Why is the work done against friction not equal to the force times distance?

[eureka_beyond]

Homework Statement

the question and answers are in the attachment, I don't understand question 8b) (ii), why is the work done against friction =f x d and not 10N x d?

Homework Equations

The Attempt at a Solution

 

[Doc Al]

For some reason, I cannot view those attachments. Can you describe the problem?

why is the work done against friction =f x d and not 10N x d?

The obvious question is: What does the friction force equal?

 

[eureka_beyond]

okay, the question goes like this:
on a rough horizontal Ground, a 3 kg block at rest is moved be a Force of 10N. The acceleration of the block is 2ms-2.
if the force ceases to act after 4 seconds,
what 's the further distance traveled by the block before it comes to rest?

 

[Doc Al]

if the force ceases to act after 4 seconds,

That means the 10 N force is no longer applied.

what 's the further distance traveled by the block before it comes to rest?

What's the only force acting to slow down the block?

 

[eureka_beyond]

that's got to be the friction, right?

 

[Doc Al]

that's got to be the friction, right?

Yes. Now use the given information to figure out the friction force. (Hint: Newton's 2nd law.)

 

[eureka_beyond]

by Newton's 2nd law
F=ma
Let the friction be f
10-f=3(2)
f=4N

 

[Doc Al]

by Newton's 2nd law
F=ma
Let the friction be f
10-f=3(2)
f=4N

Good!

 

[eureka_beyond]

yay! thanks a million. but there's another thing, how do I get the further distance traveled by the block before it comes to rest?

 

[Doc Al]

yay! thanks a million. but there's another thing, how do I get the further distance traveled by the block before it comes to rest?

Several ways:
(1) You can find the acceleration and use kinematics. (First figure out how fast the block is moving at the end of 4 seconds.)
(2) You can set the work done by friction equal to the change in kinetic energy.

 

[eureka_beyond]

ah, I see. The book must have been using the second way you describe, I get it now, thanks a lot.