Question on Work: Understanding Force, Mass, and Displacement

[MRGE]

I'm just trying to grasp the concept of work. It isn't a homework problem but if I get could feedback it would be great.

Example 1: A block with mass M is pushed with a constant force F across a frictionless table
and has a displacement across the table as D.

My first question is that does the Block increase it's displacement when F force is increased? since acceleration would increase, will it cover more ground?

My second questions is related to the first, is that if we use the same force F to push a block with the mass of 1/2(M), will the block travel further? if it does, doesn't that mean the Work will be greater than the example #1 since W= F(displacement)? But intuitively, it makes no sense to me because it feels like it should be equal.

I feel like I'm misunderstanding a certain fundamental part of Work, I'm just not sure which. Help would be great! Thanks!

 

[cupid.callin]

for (1)
Yes, block's displacement will increase provided that F has a fixed direction.

for (2)
recall Newton's eqn d = ut + 0.5at^2
and tell me that for same F ie for acceleration = F/(mass) ... what will be the d for 2 blocks.

 

[MRGE]

Wait.. if we use that. acceleration is doubled because it would be a = 2F/M if the mass is 1/2M. So D for the block with the 1/2M using the same force will increase. Right?

 

[ehild]

Read the problem. It asks the work of a given force F during a given displacement D. If the force and displacements are the same the work is also the same, no matter what the mass and acceleration are. If the force is doubled, and the displacement stays the same, the work is doubled. You know, that work is the (scalar) product of displacement and force. Apparently, you think the block moves for some time and stops and you take the displacement as the distance between the final position and the initial one. But the block never stops on a frictionless surface, even in case when you do not apply any force. ehild

 

[MRGE]

thanks ehild! Yea, i forgot to add friction. It's not a problem from a book, I just wanted to make a scenario that expresses my questions. Thanks for clarifying it for me. Helps a lot!