Now let’s ask some questions about the motion of the box.
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| 1. |
What is the force of kinetic friction acting on the box? |
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| 2. |
What is the acceleration of the box? |
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| 3. |
What is the work done on the box by the force of kinetic friction? | |
What is the force of kinetic friction acting on the box?
The normal force acting on the box is
86.6 N, exactly the same as for the frictionless inclined plane. The force of kinetic friction is defined as
, so plugging in the appropriate values for
and
N:
Remember, though, that the force of friction is exerted in the negative x direction, so the correct answer is –43.3 N.
What is the acceleration of the box?
The net force acting on the box is the difference between the downhill gravitational force and the force of friction:
. Using Newton’s Second Law, we can determine the net force acting on the box, and then solve for
a:
Because
, the direction of the acceleration is in the downhill direction.
What is the work done on the box by the force of kinetic friction?
Since
W =
F ·
d, the work done by the force of friction is the product of the force of friction and the displacement of the box in the direction that the force is exerted. Because the force of friction is exerted in the negative
x direction, we need to find the displacement of the box in the
x direction. We know that it has traveled a horizontal distance of
d and a vertical distance of
h. The Pythagorean Theorem then tells us that the displacement of the box is
. Recalling that the force of friction is –
43.3 N, we know that the work done by the force of friction is
Note that the amount of work done is negative, because the force of friction acts in the opposite direction of the displacement of the box
