Solving Inclined Plane
Problems
Inclined Plane Problems

First you have to determine if the plane has
friction or not.
 If there is no friction, the following is true:
 Work in = Work out
 Fe x de = Fr x dr
 Remember that Fr = the weight of the object
If There is no Friction
Fe
de
Fe x de = Fr x dr
dr
Fr
same as weight
Sample Problem #1
A 50 N object is being pushed up a frictionless ramp.
The ramp is 5 m long and 2 m high.
What is the work Input?
Work input = Fe x de
Do you know Fe? no
You do know the work output = Fr x dr
Work out = 50N x 2 m = 100 J
Work in = work out, so Work input = 100 J
Sample Problem #2
A 200 N object is being pushed up a frictionless ramp that
is 6 m long and 3 m high. Calculate the effort force.
Work in = Work out
Fe x de = Fr x dr
Fe x6m = 200N x 3m
Fe = 100N
Sample Problem #3
A 5 m long frictionless ramp makes a 25 degree angle with
the ground. A 1500 N object is being pushed up the ramp.
What is the work input?
In this problem, there is no height or Fe. All you know is
The de, the weight(Fr), and an angle.
Sample Problem #3
A 5 m long frictionless ramp makes a 25 degree angle with
the ground. A 1500 N object is being pushed up the ramp.
What is the work input?
First, you need to find the height since there is no way to
calculate the Fe.
Sin 25degrees = height / length
Sin 25 degrees = height/ 5m
height = 2.1 m
Sample Problem #3
A 5 m long frictionless ramp makes a 25 degree angle with
the ground. A 1500 N object is being pushed up the ramp.
What is the work input?
Now you can calculate the work output
Work out = Fr x dr
= 1500 N x 2.1 m (height)
= 3150 N
Work in = Work out = 3150 N
Inclined Plane with Friction
Fe
de
Ff
dr
F ll
Fr
F⊥
Fw
Fll
Sample Problem #4
A 1000 kg object is being pushed a 300 m ramp that has friction
and makes a 17.5 angle with the ground. Calculate the Work input
if the coefficient of Friction is 0.25. Assume that there is no acceleration
First Work in does not equal work out so you cannot just find the
height x weight.
You do need to find the weight in order to finish the problem.
Weight (Fr) = 1000 kg x 9.8 = 9800 N
Sample Problem #4
A 1000 kg object is being pushed a 300 m ramp that has friction
and makes a 17.5 ° angle with the ground. Calculate the Work input
if the coefficient of Friction is 0.25. Assume there is no acceleration.
Now you have to find the F parallel and F perpendicular.
F parallel Sin 17.5 ° = F parallel / 9800 N
F parallel = 2950 N
F perpendicular Cos 17.5 ° = F perpendicular / 9800 N
F perpendicular = 9350 N
Ff = µF perpendicular = (0.25)(9350)= 2340N
Sample Problem #4
A 1000 kg object is being pushed a 300 m ramp that has friction
and makes a 17.5 ° angle with the ground. Calculate the Work input
if the coefficient of Friction is 0.25. Assume there is no acceleration.
Next, you can calculate the Effort Force
Fe = Ff + F parallel
= 2340N + 2950N
Fe = 5290N
Work in = Fe x de
Work in = 5290N x 300 m
Work in = 1.6 x 106 J
Sample Problem #4
A 1000 kg object is being pushed a 300 m ramp that has friction
and makes a 17.5 ° angle with the ground. Calculate the Work input
if the coefficient of Friction is 0.25. Assume there is no acceleration.
What is the work output?
First find dr
Sin 17.5degrees = dr / 300 m
dr = 90.2 m
Work out = Fr x dr
Work out = 9800 N x 90.2m
Work out =8.8 x 105 J
Sample Problem #4
A 1000 kg object is being pushed a 300 m ramp that has friction
and makes a 17.5 ° angle with the ground. Calculate the Work input
if the coefficient of Friction is 0.25. Assume there is no acceleration.
What is the MA, the IMA, and the Efficiency of this ramp?
MA = Fr / Fe
MA = 9800 N/ 5290N
MA = 1.8
IMA = de/dr
IMA = 300 m / 90.2 m
IMA = 3.3
Sample Problem #4
A 1000 kg object is being pushed a 300 m ramp that has friction
and makes a 17.5 ° angle with the ground. Calculate the Work input
if the coefficient of Friction is 0.25. Assume there is no acceleration.
What is the MA, the IMA, and the Efficiency of this ramp?
Efficiency = Work out/ Work in
or Eff = MA/ IMA
Eff = 8.8 x 105 J/ 1.6 x 106 J
Eff = 1.8/3.3
Eff = .55 x 100
Eff = .55 x 100
Eff = 55%
Eff = 55%