PHYSICS 30 MOMENTUM AND IMPULSE ASSIGNMENT 4 VERSION:0 55 MARKS

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1 Clearly communicate your understanding of the physics principles that you are going to solve a question and how those principles apply to the problem at hand. You may communicate this understanding through calculation, graphically, and with diagrams but written statements are required. Vector calculations must be supported with suitable diagrams. Graphs must include complete supporting explanations.. As shown, a 0.20 kg mass is sliding on a horizontal, frictionless air track with a speed of 3.0 m/s when it instantaneously hits and sticks to a.3 kg mass initially at rest on the track. The.3 kg mass is connected to one end of a massless spring, which has a spring constant of 00 N/m. The other end of the spring is fixed. (0.00 marks) a) Determine the following for the 0.20 kg mass immediately before the impact. i. Its linear momentum ii. Its kinetic energy b) Determine the following for the combined masses immediately after the impact. i. The linear momentum ii. The kinetic energy After the collision, the two masses undergo simple harmonic motion about their position at impact. c) Determine the amplitude of the harmonic motion. d) Determine the period of the harmonic motion. 2. Several Canadian companies are redesigning and testing bulletproof vests. One company does a test that involves firing a target rifle at a crash test dummy (0.00 marks) The company is testing the vests with both regular bullets and armour-piercing bullets. The armour-piercing bullet travels.20 times faster and has.20 times the mass of the regular bullet shown above. Quantitatively compare the kinetic energy of the armour-piercing bullet with the kinetic energy of the regular bullet. How much energy is released by the explosion of the gunpowder if the transfer of energy from the explosion to the regular bullet is 90.0% efficient? The regular bullet is in the rifle barrel for.42 x 0 3 s. What is the average force exerted on the regular bullet by the expanding gases? Use this additional information to answer the next part of the question. A second test performed by the company has the regular bullet strike the vest at a glancing angle. The mass of the vest and the dummy is 56.0 kg. The bullet vest collision is inelastic. Determine the resultant speed of the vest and the dummy following the glancing collision shown above.

2 3. The graph at the right shows a force vs time graph for two people, of the same mass, involved in a collision in the same car. The driver was wearing his seat belt but the passenger was not wearing hers. (0.00 marks) A knowledgeable student suggests that the area below each graph should be equal. Explain if she is correct or not. Explain why the graph suggests that it is safer to wear the seatbelt, and relate it to the formula for impulse and the situation of being belted or not belted in. Approximate the impulse from the graph (explaining your reasoning) and use it to find the initial speed of the car, in km/h, at impact if the mass of each occupant is 55 kg. (If you are unable to find the impulse, explain how it would be use to find the velocity, to receive part marks) 2

3 Choose the best response and place your answers, using HB pencil, on the Scantron sheet provided.. If the velocity of an object is tripled and the direction changes from south to north, the momentum will change by a factor of a. negative three. b. negative one-third. c. positive one-third. d. positive three. 2. What is the momentum of a 4 t shark whale swimming at 3.0 km/h [S]? a..2 x 0 4 kg m/s [S] b. 4.2 x 0 4 kg m/s [S] c. 4.3 x 0 4 kg m/s [S] d. 7.2 x 0 5 kg m/s [S] 3. An object of mass m moves with kinetic energy K. The object has momentum of magnitude a. b. c. d. e. 4. A 5.45 kg cannonball is shot at 48 m/s [W] from a 750 kg cannon on the deck of a ship. Calculate the velocity of the cannon immediately after the cannon ball exits the barrel. The answer, expressed in scientific notation, would be a.bc x 0 d m/s [E]. The values of a, b, c, and d are,,, and.? (Record all four digits of your answer on the answer sheet.) 5. Use the information above, to calculate the average net force of the exploding powder on the cannon ball if the cannon ball leaves the cannon s after the cannon is fired. The answer, expressed in scientific notation, would be a.bc x 0 d N [W]. The values of a, b, c, and d are,,, and.? (Record all four digits of your answer on the answer sheet.) 6. 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. b. mv c. Mv d. (m + M) v e. M m m v 2 mv m + M 7. In a vehicle safety test, a 580 kg truck travelling at 60.0 km/h collides with a concrete barrier and comes to a complete stop in 0.20 s. The magnitude of the change in the momentum of the truck, expressed in scientific notation, is b x 0 w kg.m/s. The value of b is. (Record your three-digit answer in the numerical-response section on the answer sheet.). 3

4 8. At the start of mating season, two bighorn rams battle in a head-butting contest. The 8 kg older male leaps towards the challenger at 8.25 m/s [E]. The younger ram jumps toward the elder at 8.43 m/s [W]. The older ram is bounced back at 0.70 m/s [W] by the 0.28 s collision, and the younger ram also rebounds at 0.20 m/s [E]. The magnitude of the initial momentum of the older ram was a. 974 N s b. 994 N s c. 984 N s d..00 x 0 3 N s 9. Based on the above, the average net force on the younger ram during the collision was a x 0 3 N [W] b x 0 3 N [E] c x 0 3 N [W] d x 0 3 N [E] 0. Based on the information in the above narrative, the magnitude of the horizontal impulse exerted by the older ram to make the leap towards the challenger from a standing start was a. 974 N s. b. 994 N s. c. 984 N s. d..00 x 0 3 N s.. The mass of the younger ram was a. 5 kg. b. 6 kg. c. 2 kg. d. 25 kg. 2. The collision between the two rams should be classified as an a. inelastic collision because the loss of kinetic energy of the system was more than 99%. b. elastic collision because both rams had kinetic energy after the collision. c. inelastic collision because the final kinetic energy of the system was 5.22% of the initial kinetic energy. d. elastic collision because both of the rams bounced backwards after colliding. 3. A kg object moving north at 4.00 m/s collides with a kg object moving west at 8.00 m/s. The two object stick together on impact. As expressed clockwise from north, the direction of the motion after impact is. Round and record your answer to three digits ) 4. An in-line skater has a momentum of 23 kg m/s [S] when travelling at 3.66 m/s [S]. What is the skater s mass? a kg b. 209 kg c kg d kg 5. Based on the information above, what impulse was imparted to the skater to get him/her to that speed? a. 23 N s [S] b. 780 N s [S] c. N s [S] d. 27 N s [S] 6. Based on the information above, if the skater took 3.97 s to reach his/her momentum from a standing start, what average horizontal force was required? a N [S] b. 96 N [S] c. 23 N [S] d. 27 N [S] 7. If the speed of a car is increased from 20 km/h to 80 km/h, then its kinetic energy will increase by a factor of (Round and record your answer to two digits.) 4

5 8. A.6 kg colt automatic pistol fires a 5 g bullet into a 2.5 kg wooden block suspended from the ceiling as a ballistic pendulum. The bullet becomes imbedded in the block 6.9 x 0 4 s after first contact. The bullet and block swing east and rise to a height of 9.8 cm above the rest position. What was the momentum of the bullet just after it left the gun a. 3.5 kg m/s [E] b. 25 kg m/s [E] c. 2.5 kg m/s [E] d. 4.8 kg m/s [E] 9. Based on the information in the above narrative, what impulse did the bullet impart to the block? a. 3.5 N s [E] b. 25 N s [E] c. 2.5 N s [E] d. 4.8 N s [E] 20. The velocity of the bullet was a. 2.3 x 0 2 m/s [E]. b. 2.8 x 0 2 m/s [E]. c. 2.9 x 0 2 m/s [E]. d. 3.2 x 0 2 m/s [E]. 2. Based on the information above the collision between the bullet and the block should be classified as an a. inelastic collision because the loss of kinetic energy of the system was more than 99%. b. elastic collision because the kinetic energy of the bullet was transferred to the block. c. inelastic collision because the final kinetic energy of the system was about 6 % of the initial kinetic energy. d. elastic collision because the bullet and the block were seen to swing away and then swing back. 22. If the pistol was held firmly, what impulse would the recoil give to the shooter? a. 3.5 N s [W] b. 25 N s [W] c. 2.5 N s [W] d. 4.8 N s [W] 23. Students do an experiment about the conservation of energy by placing a puck at the top an inclined air table and letting the puck go so that it accelerates down to the bottom of the table. Measurements are recorded and the students calculate the puck's kinetic energy at the bottom of the incline. In this experiment, what is the manipulated variable? a. Average speed of the puck b. Acceleration due to gravity c. Distance covered by the puck d. Time for puck to go down the plane 24. Mary Jane wishes to do an experiment to demonstrate the known relationship K = R T As part of the experiment, she plans to graph R as a function of T using standard graphing techniques. Which of the following is true? a. R is the manipulated variable, K the control variable and the function is inverse. b. K is the manipulated variable, T the control variable and the function is direct as the square root c. T is the manipulated variable, K the control variable and the function is inverse d. T is the manipulated variable, R the control variable and the function is direct as the square root. 25. To straighten the graph, and form a linear relationship, Mary Jane should plot: a. R as a function of T b. T as a function of R c. K as a function of R d. R as a function of T 5