4. A variable force acts on an object from 4 =0 to t,. The impulse of the force is zero. One can conclude that (A)Ar=0 and Ap=0 (B)A=0 but possibly4p≠0 (C) possibly A≠0but4p=0 (D) possibly△F≠0 and possibly A≠0 According to the impulse-momentum theorem Fdr =Ap, the impulse of the force is zero,the ch 5. A system of N particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system? (B) B)It could be non-zero, but it must be constant (C)It could be non-zero, and it might not be constant (D)The answer depends on the nature of the internal forces in the system Solution According to the general statement of Newton's law of motion dt F=0, Protal=constant I. Filling the blanks 1. Fig. I shows an ap of force versus time during the collision of a F 58g tennis ball with a wall. This initial velocity of the ball is 32m/s perpendicular to 2 the wall; it rebounds with the same speed, also g the maximum contact force during the collision is 928N Solution Applying to the impulse-momentum theorem time(ms) I= Ap= Fdt →2×58×10×3(2+6)x10-3xFs4. A variable force acts on an object from ti = 0 to f t . The impulse of the force is zero. One can conclude that （ C ） (A) ∆r = 0 r and ∆p = 0 r . (B) ∆r = 0 r but possibly ∆p ≠ 0 r . (C) possibly ∆r ≠ 0 r but ∆p = 0 r . (D) possibly ∆r ≠ 0 r and possibly ∆p ≠ 0 r Solution: According to the impulse-momentum theorem F t p r r = ∆ ∫ f i t t d ，the impulse of the force is zero， the change of the momentum ∆p = 0 r . 5. A system of N particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system? （ B ） (A) It must be zero. (B) It could be non-zero, but it must be constant. (C) It could be non-zero, and it might not be constant. (D) The answer depends on the nature of the internal forces in the system. Solution: According to the general statement of Newton’s law of motion 0, constant , d d total total total = = = F p t p F r r v v II. Filling the Blanks 1. Fig.1 shows an approximate representation of force versus time during the collision of a 58g tennis ball with a wall. This initial velocity of the ball is 32m/s perpendicular to the wall; it rebounds with the same speed, also perpendicular to the wall. The value of Fmax , the maximum contact force during the collision is 928N . Solution: Applying to the impulse-momentum theorem ∫ I = ∆p = Fdt v v v So max 3 3 2 (2 6) 10 2 58 10 32 2 d F p mv F t SF × + × ⇒ × × × = ∆ = = = − − ∫ v v Fmax = 928 N 0123456 Fmax force (N) time (ms) Fig. 1