Friction Problems:
Unit 8c, Practice Problems
* There are two types of friction, static (fs) or sliding (kinetic-fk) friction
* Static friction occurs when trying to move a stationary object. Kinetic friction is the friction necessary
to overcome to keep an object moving.
* Usually static friction > kinetic friction
* The frictional force = Ff = ∙N, where  is the coefficient of friction (either static or kinetic) and N is the
normal force.
* When,  , the coefficient of friction is high between an object and a surface, the object does not slide
very easily. If  is small, the object slides more easily.
* Other helpful equations: Fnet = ma (Newton’s 2nd Law)
* how fast: vf = vi + a∙t
* how far: Δx = vi∙t + ½∙a∙t2
* combined (timeless): vf2 = vi2 + 2∙a∙Δx
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These problems are similar to ones on the online HW
1. A box is pushed with a horizontal force of 524 Newton. The coefficient of kinetic friction is 0.23. The
mass of the box is 153 kg.
a) Always start by drawing a force
diagram.
b) Calculate the weight of the
object.(answer = 1499.4 N)
c) What would be the normal force?
(answer = 1499.4 N)
d) Calculate the frictional force present as the box is moved (answer = 344.86 N)
e) Will the object accelerate? Are the horizontal forces balanced or unbalanced? (answer, yes,
unbalanced forces)
f) What is the horizontal net force? (answer = 179.14 N)
g) Determine the acceleration. (answer = 1.17 m/s/s)
h) Given the acceleration, what would the velocity of the box be after it is moved 10 meters, if it
started from rest? (answer around 4.84 m/s)
i) How much time would it take to move these 10 meters? (answer = 4.13 seconds)
Frictional practice problems (physics), p. 1
2. Attempting to walk his stubborn dog, Ryan resorts to pulling the dog out the door. A) If the coefficient
of static friction between the dog and the floor is 0.5, and the dog weighs 70 kg, what is the frictional
force that Ryan must overcome? B) If Ryan pulls the dog with a horizontal force = 400 N, what is the
net force on the dog? C) What is the dog’s acceleration? D) If Ryan pulls the dog for 10 seconds, how
far did he pull the dog, if it was initially at rest? And finally, E) what is the dog’s final velocity of the dog
at the end of this time if the acceleration stays constant? F) In what way(s) is this problem not very
realistic?
(answers: a) 343 N; b) 57 N; c) 0.81 m/s2; d) 40.5 m; e) 8.1 m/s)
3. I have a crateful of old records I am trying to push to the other room. I measure the mass of the crate to
be 15 kg. Attaching a forceometer, I find it takes me 80 Newtons of a horizontal force TO GET the crate
moving but only 70 Newtons to keep it moving. Determine the coefficient of static friction (μs) and the
coefficient of kinetic friction (μk). (answer = (μs) = 0.54 and (μk) = 0.48)
Frictional practice problems (physics), p. 2
4. I pull on a block of 1 kg block of wood horizontally on a flat table and find it takes
5 Newtons of force to keep it moving at a constant speed.
(a) Determine the coefficient of kinetic friction (μk) between the block and the
table. (answer = 0.51)
Now I put on a metal disk mass of an unknown weight, W, atop the block as shown
in the picture. It takes 6 Newtons now to keep it moving at a constant speed.
(b) Determine the weight, W, of the unknown weight placed atop the block.
(answer = 1.96 Newtons)
5. A sports car is travelling at 80 miles per hour (35.76 meters per second) constant speed on a level road.
On a dry day, the coefficient of friction between the tires and the roadway = 0.5. Determine how far it
would take the car to stop given the frictional coefficient. (notice that your mass cancels out)
How would the distance to stop the car change on a wet roadway with a coefficient of friction = 0.25.
Would the distance double?
(answers: It takes about 130 meters to stop the car on the dry road and about 260 meters on a wet
pavement.)
Frictional practice problems (physics), p. 3
NOTE: On these next problem, the normal force ≠ Fg. Be careful, here. When pushes or pulls are
at angles, you have to break the force up into its two components—use cosine and sine. Make a
good picture.
5. The generic man pushes a 20 kg generic lawn mower at an angle of 55 degrees relative to the horizontal with a force of 100
N. The man starts the lawn mower from rest at and gets it up to a horizontal speed of 1 m/s, in 2 sec. First, find the
acceleration on the lawn mower. Second, find the normal force on the lawn mower from the ground. Third, find the net force.
Fourth, find the kinetic friction which exists as the man pushes the lawn mower.
(answers: a) 0.5 m/s/s; 277.9 N; 10 N; 47.36 N)
6. Ryan pulls a wagon loaded with a case of root beer along a sidewalk. The wagon and root beer
have a mass of 20 kg total. Ryan pulls the wagon with a force of 100 N at an angle that is 25
degrees relative to the horizontal. The coefficient between the wagon’s wheels and the sidewalk
is 0.15.
a) What is the normal force between the wagon and sidewalk?
b) What frictional force impedes Ryan’s motion?
c) What is the net Force on the wagon in the x direction?
d) Consequently, what is the wagon’s acceleration?
e) How long did the acceleration last (in seconds) if the wagon achieves a phenomenal 10 m/s (v f) (vi = 0 m/s) during the
motion?
(answers: a) 153.74 N; b) 23.06 N; c) 67.5N; d) 3.4 m/s2; e) 2.9 s)
Frictional practice problems (physics), p. 4
Here are some for you to try!
1. A sports car has a mass of 1254 kg. Starting from rest, the car generates a horizontal force
of 4400 N. The frictional force opposing this motion is 280 N. a) If the car moves along a
horizontal road, what acceleration is produced? b) If the car produces this acceleration for 9
seconds, how far did it travel? (answers: 3.3 m/s/s; 133-134 meters, depending upon how you rounded)
2. You push a 12 kg crate across the floor at a constant velocity. Using a force
detector, you notice the force needed to push the crate against friction is 30 N.
What is the coefficient of kinetic friction, k, between the crate and the floor? (answer
= 0.255)
3. My 25 kg chair, initially at rest on a horizontal floor, requires a 365 N horizontal force to set it into
motion. Once the chair is in motion, a 327 N horizontal force keeps it moving at constant velocity. Find
the coefficients of static and kinetic friction between the chair and the floor. (μstatic = 1.49; μkinetic = 1.33)
4. A 40 kg crate, initially at rest, is pulled across a frozen pond with a rope. A force of 100 N is applied at
an angle of 30 degrees with the horizontal. The coefficient of kinetic friction, k, between the ice and the
crate is 0.05. a) What is the acceleration of the crate? b) If the box is pulled for 10 seconds, how far will
you have pulled it? And c) how fast will it be traveling by the end of this time? (answers = 1.7m/s/s; 85-87 meters,
depending upon rounding; around 17 m/s)
Frictional practice problems (physics), p. 5
5. Consider the 3 kg mass block on a rough surface. A
pull force (F) of 10 N is applied to the block and we
find that the block accelerates to the right. The block is
not moving vertically. The coefficient of kinetic
friction, µ, is 0.20.
a.
b.
c.
d.
e.
f.
g.
What is the block’s weight?
What is the normal force on the block?
What is the kinetic friction force?
If a 10 N pull force (F) is applied to the block, what is its net force horizontally?
What, then, is its horizontal acceleration?
How fast will the block be moving if the force is applied for 5.0 sec and the block starts from rest?
How far will the block have traveled during this 5.0 sec period?
(Answers: a) 29.4 N; b) 29.4 N; c) 5.88 N; d) 4.12 N; e) 1.37 m/s/s; f) 6.9 m/s; g) 17.1 m)
6. Now we are going to keep everything the same except for one thing. Now we have the pull force
acting at an angle of 40 degrees and we find that the 3 kg mass block again accelerates to the right.
Consider the block on a rough surface below. The coefficient of kinetic friction, µ, is 0.20.
40°
a. What is the block’s weight?
b. What is the horizontal component of the pull force Fpull (x)?
c. What is the vertical component of the pull force Fpull (y)?
d. What is the normal force on the block?
e. What is the kinetic friction force?
f. What is its net force horizontally that acts to accelerate the cart?
g. What, then, is its horizontal acceleration?
h. How fast will the block be moving if the force is applied for 5.0s and the block starts from rest?
i. How far will the block have traveled during this 5.0s period?
[answers: a) 29.4 N; b) 7.66 N; c) 6.43 N; d) 22.97 N; e) 4.59 N; f) 3.07; g) 1.02 m/s/s; h) 5.1 m/s; i) 12.75 m]
Frictional practice problems (physics), p. 6