Mech HW-58 Conservation of momentum in one dimension 3. Glider A, of mass m, moves to the right with constant speed v, on a frictionless track toward glider B. Glider B has mass 2m and is initially at rest. System S consists of gliders A and B. m Glider A a. In the spaces provided, draw momentum vectors for glider A, glider B, and system S. Label each vector with its magnitude (express magnitudes in terms of the given quantities m and v₁). 2m |UB=0 Glider B Momentum vectors Glider A Glider B System S Glider X, of mass 5m, (not shown in the diagram) moves to the right with speed v. (i.e., the same speed as glider A) on a second frictionless track parallel to the original track. b. Apply the Galilean transformation of velocities to determine the velocity vectors of gliders A and B in the reference frame of glider X. Draw the vectors in the space at right. Label each vector with its magnitude. (Express the magnitudes in terms of the given quantities.) c. Draw momentum vectors of gliders A and B in the reference frame of glider X. Label each vector with its magnitude. Explain your reasoning. Velocity vectors in the frame of glider X Glider A Glider B Momentum vectors in the frame of glider X Glider A Glider B d. Consider the following incorrect statement: "Glider X has momentum 5mv, to the right, so in the reference frame of glider X, the momentum of glider A is mv. - 5mv = -4mv, or 4mv, to the left." Explain the error(s) in the reasoning. Suppose glider X had a different mass (i.e., something other than 5m). Would the magnitude of the momentum of glider A in the reference frame of glider X be the same as or different than the value you determined in part c? Explain. Tutorials in Introductory Physics McDermott, Shaffer, & P.E.G., U. Wash. OPrentice Hall. Inc. First Edition, 2002 CONSERVATION OF MOMENTUM IN ONE DIMENSION c. Suppose the incline in part b is now placed on a frictionless table. i. Is the net force on the block always zero? Explain. ii. Is the net force on the incline always zero? Explain. Name Mech HW-57 iii. Is the net force on the block-incline system always zero? Explain. iv. Is the momentum of the block conserved? Explain. v. Is the momentum of the incline conserved? Explain. vi. Is the momentum of the block-incline system conserved? Explain. d. Two blocks, A and B, are connected by a massless and inextensible string. Their masses are m = 200 g and m, = 400 g. The blocks are released from rest. The pulley has negligible mass. Let S represent the system of blocks A, B, the string, and the pulley. i. Is the net force on block A always zero? Explain. ii. Is the net force on system S always zero? Explain. iii. Is the momentum of block A conserved? Explain. iv. Is the momentum of system S conserved? Explain. A 200 g Tutorials in Introductory Physics McDermott, Shaffer, & P.E.G., U. Wash. Frictionless B 400 g Prentice Hall, Inc. First Edition, 2002

Mech HW-58 Conservation of momentum in one dimension 3. Glider A, of mass m, moves to the right with constant speed v, on a frictionless track toward glider B. Glider B has mass 2m and is initially at rest. System S consists of gliders A and B. m Glider A a. In the spaces provided, draw momentum vectors for glider A, glider B, and system S. Label each vector with its magnitude (express magnitudes in terms of the given quantities m and v₁). 2m |UB=0 Glider B Momentum vectors Glider A Glider B System S Glider X, of mass 5m, (not shown in the diagram) moves to the right with speed v. (i.e., the same speed as glider A) on a second frictionless track parallel to the original track. b. Apply the Galilean transformation of velocities to determine the velocity vectors of gliders A and B in the reference frame of glider X. Draw the vectors in the space at right. Label each vector with its magnitude. (Express the magnitudes in terms of the given quantities.) c. Draw momentum vectors of gliders A and B in the reference frame of glider X. Label each vector with its magnitude. Explain your reasoning. Velocity vectors in the frame of glider X Glider A Glider B Momentum vectors in the frame of glider X Glider A Glider B d. Consider the following incorrect statement: "Glider X has momentum 5mv, to the right, so in the reference frame of glider X, the momentum of glider A is mv. - 5mv = -4mv, or 4mv, to the left." Explain the error(s) in the reasoning. Suppose glider X had a different mass (i.e., something other than 5m). Would the magnitude of the momentum of glider A in the reference frame of glider X be the same as or different than the value you determined in part c? Explain. Tutorials in Introductory Physics McDermott, Shaffer, & P.E.G., U. Wash. OPrentice Hall. Inc. First Edition, 2002 CONSERVATION OF MOMENTUM IN ONE DIMENSION c. Suppose the incline in part b is now placed on a frictionless table. i. Is the net force on the block always zero? Explain. ii. Is the net force on the incline always zero? Explain. Name Mech HW-57 iii. Is the net force on the block-incline system always zero? Explain. iv. Is the momentum of the block conserved? Explain. v. Is the momentum of the incline conserved? Explain. vi. Is the momentum of the block-incline system conserved? Explain. d. Two blocks, A and B, are connected by a massless and inextensible string. Their masses are m = 200 g and m, = 400 g. The blocks are released from rest. The pulley has negligible mass. Let S represent the system of blocks A, B, the string, and the pulley. i. Is the net force on block A always zero? Explain. ii. Is the net force on system S always zero? Explain. iii. Is the momentum of block A conserved? Explain. iv. Is the momentum of system S conserved? Explain. A 200 g Tutorials in Introductory Physics McDermott, Shaffer, & P.E.G., U. Wash. Frictionless B 400 g Prentice Hall, Inc. First Edition, 2002