Lyzinski Physics
Inclined Plane Problems

 Instead of an x-y coordinate system, inclined plane problems use a ________
coordinate system.
 There is a _______________ explanation of the why the angles above are
both “theta”.
1. Draw the full free-body diagram of a block that is getting pushed DOWN an inclined plane
by a force parallel to the incline. Assume that the incline has an angle of inclination of 
degrees and that it’s NOT frictionless.
2. Draw the full free-body diagram of a block that is getting pulled UP an inclined plane
by a force at an angle of a degrees above the inclined surface. Assume that the incline
has an angle of inclination of  degrees and that it is NOT frictionless.
3. A 100 kg block is sitting at rest on an incline plane whose angle of inclination is 10o.
Find:
a) the parallel and perpendicular components of the force due to gravity.
b) the normal force.
c) the force of friction that keeps the block from sliding.
4. A 1000 kg car has its parking brake on because it is sitting on hill with a 20o slope.
Find the force that the brake must apply to keep the car from moving. Then, find the
car’s normal force.
5. A 4 kg block is put on a 25o inclined plane. Find the box’s acceleration when it is let
go. Assume that the surface is frictionless.
6. An incline has an angle of inclination that is adjustable. A 20 kg block is put on the
incline and the angle is increased until the block begins to slide. If the coefficient of
static friction is 0.6 between the block and the incline, find the angle that causes the
block to slide.
7. A 70 kg skier is skiing down a hill with an angle of inclination of 20o. He has newly
waxed skis, which have a coefficient of kinetic friction of 0.05 with the snow. Find
his acceleration, assuming that he is not using his ski poles, but is instead skiing
downhill under gravity’s force alone. How far will he travel in 10 seconds if he starts
from rest?
8. A 10 kg block of ice slides down a ramp 20 m long, inclined at 10° to the horizontal.
a) If the ramp is frictionless, what is the acceleration of the block of ice?
b) If the coefficient of kinetic friction is 0.10, how long will it take the block to slide
down the ramp, if it starts from rest?
9. A skier has just begun descending a 20° slope. Assuming that the coefficient of kinetic
friction is 0.10, calculate:
a) the acceleration of the skier.
b) his final velocity after 8.0 seconds.
10. A 4kg box starts to slide on an incline of 25 o. If the coefficient of kinetic friction on
the incline is 0.1, how fast and how far will the box travel in 5 seconds?
11. A block of ice is placed on an inclined plane of 60o. Determine its acceleration if the
coefficient of friction is 0.2.
12. What is the coefficient of friction of an object moving down at 35 o slope at a constant
speed of 12 m/s?
13. A boy is pulling a 6 kg sled up a hill at a constant speed of 6 m/s. The hill has a slope
of 38o and a coefficient of friction of 0.2. Determine the force applied by the boy in
order to move the sled up the slope at a constant speed. Assume the boy pulls with a
force parallel to the inclined plane.
14. An object is sliding at 20 m/s when it encounters a 20 o hill with a coefficient of
friction of 0.15. How far up the hill does the object slide before coming to rest?
Answers:
3) 170.2N, 965.1N,
965.1N, 170.2N [uphill]
4) 3351.8N [uphill], 9209N
5) 4.2 m/s2 [downhill]
6) 31o
7) 2.9 m/s2 [downhill],
144.6m
8) 1.7 m/s2 [downhill],
7.4 sec
9) 2.4 m/s2 [downhill],
19.4 m/s
10) 3.3 m/s2 [downhill],
16.3 m/s, 40.6 m
11) 7.5 m/s2 [downhill]
12) 0.7
13) 45.5 N
14) 42.3 m