**94. A 5.00-kg block is placed on top of a 12.0-kg block that rests on a frictionless table. The coefficient of static friction between the two blocks is 0.600. What is the maximum horizontal force that can be applied before the 5.00-kg block begins to slip relative to the 12.0-kg block, if the force is applied to (a) the more massive block and (b) the less massive block?

Here is the free body diagram for situation (a)

Now we write out sum of force equations in the x and y directions for each block

Top Block

 

Since the block is not moving vertically

Bottom Block

 

Again, Since the block is not moving vertically

 

 

Now we are looking for the maximum horizontal force Fa that just starts the top block to slide.  SO we need the maximum static friction force acting.  Also since the block is going to just start to move, the accelerations of the top and bottom block must be the same, so

We have the following relationships

 

 

Here is the free body diagram for situation (b)

Now we write out sum of force equations in the x and y directions for each block

Top Block

 

Since the block is not moving vertically

Bottom Block

 

Again, Since the block is not moving vertically

 

 

Now we are looking for the maximum horizontal force Fb that just starts the top block to slide.  SO we need the maximum static friction force acting.  Also since the block is going to just start to move, the accelerations of the top and bottom block must be the same, so

We have the following relationships

 

 

 

 

 

 

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This page last updated on January 11, 2020