CONSERVATION OF MOMENTUM IN ONE DIMENSION Name e. Use your momentum vectors from part c to determine the magnitude and direction of the momentum of system S in the reference frame of glider X. Explain. Mech HW-59 f. Compare your results from part a and part e to answer the following: Is the magnitude of the momentum of system S the same in the reference frame of glider X as it is in the reference frame of the track? Explain. • Is the direction of the momentum of system S the same in the reference frame of glider X as in the reference frame of the track? Explain. 4. Gliders C and D, of mass 2 kg and 4 kg, respectively, collide on a frictionless track. Glider C initially moves to the right with speed 0.6 m/s relative to the track, while glider D is at rest. After the collision, glider C moves to the left with speed 0.2 m/s. System S consists of gliders C and D. C D 0.6 m/s C D 0.2 m/s 2 kg 4 kg D=0 2 kg 4kg "D=? after collision before collision a. In the table at right, draw the momentum vectors of glider C, glider D, and system S before and after the collision. Is the momentum of system S before the collision the same as it is after the collision? Explain. Before collision Pc H After collision Po H H Psystem TH I unit = 0.4 kg.m/s b. Use your results from part a to determine the magnitude and direction of the velocity of glider D relative to the track after the collision. Explain. Tutorials in Introductory Physics Prentice Hall, Inc. McDermott, Shaffer, & P.E.G., U. Wash. First Edition, 2002 Mech Conservation of momentum in one dimension HW-60 Consider reference frame R, moving to the left with constant speed 0.2 m/s relative to the track. c. Apply the Galilean transformation of velocities to draw the velocity vectors of gliders C and D in reference frame R before and after the collision. Use the velocity vectors above to draw the momentum vectors of Velocity vectors in reference frame R Before collision VCR II||I After collision VD.R ++ 1 unit =0.1 m/s Momentum vectors in reference frame R glider C, glider D, and system S in reference frame R before and Before collision After collision after the collision. Explain. PC.R HII PD.R HIIHHHH||||||||| Psys.R H d. Use your results from part c above to answer the following: 1 unit = 0.4 kg-m/s i. In reference frame R, is the e. momentum of system S before the collision the same as it is after the collision? ii. Recall the definition of conserved from part D of section II of the tutorial: "When the momentum of an object or system of objects does not change with time, the momentum of the object or system is said to be conserved." In reference frame R, is the momentum of system S conserved? Explain. Use your results from parts a and c above to answer the following: Before the collision, does the momentum of system S have the same value in reference frame R as it does in the reference frame of the track? Explain. f. Consider the following dialogue. Student 1: "The momentum of system S is conserved. That means it must have the same value in reference frame R as it does in the frame of the track." Student 2: "I disagree. Even when momentum is conserved, it could have a different value in one reference frame than it does in another. It must have the same value before and after the collision no matter which reference frame is used." With which student, if either, do you agree? Explain. Tutorials in Introductory Physics McDernoll, Shaffer, & P.E.G., U. Wash. ©Prentice Hall, Inc. First Edition, 2002

CONSERVATION OF MOMENTUM IN ONE DIMENSION Name e. Use your momentum vectors from part c to determine the magnitude and direction of the momentum of system S in the reference frame of glider X. Explain. Mech HW-59 f. Compare your results from part a and part e to answer the following: Is the magnitude of the momentum of system S the same in the reference frame of glider X as it is in the reference frame of the track? Explain. • Is the direction of the momentum of system S the same in the reference frame of glider X as in the reference frame of the track? Explain. 4. Gliders C and D, of mass 2 kg and 4 kg, respectively, collide on a frictionless track. Glider C initially moves to the right with speed 0.6 m/s relative to the track, while glider D is at rest. After the collision, glider C moves to the left with speed 0.2 m/s. System S consists of gliders C and D. C D 0.6 m/s C D 0.2 m/s 2 kg 4 kg D=0 2 kg 4kg "D=? after collision before collision a. In the table at right, draw the momentum vectors of glider C, glider D, and system S before and after the collision. Is the momentum of system S before the collision the same as it is after the collision? Explain. Before collision Pc H After collision Po H H Psystem TH I unit = 0.4 kg.m/s b. Use your results from part a to determine the magnitude and direction of the velocity of glider D relative to the track after the collision. Explain. Tutorials in Introductory Physics Prentice Hall, Inc. McDermott, Shaffer, & P.E.G., U. Wash. First Edition, 2002 Mech Conservation of momentum in one dimension HW-60 Consider reference frame R, moving to the left with constant speed 0.2 m/s relative to the track. c. Apply the Galilean transformation of velocities to draw the velocity vectors of gliders C and D in reference frame R before and after the collision. Use the velocity vectors above to draw the momentum vectors of Velocity vectors in reference frame R Before collision VCR II||I After collision VD.R ++ 1 unit =0.1 m/s Momentum vectors in reference frame R glider C, glider D, and system S in reference frame R before and Before collision After collision after the collision. Explain. PC.R HII PD.R HIIHHHH||||||||| Psys.R H d. Use your results from part c above to answer the following: 1 unit = 0.4 kg-m/s i. In reference frame R, is the e. momentum of system S before the collision the same as it is after the collision? ii. Recall the definition of conserved from part D of section II of the tutorial: "When the momentum of an object or system of objects does not change with time, the momentum of the object or system is said to be conserved." In reference frame R, is the momentum of system S conserved? Explain. Use your results from parts a and c above to answer the following: Before the collision, does the momentum of system S have the same value in reference frame R as it does in the reference frame of the track? Explain. f. Consider the following dialogue. Student 1: "The momentum of system S is conserved. That means it must have the same value in reference frame R as it does in the frame of the track." Student 2: "I disagree. Even when momentum is conserved, it could have a different value in one reference frame than it does in another. It must have the same value before and after the collision no matter which reference frame is used." With which student, if either, do you agree? Explain. Tutorials in Introductory Physics McDernoll, Shaffer, & P.E.G., U. Wash. ©Prentice Hall, Inc. First Edition, 2002