Name: Regents Physics Date: Mr. Morgante UNIT 2E Forces on Inclined Planes
1. Frictionless Plane Forces on An Inclined Plane +y +y m VS. +x +x m 2. Free Body Diagram (FBD) m= mass=10kg F N +y = 30 F g =Force Weight=(m g) +x F ll = Force Parallel F =Force Perpendicular F ll F F N = Force Normal F W Enhanced View of FBD: F ll F N F w F Note: F w is always the Resultant/Hypotenuse of the vector triangle. Relationships based on Newton s 3 rd Law (Action-Reaction) F N = F 2
Example: F N F ll 30 F w F CLOSE UP VIEW OF FBD: Solve Below: F N +y +x F ll = Newton s 3 rd Law F N = F = 30 M object = 20 kg F ll F w F F = F N = *F w is ALWAYS the resultant/hypotenuse of the vector Triangle* The vector triangle has been rearranged using Tip to Tail Method 30 60 F ll F F w = mg =20kg(9.81m/s 2 ) =200N F = 200N(sin60)= 173N F ll = 200N(cos60)= 100N 3
Friction Case F N F f F ll θ F θ F w Note: You can never ever ever draw either F, F ll, F N, F f greater than F w! Only difference from previous example is we now have F f vector! Newton s 3rd Law Relationships - Similar to Object on Horizontal Plane F N =F & F f =F ll F f =μ(f N ) +y F N a F f Fapp F ll F net =m a +x Fw=m g F w =m g F f =μ F N Ff=40N F Net= 70N F net in +x-direction= 30N μ =Coefficient Of Friction μ K OR μ s Kinetic OR Static 4
Name Date Regents Physics Inclined Plane Notesheet Mr. Morgante m=1 kg 1. Using a protractor, a) draw the normal force acting on the block, b) draw the weight vector of the block c) label angle. d) verify that = the angle between the weight vector and the normal vector. 2. Complete the table below using the inclined plane above & varying angles: F N F mg sin 10 20 30 40 50 60 3. As increases, F N, F 4. What relationship, if any exists between F and (mg sin 5
Name: Regents Physics Date: Mr. Morgante Inclined Plane Worksheet 1. A cart rolls down an inclined plane with constant speed as shown in the diagram below. Which arrow represents the direction of frictional force? (1 ) A (2 ) B (3 ) C (4 ) D 2. The diagram below represents a 10.-newton block sliding down a 30-degree incline at a constant speed. The force of friction on the block is approximately (1 ) 5.0 N (2 ) 10. N (3 ) 49 N (4 ) 98 N 3. The diagram below represents a car resting on a hill. Which vector best represents the weight of the car? (1 ) A (2 ) B (3 ) C (4 ) D 4. State below what happens to each of the forces on an inclined plane with friction as the angle between the incline and the horizontal increases. (OVER) 6
5. a. Sketch and label the forces on the 250 g. block below at constant velocity: This is not a frictionless plane! =33 b. Determine all the forces on the block. Show all of your work below. c. Determine k, show all of your work below. d. What are the all of the forces if the angle is increased to 90 degrees? Show your work and/or explain your answer below. 7
6. Three forces act on a box on an inclined plane as shown in the diagram below. (Vectors are not drawn to scale) Normal Force Friction horizontal Weight If the box is at rest, the net force acting on it is equal to (1) the weight (2) friction (3) the normal force (4) zero (over) 7. The diagram below shows a 10.0-kilogram mass held at rest on a frictionless 30.0º incline by force F. 10.0 kg F 30.0º What is the approximate magnitude of force F? (1) 49.1N (2) 98.1 N (3) 85 N (4) 9.81 N 8
Name Regents Physics Date Mr. Morgante Inclined Plane Practice (SHOW ALL WORK) 1. A 2.0-kg block slides down a 3 m long plane at constant velocity +y θ= 25º +x Calculate the acceleration of the block: Calculate the weight of the block: Show the F g and F N vectors on the drawing: Calculate the F & Ff for the block above: F = Ff = 2. a. Sketch and label the forces on the 4 g. block below that accelerates up the incline at 4 m/s 2 : This is a frictionless plane! =62 e. Determine all the forces on the block. Show all of your work below. f. Determine k, show all of your work below. g. What are the all of the forces if the angle is increased to 90 degrees? Show your work and/or explain your answer below. 9
3. Sketch and label the forces on the 4 g. block below: This is a frictionless plane! =62 a. Determine all the forces on the block. Show all of your work below with FBD. b. Determine k, show all of your work below. c. What happens to the forces if the angle is increased? Show your work and/or explain your answer below. d. What is the net force on the block? 10
Name Score Regents Physics Mr. Morgante Inclined Plane Problems Level III 1. A 5.0-kg block that starts from rest slides down a frictionless plane with a 3 N & 1N external force as shown below: 1N +y a. Draw the complete FBD here (6 pts): +x θ= 25º 3N Magnitude Direction b. (3 pts) Calculate the acceleration of the block: c. (2 pts) Calculate the weight of the block: d. (8 pts) Calculate the F, F N, F & F f : F = Show calculations for part d. here: F N = F = F f = (OVER) 11
1. (CONT.) Magnitude Direction e. (1 pt) How far does the block travel in 1.5 secs.? f. (1 pt) What is the V f of the block at t=1.5 secs.? (3 pts) g) Sketch the d-t, v-t & a-t graphs for the motion of the block below: 2. A 390-Dg block slides down a long plane at constant speed with a 1 N external force as shown below. The block travels 7m in 2.5 secs. +x +y 1N θ= 30º a. Draw the complete FBD here (6 pts): Magnitude Direction b. (2 pts) Calculate the weight of the block: (OVER) 12
c. (8 pts) Calculate the F, F N, F & F f : F = Show calculations for part c. here: F N = F = F f = Magnitude Direction d. (1 pt) How far does the block travel in 1.5 secs.? e. (1 pt) What is the V f of the block at t=1.5 secs.? f) Sketch the d-t, v-t & a-t graphs for the motion of the block below (3 pts): Z:\Physics\Regents Physics\Class Material\Unit 2E Inclined Planes 1-7-10.doc 13