Work done by friction on a two-block system

[Physics lover]

Homework Statement

A force F=0.5N is applied on lower block as shown in figure.The work done by lower block by lower block on upper block for a displacement of 6m of the upper block with respect to ground is (in J).Take g=10m/s^2.
The figure is in attempt at a solution.

Relevant Equations

Friction=uN
Work done=Fdcostheta

I calculated friction = 1N.But since force is more than maximum friction,therefore lower block will not move and a force of 0.5N will be applied to upper block.
Therefore its work done by friction will be W=0.5×6=3 J.
But answer given is 1 J.
Can anyone help.

 

[Doc Al]

I calculated friction = 1N.

Note: μmg gives the maximum possible static friction; the actual friction force acting between the blocks will be less.

But since force is more than maximum friction,therefore lower block will not move and a force of 0.5N will be applied to upper block.

Both blocks will certainly move. (Note that the surface is frictionless.) Hint: Use Newton's 2nd law to find the acceleration of the system.

 

[Physics lover]

Note: μmg gives the maximum possible static friction; the actual friction force acting between the blocks will be less.

Both blocks will certainly move. (Note that the surface is frictionless.) Hint: Use Newton's 2nd law to find the acceleration of the system.

Can you explain me why will the lower block will also move.Will friction not balance the force on the lower block.

 

[Doc Al]

Can you explain me why will the lower block will also move.

It's being pushed!

Will friction not balance the force on the lower block.

Do you mean: Will the friction force on the lower block equal and thus cancel the applied force on the lower block? No.

First thing you need to do, though it will require several steps, is to figure out the friction force needed to keep the top block moving with the bottom one. (It will be less than μmg.) Do this: Assume the two blocks move as one. Figure out the acceleration of the system, then use that to find the needed friction force.

 

[Physics lover]

It's being pushed!

Do you mean: Will the friction force on the lower block equal and thus cancel the applied force on the lower block? No.

First thing you need to do, though it will require several steps, is to figure out the friction force needed to keep the top block moving with the bottom one. (It will be less than μmg.) Do this: Assume the two blocks move as one. Figure out the acceleration of the system, then use that to find the needed friction force.

Can you please explain why it is a no.

 

[Doc Al]

Can you please explain why it is a no.

How about you first do as I suggested. Things will make much more sense then.

 

[Doc Al]

Here are some additional thoughts that might help. First, realize that static friction acts to prevent slipping between surfaces. So, when the bottom block is pushed, the two blocks will move as one as long as there is sufficient static friction to accelerate the upper block along with the bottom block so they move together. (If the acceleration created by the applied force is too much, then there will not be enough static friction and the blocks will slip with respect to each other. Either way, they both move, just not with the same acceleration.)

Your job is to figure out what friction force is required to keep those blocks together. To do that, follow the suggestions I've given above.

 

[Physics lover]

Here are some additional thoughts that might help. First, realize that static friction acts to prevent slipping between surfaces. So, when the bottom block is pushed, the two blocks will move as one as long as there is sufficient static friction to accelerate the upper block along with the bottom block so they move together. (If the acceleration created by the applied force is too much, then there will not be enough static friction and the blocks will slip with respect to each other. Either way, they both move, just not with the same acceleration.)

Your job is to figure out what friction force is required to keep those blocks together. To do that, follow the suggestions I've given above.

Ok i understood it.Thanks i got the answer too.