Physics 12 Inclined Planes Push it Up Song 1
Bell Work A box is pushed up a ramp at constant velocity. Draw a neatly labeled FBD showing all of the forces acting on the box. direction of motion θ F p F f 2
N There are always at least two forces acting upon any object that is positioned on an inclined plane the force of gravity and the normal force. The force of gravity (also known as weight) acts in a downward direction; yet the normal force acts in a direction perpendicular to the surface. 3
The task of determining the net force acting upon an object on an inclined plane is a difficult manner since the two (or more) forces are not directed in opposite directions. For these problems, the force of gravity will need to be resolved into two perpendicular components one directed parallel to the inclined surface and the other directed perpendicular to the inclined surface. N The equations for the parallel and perpendicular components are: 4
In the absence of friction and the other forces (tension, applied, etc.) the acceleration of an object on an incline can be calculated using a simple formula. N 5
In the absence of friction and other forces: a = g sinθ Check: If the plane were vertical, θ = 90 o, the magnitude of the acceleration would be g. This makes sense because the object would be in free fall. 6
Incline Plane Physics The inclined plane Alevel Physics help 7
Example A 1200 kg car is on an icy (frictionless) hill that is inclined at an angle of 12 0 with the horizontal. What is the acceleration of the car down the hill? 8
Usually there is friction between the object and the inclined plane. If an object slides down a plane at constant velocity, in which direction does the force of friction act? direction of motion F f F f F N θ θ F F g F p 9
CYU A 1200 kg car is on an icy hill that is inclined at an angle of 12 o with the horizontal. As the car starts sliding, the driver locks the wheels. The coefficient of friction between the locked wheels and the icy surface is 0.14. What is the acceleration of the car down the hill? 10
Sample Problems - Inclined Planes 1. A 7.6 kg object is at rest on an inclined plane. If the inclined plane makes an angle with the horizontal of 33 o, what is the normal force acting on the object? 2. A 445 N box is sliding down a frictionless 25.0 o inclined plane. Determine the parallel component of the weight that causes the box to slide down the inclined plane. 3. A 325 N box is sliding down a frictionless inclined plane. If the incline makes an angle of 30.0 o with the horizontal, what is the magnitude of the box's acceleration along the incline? 4. A 275 N box is sliding down a 35.0 o incline. If the force of friction along the incline is 96.0 N, what is the magnitude of the acceleration of the box? 11
5. A 435 N box is sliding down a 40.0 o incline. If the magnitude of the box's acceleration is 0.250 m/s 2, what is the force of friction on the box? 12
Sample Problems 1. A 7.6 kg object is at rest on an inclined plane. If the inclined plane makes an angle with the horizontal of 33 o, what is the normal force acting on the object? m = 7.6 kg o = 33 0 F N =? F N = F g cos o = mg cos o = (7.6)(9.8)(cos 33) = 62 N 13
2. A 445 N box is sliding down a frictionless 25.0 o inclined plane. Determine the parallel component of the weight that causes the box to slide down the inclined plane. 14
3. A 325 N box is sliding down a frictionless inclined plane. If the incline makes an angle of 30.0 o with the horizontal, what is the magnitude of the box's acceleration along the incline? 15
4. A 275 N box is sliding down a 35.0 o incline. If the force of friction along the incline is 96.0 N, what is the magnitude of the acceleration of the box? 16
5. A 435 N box is sliding down a 40.0 o incline. If the magnitude of the box's acceleration is 0.250 m/s 2, what is the force of friction on the box? 17
Answer Key 1. 63 N 2. 188 N 3. 4.90 m/s 2 4. 2.20 m/s 2 5. 269 N 18
Bell Work Independent Work Sept. 25, 2009 You have ~ 10 minutes to answer this question. Write your solution in your Hilroy scribbler. A crate is pulled up a slope at constant velocity by a rope. The slope is inclined at an angle of 25.0 o to the horizontal. The crate s mass is 55.0 kg and the coefficient of kinetic friction between the crate and the slope is 0.120. Find the magnitude of the tension in the rope. 19
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Friction and Inclined Planes If an object is at rest on an inclined plane, the force of static friction must equal the parallel component of the object's weight. As the angle of inclination, θ, increases, F p increases in magnitude. Eventually F p will exceed the maximum value of the force of static friction and the object will begin to slide down the incline. At what angle will an object just begin to slide down an inclined plane? s The normal force is equal to the perpendicular component of the object's weight. The force of friction must equal the parallel component of the object's weight. Making a couple of substitutions, we get: s s the angle at which the object will "just begin to slide down" the inclined plane. 21
Note If an object is sliding down an inclined plane at constant speed, then: 22
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Physics 12 Sample Problems Inclined Planes 1. A trunk weighing 562 N is resting on a plane inclined at 30.0 o from the horizontal. Find the components of the trunk's weight parallel and perpendicular to the plane. 2. A 1975 kg car is rolling down a hill inclined at an angle of 15 o. What is the acceleration of the car? Neglect friction. 3. You slide a 325 N trunk up a 20.0 o inclined plane with a constant velocity by exerting a force of 211 N parallel to the inclined plane. a) What is the sum of your applied force, friction and the parallel component of the trunk's weight? Justify your answer. b) What is the magnitude and direction of the force of friction? c) What is the coefficient of friction? 4. a) A worker places a large plastic waste container with a mass of 84 kg on the ramp of a loading dock. The ramp makes an angle of 22 o with the horizontal. The worker turns to pick up another container before pushing the first one up the ramp. If the coefficient of static friction is 0.47, will the crate slide down the ramp? b) The worker starts to push the container up the ramp with an applied force parallel to the incline. With what force will he be pushing when the container begins to move? c) If the worker continues to push with the same force after the container starts moving, and the coefficient of kinetic friction is 0.25, at what rate will the container start to accelerate? 5. A skier coasts down a 3.5 o slope at a constant speed. Find the coefficient of kinetic friction between the skis and the snow covering the slope. 25
From "Sample Problems Worksheet" 3. A worker places a large plastic waste container with a mass of 84 kg on the ramp of a loading dock. The ramp makes an angle of 22 o with the horizontal. The worker turns to pick up another container before pushing the first one up the ramp. If the coefficient of static friction is 0.47, will the crate slide down the ramp? No, the container will not move. The maximum value for the force of static friction is greater than the magnitude of F parallel. The worker starts to push the container up the ramp with an applied force parallel to the incline. With what force will he be pushing when the container begins to move? (The container's acceleration will be zero until the applied force has overcome the force of static friction.) If the worker continues to push with the same force after the container starts moving, and the coefficient of kinetic friction is 0.25, at what rate will the container start to accelerate? 26
Answers 1. 281 N, 487 N 2. 2.5 m/s 2, down the hill 3. a) 0 N b) 99.8 N, down the inclined plane c) 0.327 4. a) It will not slide down the ramp (F f > F p ) b) 6.7 x 10 2 N c) 2.0 m/s 2 up the ramp 5. 0.061 27
Module Summary In this module Force vectors can be broken into components so that dynamics situations can be analyzed using free body diagrams and Newton's Second Law. Situations involving inclined planes (ramps)can be analyzed by rotating the coordinate system so that the x axis is parallel to the ramp and the y axis is perpendicular to the ramp. The components for force of gravity can then be given by x y 28
Assignment 1 29
Attachments Push it Up Song The inclined plane Alevel Physics help Incline Plane Physics A box sliding down an incline plane with friction: physics challenge problem Friction on an Incline Plane