Answer each question and show your work. A correct answer with no supporting reasoning may receive no credit. Unless directed otherwise, please use g=10.0 m/s 2. Name: 1. (15 points) A 3.0 kg block travels on a horizontal frictionless surface and is pushed by a constant force A = 5.0 N (as shown in the figure below) What is the acceleration of the block? A. 0.5 m/s 2 B. 1.0 m/s 2 C. 1.7 m/s 2 D. 3.0 m/s 2 E. 8.0 m/s 2 2. (15 points) Referring to the previous problem, what is the magnitude of the normal force exerted by the surface on the block? (use g=10 m/s 2!) A. 10.0 N B. 15.0 N C. 20.0 N D. 25.0 N E. 30.0 N 3. (15 points) A 30.0 kg child is sitting on a tire swing (tire mass = 10.0 kg; and a single rope holds up the tire). At the lowest point of the swing, the child s speed is 10.0 m/s, and the tension in the string is 2400 N. What is the length of the rope? (disregard the size of the tire, or imagine it to be negligibly small in size, but not negligibly small in mass!) A. 1.0 m B. 1.4 m C. 1.8 m D. 2.0 m E. 2.2 m Dept. of Physics Page 1 of 8 Fall 2011
4. (15 points) A 2.50 kg block sits on a horizontal frictionless surface and is pushed by a force B = 5.0 N which is inclined at an angle of 30 o above the horizontal (as shown in the figure below) What is the acceleration of the block? A. 0 m/s 2 B. 1.7 m/s 2 C. 2.1 m/s 2 D. 3.3 m/s 2 E. 5.0 m/s 2 5. (15 points) Referring to the previous problem, what is the magnitude of the normal force exerted by the surface on the block? (use g=10 m/s 2!) A. 25.0 N B. 24.5 N C. 23.5 N D. 22.5 N E. 21.0 N Dept. of Physics Page 2 of 8 Fall 2011
A 5.0 kg block is at rest at the bottom of a 30 o incline. If you push horizontally with a force P = 100 N, and the coefficient of kinetic friction is µ k = 0.20, answer the following two questions. (Again, use g=10 m/s 2!) 6. (15 points) What is the magnitude of the normal force on the block? A. 48.1 N B. 74.5 N C. 87.3 N D. 93.3 N E. 97.9 N 7. (15 points) What is the acceleration of the block up the incline? A. 0.8 m/s 2 B. 1.3 m/s 2 C. 8.6 m/s 2 D. 9.0 m/s 2 E. 9.1 m/s 2 Dept. of Physics Page 3 of 8 Fall 2011
8. (15 points) A merry-go-round is initially rotating with an angular velocity of 4.0 rad/s. At t=0, the merry-go-round begins to slow down. If it decelerates at a uniform rate and comes to rest after making exactly 4.0 revolutions, how much time elapsed? A. 12.6 s B. 13.0 s C. 15.2 s D. 16.1 s E. 17.6 s 9. (15 points) Suppose that after the merry-go-round comes to rest (reset your clock to t=0 now), we now impart an angular acceleration of 10.00 rad/s 2. At t= 3.000 seconds consider a point on the rim 2.0000 meters from the axis of rotation. Calculate the magnitude of the total acceleration vector for this point. (I m not asking for the angular acceleration!) A. 1800.0 m/s 2 B. 1800.1 m/s 2 C. 1800.2 m/s 2 D. 1800.25 m/s 2 Dept. of Physics Page 4 of 8 Fall 2011
Three identical blocks (each of mass 3.0 kg) are joined by two different ropes as shown. The coefficient of friction between the blocks and the and the table is 0.1. The pulley is massless and frictionless, and air resistance is negligible. 10. (15 points) What is the acceleration of the system? (again, use g=10.0 m/s 2 ). A. 2.67 m/s 2 B. 3.33 m/s 2 C. 4.67 m/s 2 D. 5.33 m/s 2 E. 1.24 m/s 2 11. (15 points) What is the tension T 1? A. 10 N B. 11 N C. 12 N D. 12.5 N E. 13 N Dept. of Physics Page 5 of 8 Fall 2011
12. (15 points) The figure below shows a view from directly above a horizontal air hockey table; three masses of putty are moving on this perfectly frictionless table and they collide and stick together (I tried to show them as a faded lump in the center of the figure). What is the final speed of this lump of three system after they collide? A. 2.12 m/s B. 2.29 m/s C. 2.30 m/s D. 2.32 m/s E. 2.34 m/s Dept. of Physics Page 6 of 8 Fall 2011
13. (15 points) A ball of diameter d and mass m is dropped from an initial height h i (h i >> d) and rebounds to a final height h f (h f < h i ). Derive an expression for the average force acting on the ball during impact by assuming that the time during which the ball is in contact with ground is roughly approximated by the time for sound (speed = v s ) to propagate across the diameter of the ball. Calculate this average force for the case of a lacrosse ball (d 6.25 cm, and m 145 grams) assuming that the initial height is 1.8 meters and the final rebound height is 1.1 m. The velocity of sound in rubber is around 60 m/s. Dept. of Physics Page 7 of 8 Fall 2011
Exam Summary Page Page Points Score 1 45 Question Points My Answer 1 15 2 15 3 15 4 15 5 15 6 15 7 15 8 15 9 15 10 15 11 15 12 15 13 15 Total: 195 2 30 3 30 4 30 5 30 6 15 7 15 Total: 195 Dept. of Physics Page 8 of 8 Fall 2011