Activity 2.4-Newton's Second Law Problems Use the free body diagram method to solve the following problems. Please show all steps. 1. A ball with a mass of M=60 grams toward the ceiling where it bounces. It hits the ceiling and bounces off at the same speed of v, 15 m/s and at an angle = 20° as shown. The collision takes At=0.3 sec. a. Determine the magnitude of the acceleration while the ball is in contact with the ceiling. In the space provided, draw a labeled free body diagram showing the forces acting on the ball while it is in contact with ceiling. Start by defining a coordinate system (a +y direction) and writing the relation you will use symbolically. It is usually most convenient if you choose the +y to be in the direction of the acceleration. Note: the acceleration is not 100 m/s² nor is it zero. If you got either answer for the acceleration, recall how to subtract vectors. AI "1 O b. Use the FBD method to determine the average force that the ceiling exerts the ball during the collision. Show all the steps in the FBD method () Draw a labeled free body diagram for the ball. (ii) Define a coordinate system (+x and/or +y directions) and write out Newton's 2nd law in the appropriate directions using the symbols in your FBD. (iii) Solve symbolically for what you want. Do not substitute in numbers yet. c. Determine the numerical value of the average force the ceiling exerts on the ball during the collision. Show numbers you used. d. What is the magnitude and direction of the force that the ball exerts on the ceiling during the collision? 2. A book of mass m = 5 kg is slid across a ceiling using force P = 100 N as shown. A kinetic friction force of fr, 48 N opposes the motion. We want to find the normal force and the acceleration. a. In the space provided, draw a labeled free body diagram showing the forces acting on the book. To the right of the "a" draw an arrow labeled "Ma" in the direction of the acceleration or write "0" if the acceleration is zero. b. Use your free body diagram to write out Newton's 2 law in the x and y directions in terms of the labels in your FBD and the givens. Break up the forces into components and pay attention to signs. On the right-hand side (RHS), set Ma, and Ma, to +Ma, -Ma, or zero depending on the direction of the acceleration. Do not substitute in numbers yet. 8-60 ΣΕ, = ma ΣΕ, = may c. What is the normal force between the book and the ceiling? Solve symbolically first before substituting in numbers. Show numbers you used. d. Determine the acceleration. Solve symbolically first before substituting in numbers. Show numbers you used. e. The book is initially moving at 0.2 m/s, what is the distance the book slides in 3 seconds? Start by writing the relation you use symbolically.