Answer to Question #242911 in Physics for rshiii

Question

13. A hockey puck 𝐵 rests on a smooth ice surface and is struck by a second puck A, which was originally traveling at 40.0 m/s and which is deflected 30.0 o from its original direction shown in Figure 2. Puck 𝐵 acquires a velocity of a 45.0 o angle to the original direction of 𝐴. The pucks have the same mass (Figure 74). a) Compute the speed of each puck after the collision. b) What fraction of the original kinetic energy of puck A is dissipated during the collision?

Answer 1

Apply momentum conservation along x- and y-axes:

$$x: mv_{Ax}=mu_{Ax}+mu_{Bx},\\ y: mv_{Ay}=mu_{Ay}+mu_{By}.\\ x: v_{Ax}=u_{A}\cos30°+u_{B}\cos45°,\\ y: v_{Ay}=u_{A}\sin30°+u_{B}\sin45°.\\\space\\ x: 40=u_{A}\cos30°+u_{B}\cos45°,\\ y: 0=u_{A}\sin30°+u_{B}\sin45°.\\\space\\ u_A=29.3\text{ m/s},\\ u_B=20.1\text{ m/s}.$$

Find the fraction of energy dissipated:

$$\epsilon_E=\frac{mv_A^2-mu_A^2}{mv_A^2}=0.46.$$