Inclined Plane Notes
Draw the free-body diagram for the box on the incline in figure 1. Assume no friction is present.
Figure 2
Figure 1
1. Gravity pulls objects
INTO
and DOWN
inclined planes!
2. The vertical component of the weight force is equal to the normal force because the object stays on
the inclined plane.
3. The horizontal component of the weight force is the unbalanced force that makes the object
accelerate down the ramp.
Draw the free-body diagram for the box on the incline in figure 1. Assume friction is present.
Figure 2
Figure 1
4. If friction is present it opposes the horizontal component of the weight force IF the object is moving
down the ramp.
5. If friction is present it ADDS to the horizontal component of the weight force IF the object is moving
up the ramp.
Practice Problems
1. A 42kg bag of luggage is sliding down the chute at the airport. If the chute is at a 39o angle, what force
will the bag be pulled down the chute?
2. Brynne is sledding down an ice-covered hill inclined at an angle of 15o with the horizontal. If Brynne
and the sled have a combined mass of 54-kg, what is the magnitude of the force pulling them down the
hill?
Friction Notes
Friction: the force that acts to oppose the motion between two materials moving past one another
Static Friction: the resistance force that must be overcome to start an object in motion
Kinetic Friction: the resistance force between the surface and an object already in motion
Force of friction = (coefficient friction) (normal force)
Ff = µ FN
 A high coefficient of friction, µ, means that the object is not likely to slide easily (close to 1.0)
 A low coefficient of friction, µ, is found between really slippery surfaces (close 0.0)
 Because the coefficient of friction is simply a ratio of the force of sliding friction to the
normal force, it has no units.
Practice Problems:
1. Brian is walking through the school cafeteria but does not realize that the person in front of
him has just spilled his glass of chocolate milk. As Brian, who weighs 420N, steps in the milk,
the coefficient of sliding friction between Brian and the floor is reduced to 0.040. What is the
force of kinetic friction between Brian and slippery floor?
2. While redecorating her apartment, Kitty slowly pushes an 82-kg china cabinet across the
wooden dining room floor, which resists he motion with a force of friction of 320 N. What is
the coefficient of kinetic friction between the china cabinet and the floor?
3. At Sea World, a 900-kg polar bear slides down a wet slide inclined at an angle of 25o to the
horizontal. The coefficient of friction between the bear and the slide is 0.0500. What static
frictional force impedes the bear’s motion down the slide?
Inclined Plane and Friction Practice Problems
1. Unbeknownst to the students, every time the school floors are waxed, Mrs. Prentice, the principal, likes to slide
down the hallway in her socks. Mrs. Prentice weighs 500N and the force of friction that opposes her motion
down the hall is 102 N. What is the coefficient of friction between Mrs. Prentices sock and the newly waxed
floor?
2. Lauren is trying to make her 70kg Saint Bernard go out the back door but the dog refuses to walk. If the
coefficient of sliding friction between the dog and the floor is 0.50, how hard must Lauren push in order to move
her dog with a constant speed?
3. Rajiv’s favorite rides at Six Flags are the roller coasters. The rollercoaster car and passengers have a combined
mass of 1620kg and they descend the first hill at an angle of 45o to the horizontal. With what force is gravity
pulling them down the hill?
4. Rather than taking the stairs, Max gets from the second floor of his house to the first floor by sliding down the
banister that is inclined at an angle of 30o to the horizontal.
a. If Max has a mass of 45 kg and the coefficient of sliding friction between Max and the banister is 0.20,
what is the force of friction that impedes his motion?
b. If the banister is made steeper, what effect, if any, will this have on the force of friction?