why isn't work = force x distance ?? force have to be parallel?

[knooch]

came from BK Physics.

Basically energy conversions. Have a hill (point A is on top of hill), point B is on bottom of hill, than at base of hill is some ground with friction. Basically a box or another object slides from top of hill (point A) to base of hill (point B) than encounters friction as it slides on ground to point C at the end of ground.

Question asked how much work done by friction from points B to C.
I was thinking work = force X distance, so Mass X Gravity X distanceB-C
but answer is Mass X gravity X height of top of hill (point A).

Am I wrong because Force isn't mass X gravity here, because the force has to be parallel?

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[FeinMS]

Friction is given by (mu)*N which usually equals (mu)Mg. You're finding the work done by the friction which is indeed parallel but opposite direction of the distance. Weight (mg) does no work because as you said it's not parallel to the distance.

 

[CarefreeSurfboard]

I am assuming that the velocity of the box at point C is 0.

If that is true, and there is no loss of energy to heat, then the potential energy that the box had at point A (mgh) should equal to the work done from points B to C to bring the block's velocity to 0.

The key point here being that energy is conserved between points A and C.

 

[sazerac]

It's friction. Of course kinetic energy is being converted to heat.

It isn't "lost" though. Just in a less usable form.

 

[frochocinco]

yes, energy is converted to heat but its not lost.
A = mgh
B = 1/2 mv^2
C = uN= W

given conservation of energy, we know that the total energy at the top (A) equals the total energy at the bottom (B). therefore, assuming it comes to rest at C, the energy at the end (C) must be equal to the energy at (B)

By simply applying the transitive property and remembering the concept of conservation of energy..

if A=B and B=C, THEN A=C. Further, we know that at A, E = mgh, therefore, we can set mgh = Work done by friction at the end