Physics 1 Lesson 8 Forces and Momentum Homework Outcomes 1. Define linear momentum. 2. Determine the total linear momentum of a system. 3. Apply the Law of Conservation of Momentum to solve problems. 4. Apply the impulse-momentum theorem to solve problems. 5. Define elastic and inelastic collisions. 6. Solve problems involving elastic and inelastic collisions. 7. Define the relationship between elastic collisions and energy conservation. 8. Define the relationship between inelastic collisions and energy conservation. Name Date Period Problem Solving Practice Multiple Choice Answer Question Number Question The magnitude of the momentum change of the ball is 1. 2. 3. 4. 5. A tennis ball of mass m rebounds from a racquet with the same speed v as it had initially, as shown above. Two pucks are attached by a stretched spring and are initially held at rest on a frictionless surface, as shown above. The pucks are then released simultaneously. (A) 0 (B) mv (C) 2mv (D) 2mv sin θ (E) 2mv cos θ If puck I has three times the mass of puck II, which of the following quantities is the same for both pucks as the spring pulls the two pucks toward each other? (A) Speed (B) Velocity (C) Acceleration (D) Kinetic energy (E) Magnitude of momentum Which of the following is true when an object of mass m moving on a horizontal frictionless surface hits and sticks to an object of mass M > m, which is initially at rest on the surface? (A) The collision is elastic. (B) All of the initial kinetic energy of the less-massive object is lost. (C) The momentum of the objects that are stuck together has a smaller magnitude than the initial momentum of the less-massive object. (D) The speed of the objects that are stuck together will be less than the initial speed of the less-massive object. (E) The direction of motion of the objects that are stuck together depends on whether the hit is a head-on collision Two objects having the same mass travel toward each other on a flat surface, each with a speed of 10 meter per second relative to the surface. The objects collide head-on and are reported to rebound after the collision, each with a speed of 20 meters per second relative to the surface. Which of the following assessments of this report is most accurate? (A) Momentum was not conserved, therefore the report is false. (B) If potential energy was released to the objects during the collision, the report could be true. (C) If the objects had different masses, the report could be true. (D) If the surface was inclined, the report could be true. (E) If there was no friction between the objects and the surface, the report could be true. A railroad car of mass m is moving at speed v when it collides with a second railroad car of mass M which is at rest. The two cars lock together instantaneously and move along the track. What is the speed of the cars immediately after the collision? a) v 2 b) mv M c) Mv m d) (m+m)v m e) mv m+m 1
6. An open cart on a level surface is rolling without frictional loss through a vertical downpour of rain, as shown above. As the cart rolls, an appreciable amount of rainwater accumulates in the cart. The speed of the cart will a) increase because of conservation of momentum b) increase because of conservation of mechanical energy c) decrease because of conservation of momentum d) decrease because of conservation of mechanical energy e) remain the same because the raindrops are falling perpendicular to the direction of the cart's motion What is the y-component of the velocity of the 0.1 kg object immediately after the collision? 7. Two objects of mass 0.2 kg and 0.1 kg, respectively, move parallel to the x-axis, as shown above. The 0.2 kg object overtakes and collides with the 0. 1 kg object. Immediately after the collision, the y-component of the velocity of the 0.2 kg object is 1 m/s upward. (A) 2 m/s downward (B) 0.5 m/s downward (C) 0 m/s (D) 0.5 m/s upward (E) 2 m/s upward Two people of unequal mass are initially standing still on ice with negligible friction. They then simultaneously push each other horizontally. Afterward, which of the following is true? 8. (A) The kinetic energies of the two people are equal. (B) The speeds of the two people are equal. (C) The momenta of the two people are of equal magnitude. (D) The center of mass of the two-person system moves in the direction of the less massive person. (E) The less massive person has a smaller initial acceleration than the more massive person. What are the magnitude and direction of the velocity of the piece having mass 3m? 9. A stationary object explodes, breaking into three pieces of masses m, m, and 3m. The two pieces of mass m move off at right angles to each other with the same magnitude of momentum mv, as shown in the diagram above. 10. 11. An empty sled of mass M moves without friction across a frozen pond at speed v o. Two objects are dropped vertically into the sled one at a time: first an object of mass m and then an object of mass 2m. Afterward the sled moves with speed v 1. The two blocks of masses M and 2M shown above initially travel at the same speed v but in opposite directions. They collide and stick together. What would be the final speed of the sled if the objects were dropped into it in reverse order? (A) v f / 3 (B) v f / 2 (C) v f (D) 2 v f (E) 3 v f How much mechanical energy is lost to other forms of energy during the collision? (A) Zero (B) 1/2 Mv 2 (C) 3/4 Mv 2 (D) 4/3 Mv 2 (E) 3/2 Mv 2 12. Which pair of terms are vector quantities? A) distance and displacement B) speed and velocity C) force and mass D) momentum and acceleration 2
13. The diagram below shows two carts on a horizontal, frictionless surface being pushed apart when a compressed spring attached to one of the carts is released. Cart A has a mass of 3.0 kilograms and cart B has a mass of 5.0 kilograms. The speed of cart A is 0.33 meter per second after the spring is released. If the carts are initially at rest, what is the approximate speed of cart B after the spring is released? A) 0.55 m/s B) 0.20 m/s C) 0.12 m/s D) 0.33 m/s 14. The diagram below represents two identical carts, attached by a cord, moving to the right at speed V. If the cord is cut, what would be the speed of cart A? A) 0 C) V 2 B ) 2V D) V 15. A spring is compressed between two stationary blocks as shown in the diagram below. Block A has a mass of 6.0 kilograms. After the spring is released, block A moves west at 8.0 meters per second and block B moves east at 16 meters per second. What is the mass of block B? [Assume no frictional effects.] A) 16 kg B) 12 kg C ) 6.0 kg D) 3.0 kg 16. 17. 18. 19. 20. 21. A 2.0-kilogram toy cannon is at rest on a frictionless surface. A remote triggering device causes a 0.005- kilogram projectile to be fired from the cannon. Which equation describes this system after the cannon is fired? A) velocity of cannon + velocity of projectile = 0 B) momentum of cannon + momentum of projectile = 0 C) mass of cannon + mass of projectile = 0 D) speed of cannon + speed of projectile = 0 A 2.0-kilogram ball traveling north at 4.0 meters per second collides head on with a 1.0-kilogram ball traveling south at 8.0 meters per second. What is the magnitude of the total momentum of the two balls after collision? A) 8.0 kg m/s B) 0 kg m/s C) 16 kg m/s D) 32 kg m/s A 2.0-kilogram rifle initially at rest fires a 0.002-kilogram bullet. As the bullet leaves the rifle with a velocity of 500 meters per second, what is the momentum of the rifle-bullet system? A) 2.0 kg m/s B) 0 kg m/s C) 0.5 kg m/s D) 2.5 kg m/s A 1.0-kilogram mass changes speed from 2.0 meters per second to 5.0 meters per second. The change in the object's momentum is A) 29 kg m/sec B) 21 kg m/sec C) 9.0 kg m/sec D) 3.0 kg m/sec If a net force of 10. newtons acts on a 6.0-kilogram mass for 8.0 seconds, the total change of momentum of the mass is A) 480 kg m/s B) 60. kg m/s C) 48 kg m/s D) 80. kg m/s In a baseball game, a batter hits a ball for a home run. Compared to the magnitude of the impulse imparted to the ball, the magnitude of the impulse imparted to the bat is A) less B) the same C) greater 3
Free Response Practice 1. A student is interested in determining the horizontal velocity of a bullet fired from a gun, but he doesn t have the appropriate equipment to time the bullet for a given distance. However, the student has a wooden block, some string, a meterstick, a protractor, and an electronic scale. The student thinks that his best set-up is the one shown above. 4
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2. Two objects of masses M 1 = 1 kilogram and M 2 = 4 kilograms are free to slide on a horizontal frictionless surface. The objects collide and the magnitudes and directions of the velocities of the two objects before and after the collision are shown on the diagram above (sin 37 = 0.6, cos 37 = 0.8, tan 37 = 0.75). The angle of M 2 after the collision is 37 degrees. Calculate the x and y components (p x and p y respectively) of the momenta of the two objects before and after the collision, and write your results in the proper places in the following table. (a) Show, using the data that you listed in the table, that linear momentum is conserved in this collision. (b) Calculate the kinetic energy of the two-object system before and after the collision. (c) Is kinetic energy conserved in the collision? 6
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