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1 Name: Physics Chapter 4 Study Guide Useful Information: F = ma µ = F fric a = v f " v i t # x = v f + v & i % ( t x = v $ 2 i t at 2 v 2 f = v 2 i + 2ax ' F norm A Basic Understanding: Chapter 4 Odd Numbered Core Problems Chapter 4 Review Problems:! 6, 11, 12, 13, 19, 21, 29, 36, 45, 51. Friction on an Incline Part I. Adding Vectors sections A - D. Pushing to be Better: Chapter 4 Your Try Problems Chapter 4 Even Numbered Core Problems Chapter 4 Review Problems: 1, 2, 3, 4, 9, 10, 16, 20, 23, 24, 25, 27, 31, 32, 38, 39, 40, 41, 46, 47, 48, 49, 52. Standardized Test Prep 1-9. Friction on an Incline Part II. Adding Vectors sections A - E (done neatly, accurately and completely) Digging Deeper: Problem 40: Now assume that µ = 0.2. What are the min and max F s (Force vector as marked on diagram) that will keep the block stationary? Chapter 4 Review Problems: 14, 22, 34, 54. Insightful answer to Adding Vectors section F. Individual Inquiry Note on Equations: F = ma Force (measured in Newtons) equals mass (measured in kilograms) times acceleration (measured in meters per second squared). The coefficient of friction (no units) µ = F fric The coefficient of friction (no units) is equal to the force due to friction F norm (measured in Newtons) divided by the normal force (the force perpendicular to a contact surface between two objects; also measured in Newtons). The coefficient of friction is an extremely difficult number to pin down. It depends on what two objects are in contact with each other, as well as other factors such as whether they are clean and dry or wet, dirty, oily, etc... Physics Ch. 4 Study Guide page 1 of 1

2 Name: Chapter 4 Worked Examples Physics 1) A big truck consists of a tractor, a big trailer and a smaller trailer. The tractor has a mass of 5000 kg. The large trailer has a mass of kg. The smaller trailer has a mass of kg. Starting from rest, the truck accelerates to 65 mph in 2 minutes. a) Calculate the total force produced by the tractor. b) Calculate the tension in the first hitch. c) Calculate the tension in the second hitch. image from < You try: A big truck consists of a tractor, a big trailer and a smaller trailer. The tractor has a mass of 500 kg. The large trailer has a mass of 1500 kg. The smaller trailer has a mass of 1000 kg. The truck is going up a 7.0 hill at a constant speed of 20 mph. a) Calculate the total force produced by the tractor. b) Calculate the tension in the first hitch. c) Calculate the tension in the second hitch. Physics Ch. 4 Worked Examples page 1 of 2

3 2) The coefficient of kinetic friction between a brick and a board is The brick has a mass of 1.89 kg and the board is inclined at 40. Calculate the force necessary to pull the brick up the board at a constant speed. Your try: A block of wood, which has a mass of 1.50 kg, is placed on a board that is inclined at 23. The coefficient of kinetic friction between the block and the board is What is the acceleration of the block of wood down the incline? Physics Ch. 4 Worked Examples page 2 of 2

4 Physics Chapter 4 Your Try Problems (Based on various worked examples.) 3) Video 4c: Calculate the force necessary to give a 1500 kg car an acceleration of 0.75m / s 2. 4) Video 4e: Three ropes come meet in the center of a table. The knot is free to move, but the three forces keep it stationary in the middle of the table. Rope 1 has a tension of 13N. Rope 2 has a tension of 21N. There is an angle of 95 between Rope 1 and Rope 2. a) Find the tension in Rope 3. b) Find the angle that Rope 3 makes with Rope 1. 5) Video 4i: A 1.25kg book is slid along a table. It s initial velocity is 2.3 m/s. It comes to rest after sliding 1.75m. Calculate the coefficient of friction between the book and the table. 6) Video 4j: Calculate the force needed to accelerate a 1500 kg car at 0.75m / s 2 up a road inclined at 12 above horizontal. (Ignore friction.) 7) Video 4L: Considering friction, what is the minimum friction needed between the tires and the road, if a car can sit stationary on a road inclined at 12 without sliding down. (In other words, suppose it s an icy day, and it s a steep road. You don t want to drive, you just want to park. What is the minimum coefficient of friction that would allow you to park on the road without sliding down.)

5 Answers to Chapter 4 Your Try Problems Worked Example 1: A big truck consists of a tractor... a) 3600 N b) 3000 N c) 1200 N Worked Example 2: A block of wood, which has a mass of 1.50 kg... a = 2.03 m s 2 3) Video 4c: Calculate the force necessary to give a 1500 kg car... F = 1125 N 4) Video 4e: Three ropes come meet in the center of a table... a) Rope 3 tension = 23.7 N b) Angle of Rope 3 with Rope 1 = ) Video 4i: A 1.25kg book is slid along a table... µ = ) Video 4j: Calculate the force needed to accelerate a 1500 kg car... F = 4180 N 7) Video 4L: Considering friction, what is the minimum friction needed... µ = 0.21

6 Name: Physics Chapter 4 Core Problems 1) (5pts) The Normal Force is: a) Force friction divided by the coefficient of friction. b) The force in the direction of the acceleration. c) The contact force that acts perpendicular to a surface. d) A regular or natural force like a rope pulling or somebody pushing. e) Equal to Force Gravity. 2) (3pts) A small boat pulls up to a dock. A person steps from the boat onto the dock. When they do so, they cause the boat to move backwards away from the dock. This is a good example of: a) Vector Addition b) Equations for Constant Acceleration c) Newton's 3rd Law d) Newton's 2nd Law e) Newton's 1st Law 3) (8pts) A pitcher throws a fast ball at 90 miles per hour. The baseball starts from rest and pitcher s hand moves a total of 2.00 meters before the ball is released. A baseball has a mass of 145g. Calculate the average force the pitcher exerts on the baseball. 4) (12pts) A brick has a mass of 2.34 kg and slides down a board that is inclined at 26. The coefficient of friction between the brick and the board is How far does the brick slide in 2.00 seconds? 2.34 kg 26 Physics Ch. 4 Core Problems page 1 of 2

7 5) (12pts) A brick has a mass of 1.5 kg. It is hung from a string as shown in the diagram below. Calculate the tension in the string. 90 Physics Ch. 4 Core Problems page 2 of 2

8 Name: Friction on an Incline Physics Procedure: I: Friction on an Incline. A: Set up an incline. Calculate the angle of the incline. B: Weight a cart using a spring scale. Pull the cart up the ramp using a spring scale. How much force does is take to pull the cart up at a slow pace? How much does is take to lower it down at a slow pace? C: Weigh a Physics book and pull it up the ramp. (slide it up, don't use the cart) Answer the same questions as part B. D: Repeat the procedure with a brick. E: Change the angle of the incline and repeat steps B through D. F: Make sure you have recorded all relevant information. II: Drawing vector diagrams and calculating the coefficient of friction. A: For each incline calculate the normal force on the cart, brick and wood. B: Calculate the force of friction in each instance. C: From A and B, determine the coefficients of friction for all situations. D: List the four forces that act on an object on an inclined plane. Draw a sketch to show the direction of that force. E: For two situations, studied earlier, give the magnitude and direction of each force. Angles should be measured off the horizontal. F: For those two situations make a scale diagram of the inclined plane and the object. Draw all of the forces on the object. Make sure everything is to scale and in the correct directions. E: On graph paper, add the four vectors using the tip-to-tail method. Did you end up at your original point?

9 Name: Adding Vectors Physics Procedure: A: Weigh a brick using a spring scale. Now hang the brick from the middle of piece of string (so that the string can slide). Attach two spring scales to the ends of the string. Hold both spring scales directly above the brick and measure the force on each scale. Try to hold them so that the readings are identical on each scale. B: Now separate the scales so that the two ends of the string make a V. Measure the angle of the V, measure the force on each spring scale. C: Do this for 4 more angles (your angles should be evenly spaced between 20 and 140 ) D: Plot this information on polar graph paper. Show the weight of the brick and the force of the two pulls. Make sure your diagrams are to scale. E: For your middle two angles, plot the three forces on standard graph paper. Use the tip to tail method of vector addition to show that the total force on the brick is zero. F: Write a paragraph discussing the graph that you constructed in part D, and what you learned from it. Physics Adding Vectors page 1 of 1