# Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis

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1 * By request, but I m not vouching for these since I didn t write them Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis There are extra office hours today & tomorrow Lots of practice exams online Lots of optional smartphysics problems* This morning s HW deadline moved to Friday (80% deadline not moved still next Tuesday) Pay attention (lecture, webpage, , )

2 Hour Exam 2 Center of Mass X cm x m i m i i Work Energy W NC KE PE Impulse-Momentum F t P

3 Two ice-skaters of mass 70 kg and 50 kg, each having an initial velocity of 10 m/s in the directions shown, collide and fall and slide across the ice together. The ice surface is horizontal & frictionless. 1. What is the speed of the skaters after the collision? A) V = 0 m/s B) V = 1.7 m/s C) V = 2.7 m/s D) V = 10 m/s E) V = 20 m/s 2. What is the angle q relative to the x axis that the two skaters travel after the collision? A) q = 41 degrees B) q = 28 degrees C) q = 25 degrees

4 A cart of mass M = 9 kg rolls without friction on a horizontal surface. It is attached through a freely pivoting initially-horizontal massless rod of length L to a ball of mass m = 3 kg. The system is initially at rest when the ball is released. The pendulum swings down and to the left, and at the bottom of its swing the ball is observed to have a velocity of 3.5 m/sec to the left. 3. Which of the following remain constant as the pendulum swings down? A) Horizontal component of the momentum of the ball B) Horizontal component of the momentum of the cart C) Horizontal component of the momentum of the ball + cart

5 A cart of mass M = 9 kg rolls without friction on a horizontal surface. It is attached through a freely pivoting initially-horizontal massless rod of length L to a ball of mass m = 3 kg. The system is initially at rest when the ball is released. The pendulum swings down and to the left, and at the bottom of its swing the ball is observed to have a velocity of 3.5 m/sec to the left. 4. What is the speed of the cart when the ball is at the bottom? A) V cart = 1.17 m/s B) V cart = 1.75 m/s C) V cart = 2.44 m/s D) V cart = 2.91 m/s E) V cart = 3.37 m/s

6 A cart of mass M = 9 kg rolls without friction on a horizontal surface. It is attached through a freely pivoting initially-horizontal massless rod of length L to a ball of mass m = 3 kg. The system is initially at rest when the ball is released. The pendulum swings down and to the left, and at the bottom of its swing the ball is observed to have a velocity of 3.5 m/sec to the left. 5. What is the length L of the pendulum? A) 0.59 m B) 0.83 m C) 1.18 m

7 A cart of mass M = 9 kg rolls without friction on a horizontal surface. It is attached through a freely pivoting initially-horizontal massless rod of length L to a ball of mass m = 3 kg. The system is initially at rest when the ball is released. The pendulum swings down and to the left, and at the bottom of its swing the ball is observed to have a velocity of 3.5 m/sec to the left. 6. How far to the right has the cart moved, when the ball is at the bottom? A) L/2 B) L/3 C) L/4

8 7. A comet of mass 10 9 kg is observed at a distance from the sun of 8 x m (mass of sun = 2 x kg) at a speed of m/s. Assuming no forces on it other than the sun's gravity, how fast will it be going when it is a distance of 2.25 x m from the sun? (The universal gravitational constant is G = 6.67x10-11 Nm 2 /kg 2 ) A) 12,900 m/s B) 18,300 m/s C) 23,700 m/s D) 29,200 m/s E) 33,800 m/s

9 8. Two fishermen, of masses 70 and 90 kg stand at opposite ends of their 20 meter boat. The boat (without fishermen) has a mass of 400 kg. There is no wind or current and the boat can move without friction on the water s surface. The 90 kg fisherman walks to the left end of the boat. How far has the boat moved when the fisherman reaches the left end? A) 5.8 m to the right B) 3.2 m to the right C) The boat does not move D) 3.2 m to left E) 5.8 m to left

10 9. The centers of three spheres having masses 1 kg, 2 kg, and 3 kg are placed at the corners of an equilateral triangle whose sides are each 1 meter long, as shown below. What is the horizontal position of the center of mass? A) x cm = 0.50 m B) x cm = 0.58 m C) x cm = 0.76 m y 3 kg 1 kg 1 m 2 kg x

11 An artillery shell of mass 20 kg is fired from a rail car which is initially at rest on a horizontal frictionless track. The combined mass of the car and cannon is 2000kg. As viewed by someone on the ground the shell moves with an initial speed of 300 m/s at an angle of 27 degrees above the horizontal and the rail car recoils to the right. 10. Relative to the ground, what is the speed of the rail car after the shell is fired? A) 1.36 m/s B) 2.67 m/s C) 3.00 m/s

12 An artillery shell of mass 20 kg is fired from a rail car which is initially at rest on a horizontal frictionless track. The combined mass of the car and cannon is 2000kg. As viewed by someone on the ground the shell moves with an initial speed of 300 m/s at an angle of 27 degrees above the horizontal and the rail car recoils to the right. 11. If the shell was accelerated through the cannon for a time of 0.03 seconds, what was the average force on the shell during this time? A) 200 N B) 2,300 N C) 15,000 N D) 90,000 N E) 200,000 N

13 A block of mass m = 1.8 kg starts at rest on a rough inclined plane a height H = 8m above the ground. It slides down the plane, across a frictionless horizontal floor, and then around a frictionless loop-the-loop of radius R = 2.0 m. On the floor the speed of the block is observed to be 11 m/s. 12. What is the work done by friction on the block as it slides down the inclined plane? A) -49 J B) -28 J C) -78 J D) -23 J E) -32 J

14 A block of mass m = 1.8 kg starts at rest on a rough inclined plane a height H = 8m above the ground. It slides down the plane, across a frictionless horizontal floor, and then around a frictionless loop-the-loop of radius R = 2.0 m. On the floor the speed of the block is observed to be 11 m/s. 13. What is the magnitude of the normal force exerted on the block at the top of the loop? A) 0 N B) 5.1 N C) 9.8 N D) 17.6 N E) 20.6 N

15 2.5 kg k=250 N/m h=1.5 m = 0.4 d = 0.50 m A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5 meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right. 14. What is the speed of the box at the bottom of the ramp? A) 5.4 m/s B) 3.7 m/s C) 2.8 m/s

16 2.5 kg k=250 N/m h=1.5 m = 0.4 d = 0.50 m A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5 meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right. 15. What is the maximum distance the spring is compressed by the box? A) 0.50 m B) 0.66 m C) 0.83 m D) 0.94 m E) 1.21 m

17 2.5 kg k=250 N/m h=1.5 m = 0.4 d = 0.50 m A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5 meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right. 16. What is the maximum height to which the box returns on the ramp? A) 1.1 m B) 1.3 m C) 1.5 m

18 In case 1 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball bounces off the box and after the collision the box is moving to the right with V 1 and the ball is moving to the left with speed v f. In case 2 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball sticks to the box and after the collision the box (with the ball stuck to it) is moving to the right with speed V 2. In both cases the box slides without friction. Assume all motion is horizontal. 17. In which case is the change in momentum of the ball the biggest? A) Case 1 B) Case 2 C) The change in momentum of the ball is the same in both cases.

19 In case 1 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball bounces off the box and after the collision the box is moving to the right with V 1 and the ball is moving to the left with speed v f. In case 2 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball sticks to the box and after the collision the box (with the ball stuck to it) is moving to the right with speed V 2. In both cases the box slides without friction. Assume all motion is horizontal. 18. Which of the following statements best describes V 1 and V 2? A) V 1 < V 2 B) V 1 = V 2 C) V 1 > V 2

20 In case 1 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball bounces off the box and after the collision the box is moving to the right with V 1 and the ball is moving to the left with speed v f. In case 2 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball sticks to the box and after the collision the box (with the ball stuck to it) is moving to the right with speed V 2. In both cases the box slides without friction. Assume all motion is horizontal. 19. In case 2 it is observed that V 2 = v 0 /3. What is the ratio of masses M/m? A) M/m = 1/2 B) M/m = 3/4 C) M/m = 4/3 D) M/m = 3/2 E) M/m = 2

21 In case 1 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball bounces off the box and after the collision the box is moving to the right with V 1 and the ball is moving to the left with speed v f. In case 2 a ball of mass m is thrown horizontally with speed v 0 at a stationary box of mass M. The ball sticks to the box and after the collision the box (with the ball stuck to it) is moving to the right with speed V 2. In both cases the box slides without friction. Assume all motion is horizontal. 20. In case 1 it is observed that v f = v 0 /2. What V 1 /v 0? A) V 1 /v 0 = 3M/2m B) V 1 /v 0 = 2M/3m C) V 1 /v 0 = 3m/2M D) V 1 /v 0 = 2m/3M E) V 1 /v 0 = m/2m

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