on the 1-kg block in both the horizontal and vertical directions, and ensure that these forces are balanced in order to prevent slipping. By taking into account the horizontal coefficient of friction, we can determine the minimum force needed to prevent slipping and the minimum force needed to move the block horizontally.