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Practice: Inclined Plane Theory

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Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Free Body Diagrams

4 Activities

Wize University Physics Textbook (Master) > Newton's Laws of Motion: Forces and Dynamics

Inclined Surfaces

3 Activities

Inclined Plane

  • Sliding down an inclined plane is another example of motion with constant acceleration.
  • Source of the motion is still gravity of earth but only part of it is affecting the sliding of the object
  • To find the acceleration of an object over an inclined surface, one should first find the acceleration using the second law of Newton
  • For inclined surfaces, it is easier to choose the coordinates such that x-axis is parallel to the surface and y-axis is perpendicular to the surface.
  • Find the acceleration in the x and y direction shown in the free body diagram below.


Free body diagram of a skier of mass m glides down a slope at angle θ. We assume the snow is frictionless.










  • Note that usually the sliding object always remains in contact with surface which means that there is no motion along the y-axis we defined above!

More Free Body Diagrams Questions:
Practice: Three books on a table
Three books are sitting at rest on a table.
a) Draw a sketch.
b) Draw a complete free-body diagram for each book.
Example Problem: force of tension
Two blocks of mass m1=2Kgm_1 = 2Kg and m2=3Kgm_2 = 3Kg linked by a string through a pulley, where the block of mass m1 slides on the frictionless table. We assume that the string is massless and the pulley is massless and frictionless
a) Find the magnitude of the acceleration of the two masses b) Find the tension in the string
Two tennis players are rallying a tennis ball. Draw a free body diagram for the ball when it is in flight between the two players. Neglect air resistance.
Practice: Three books on a table
Three books are sitting at rest on a table.
a) Draw a sketch.
b) Draw a complete free-body diagram for each book.
A 45 kg45\ kg man is standing in an elevator.
Draw a free body diagram of the system then determine whether the statements about the apparent weight of the man are true. Let upward be +y.
Two tennis players are rallying a tennis ball.
Describe the forces (draw a FBD) on the ball when it is:
a) In flight
A 2.0 kg ball is suspended by a 1.20 m long string. A girl grabs the string and swings it downwards in front of her at a constant speed. The string makes an angle of 35º with the vertical. Determine the speed of the ball.
If the angle that the string makes with the vertical increases, what happens to the ball speed?
A block of mass 4 kg is suspended on two strings between two walls. The angles each string makes below the horizontal is 30°. What is the tension forces in each string? Provide an answer in Newtons and 1 decimal place.
Normal force
A man pulls 200Kg crate with rope angles 30 o above the horizontal with force 200N. The crate sits on the frictionless surface. Calculate the normal force. Enter answer in N.
Example Problem: force of tension
Two blocks of mass m1=2Kgm_1 = 2Kg and m2=3Kgm_2 = 3Kglinked by a string through a pulley, where the block of mass m1 slides on the frictionless table. We assume that the string is massless and the pulley is massless and frictionless
a) Find the magnitude of the acceleration of the two masses b) Find the tension in the string
A 65 kg man is riding a Ferris wheel with radius of 15 m, that moves at 1.5 rpm. Determine the normal force that the man experiences at the top of the ferris wheel and at the bottom.
New Practice Question
An engineer plans to design a levitating piston which can support loads up to 500kg. He decides to make a cylindrical chamber with radius of 0.5m with a moving piston which weighs 20kg. The chamber is filled with 10 moles of a diatomic ideal gas which is initially kept at 200K. By adding loads on the piston, the gas underneath is heated such that the height of the piston remains unchanged. (Assume that heating process is happening extremely fast such that the height of the piston remains constant while the gas is heated)
a) When there is no load on the piston, what is the pressure of the gas inside the chamber?
b) What is the temperature of the gas when maximum load is added to the piston?
More Inclined Surfaces Questions:
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
Forces: Block on slope with friction
A mass of 5 kg5\ kg is stationary on the surface of an inclined surface with angle of θ\theta and coefficient of kinetic friction of 0.30.3 and coefficient of static friction of 0.50.5. You start increasing the angle of the inclines surface.
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
trapezoid and friction
Two blocks are attached by a rope over a pulley and are placed on an incline as shown below. A force F is applied to prevent the top block from moving toward the right. If the static and kinetic coefficients of friction of all surfaces are 0.15 and 0.08 respectively, what is the minimum magnitude of F required to prevent being pulled to the right? (Hint: always start these problems with a free-body diagram!)
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60
Find the acceleration
What is the tension in the string?
A 1.2 kg is at rest on a spring at the base of a 35 degree inclined plane. If the spring constant is 105 N/m, and the spring is compressed by 12 cm, how far will it travel up the incline when it is release?
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope.
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Stacked blocks on a pulley and slope
Practice: Stacked Blocks on Pulley with Slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Problems on Work and Energy
Practice: Block with Spring and Ramp
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
Forces: Block on slope with friction
A mass of 5 kg5\ kg is stationary on the surface of an inclined surface with angle of θ\thetaand coefficient of kinetic friction of 0.30.3 and coefficient of static friction of 0.50.5. You start increasing the angle of the inclines surface.
Two masses on a pulley on a slope
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60,
Find the acceleration of the system.
What is the tension in the string?
Minimum sliding angle
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope. Give your answer to two sig figs in degrees.
I over-packed a box and it weighs 50kg. I'm pulling it across a rough surface at an angle of 45 degrees above the horizontal with a force of 280N. The coefficient of kinetic friction of the floor is 0.50. I pull for 10 seconds, which causes the box speed up from rest. Then I release it, and it continues to slide, as it slows to a halt.
a) What is its maximum speed?
b) How long until it stops?
Stacked blocks on a pulley and slope
Block A with mass 5 kg is connected to block B with mass 10 kg via a pulley. They are initially at rest on a 30-degree slope. Write out the equations from Newton's laws and find the distance they have moved in 4s. Neglect friction.
Inclined pully system
Two blocks are connected by a pulley system. One block (10 kg) rests on a plane inclined at 35º to the horizontal, while the other block (9.0 kg) hangs off the edge of the incline. The coefficient of friction between the block and the table is 0.30. The blocks are released from rest, what are their accelerations and what is the tension?
Practice: Springs and slopes
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
Component vectors practice 2
A block of weight 30 N is sitting on an incline of 19 degrees.
a) What are the components of the block's weight in the directions parallel to, and perpendicular to, the slope?
b) What is the mass of this block?
Forces: Inclined surfaces
Consider a segment of a light rail train banked at 4.0 degrees from horizontal spanning a turn with a radius of curvature of 450 meters. Neglect friction. What speed was this light rail designed for? (in m/s, rounded to 1 decimal place)
This question is adapted from Chapter 6, problem #75 in the Openstax Physics textbook, which is free and open-source: https://openstax.org/details/books/university-physics-volume-1
Slide and collide
A 5.00kg box is sliding down a 20.0m tall slide that makes an angle of 60.0o with the ground. The coefficient of friction for the slide is 0.750.
At the bottom of the slide it slides on a frictionless surface and collides with a 2.50kg stationary mass.
If the coefficient of static friction between the 2.00kg block and the ramp is 0.4000.400, find the minimum angle such that the block will slide down the slope (in degrees).
Problems on Work and Energy
A 2.00-kg block is pushed against a spring with negligible mass and force constant k= 400 N/m, compressing it 0.220 m. When the block is released , it moves along a friction-less , horizontal surface and then up a friction-less incline with slope 37.0∘37.0^{\circ}(Fig).
(a) What is the speed of the block as it slides along the horizontal surface after having left the spring?
(b) How far does the block travel up the incline before starting to slide back down?
Work on wagon
A 20kg wagon rests on an inclined plane with angle 30°. The wagon is pulled by a 200N tension force along the plane and is displaced by 2 m. The coefficient of kinetic friction between the surfaces is 0.30.
a) Draw a free-body diagram for the wagon.
b) Find the work done by each force on the wagon.
Block on Slope with Friction
A mass of 5.0 kg5.0\ kg is stationary on the surface of an inclined surface with angle of θ\thetaand coefficient of kinetic friction of 0.300.30 and coefficient of static friction of 0.500.50. You start increasing the angle of the inclines surface.
a) At what angle does the mass start to slide down? (Round to the nearest whole number)
b) If you set the system at an angle which is 5 degrees more than the angle you found in part a), how much time does it take for the speed of the mass to reach 2.0 m/s2.0\ m/s? (Units are in seconds, write the answer so that it has one digit)
A block with mass m is set to move up an inclined plane.
a) Assume there is no friction, how far will the block slide before come to a stop?
b) Now, assume there is friction between the block and the plane, how far will the block go up the plane?
1) Two masses are attached together by a rope as shown in the picture. If the system is released from the rest, what is the direction of the motion and acceleration for each mass? (Imagine there is no friction between masses and the inclined surface) M2 = 2M1 = 2kg
Two blocks of mass m and M are connected via pulley with a configuration as shown. The surfaces are frictionless. If M=15 kg and m=8 kg and θ1=30 and θ2=60\theta_1=30\ {\rm and}\ \theta_2=60
Find the acceleration
What is the tension in the string?
trapezoid and friction
Two blocks are attached by a rope over a pulley and are placed on an incline as shown below. A force F is applied to prevent the top block from moving toward the right. If the static and kinetic coefficients of friction of all surfaces are 0.15 and 0.08 respectively, what is the minimum magnitude of F required to prevent being pulled to the right? (Hint: always start these problems with a free-body diagram!)
Practice: Inclined Plane
A box of 10 Kg10\ Kg is released from rest at t=0 st=0\ sfrom the top of a frictionless inclined surface with θ=45°\theta=45\degree. If the box is initially at the top of inclined surface with height of 2 m2\ mrespect to the bottom of the ramp, at what time the box gets to the ground?
Practice: Friction
A 10-kg box is initially at rest on flat surface. A horizontal force of 28 Newton is applied on it. The static and kinetic coefficient of friction between the box and the floor is 0.32 and 0.18. What is the magnitude of the friction force?
Work Done by Multiple Forces
A 20 kg wagon rests on an inclined plane with angle 30°. The wagon is pulled by a 200 N tension force along the plane and is displaced by 2 m. The coefficient of kinetic friction between the surfaces is 0.3.
a) draw all the forces.
b) Find the work done by each force on the box.
Two different boxes of masses m1 = 125kg and m2 = 45kg are sliding down a rough inclined plane angled at θ=35∘\theta = 35^\circ , as seen in the figure. The coefficient of kinetic friction between m1 and the plane is 0.3. The coefficient between m2 and the plane is 0.5. Find the acceleration of the two boxes and the contact force between them.
A 1400-kg truck ascends a steep road at a speedy 60 km/h, against a 450-N force of air resistance. If the engine supplies energy to the drive wheels at the rate of 38 kW, what is the slope of the road?
A fixed triangular wedge has two inclined surfaces forming a double inclines plane. Two masses m1 = 5 kg and m2 = 10 kg are attached to a massless pulley connected with an inextensible string. The inclined surface I1 and I2 make an angle α1=60∘\alpha_1=60^\circ and α2=30∘\alpha_2=30^\circ with the horizontal respectively. The coefficient of kinetic friction is μ=0.01.\mu=0.01. Assume g = 10 m/s2.
a) Draw a free body diagram.
b) Is the system stationary? If not what will be the net acceleration?
A 1.2 kg is at rest on a spring at the base of a 35 degree inclined plane. If the spring constant is 105 N/m, and the spring is compressed by 12 cm, how far will it travel up the incline when it is release?
A stationary snow/water skier starts to slid down an icy slope inclined 11° until it hits the water. Initially skier is 200 meter away from the surface on the inclined surface. When he hits the water, the skier comes to full stop in 80 meters on the surface of water.
a) What is the acceleration of the skier on the icy slope?
b) How long does it take for the skier to hit the water?
A car travelling at 25 m/s on an uphill with θ = 20° slope runs out of the gas. a) How far up the hill it can move before starting to roll back down?
b) How long does it take for the car to get to the turning point?
a) Dave is trying to push a 60kg box up a greased ramp inclined 30°, pushing with a force of 350N. He pushes the box perfectly horizontally, rather than up the ramp, because he’s not terribly bright. What is the box’s acceleration?
b) If Dave forgot his grease at home, the ramp would have μsmax=0.10\mu_{\rm smax}=0.10 and μk=0.05.\mu_k=0.05. He still insists on pushing the box horizontally, with the same force. What would the box’s acceleration be now?
I'm moving and packed all my books into a box that weighs 17kg. I pull the box on a weightless dolly with a force of 60N at an angle of 30° to the horizontal surface. What is the acceleration of the box?
If the coefficient of static friction between the block and the ramp is 0.40.4, find the minimum angle such that the block will slide down the slope.
Forces: Inclined surface
A 40kg wagon attached to a rope is pulled up a hill at an incline of 19° to the horizontal. If the wagon starts from rest and takes 50 seconds to move 92 m up the hill, what is the force of tension in the rope? Find the acceleration of the block.