potential energy and energy conservation

Question

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https://www.flipitphysics.com/Content/smartPhysics/Media/UserData/ebfae213-ad62-da58-2e01-ff6f3e3c551b/path.jpg

A 3.1 kg block is slid along the floor through different paths as shown above. The co-efficient of kinetic friction between the block and the floor is 0.23.

1)What is the work down by friction when the block moves from point A to point B along back 3?

W_Fric-3 =

2)What is the work done by friction if the block moves in a closed loop, starting at point A along path 2 and then back along path 3? W_Fric-23 =

3)What is the work done by friction if the blcok moves in a closed loop, starting at point A along path 1 and then back along path 2?W_Fric-12 =

4)What is the work done by friction if the block moves in a closed loop, starting at point A along path 1 and then returning along the same path?

W_Fric-11 =

Answer 1

Note that the work done by friction is always negative, because for any part of the journey the force is opposite to the displacement.

Next, we need to find the force.

F = µ N = µ m g = 0.23 * 3.1 * 9.8 N = 7.0 N

Then for each of the scenarios you need to multiply the force by the path length (and do not forget the negative sign!)

W_Fric-3 = - 7.0 N * 7 m = - 49 J

W_Fric-23 = - 7.0 N * 10 m = - 70 J

W_Fric-12 = - 7.0 N * 14 m = - 98 J

W_Fric-11 = - 7.0 N * 22 m = - 154 J

The take-home message of this exercise is to demonstrate that the force of friction is unlike the force of gravity, where the work only depends of the starting and ending points and is independent of the path. In other words friction is NOT a conservative force, hence path matters.