First exercise (7.5 pts): Determination of the speed of a buller A gun is used to shoot bullets, each of mass m - 50 [ with a horizontal velocity . of value I' In order to determine la, we consider a setup formed of a wooden block of mass M - 950 it suspended from the ends of two inextensible sting of negligible mass and of the same length E= 1 m, This setup can be taken as a block of wood suspended from the free end a string of length C- I'm, initially the pendulum attains an angular deviation n- 37" and released from rest (Figure1). When the wooden block reach equilibrium at G2, a bullet having the velocity Vo. hits the block and is embedded in at the level of the center of muss G of the block {Figure ?). Just after impact, the system ( block, bullet) moves with a horizontal velocity The pendulum thus attains a maximum angular deviation /1=26' backward in the positive direction at G3 ( Figure 31, Take the horizontal plane through G2 at equilibrium as a gravitational potential energy reference. Neglect friction with air resistance Take cos 37 = 0.8 and cos26 -0.9 and takeg = 10 m/s. Fruum 2 Before Collision During Collision Aher Collision 1. Calculate the speed of wooden block V when it reached equilibrium 2. Determine the expression of the speed of the speed of the system wooden black and bullet Va of the velocity , after the impact in terms of M. m and V and VoDetermine, Just after impact, the mechanical energy of the system [ pendulum Earth) in terms of Va. V. M, and m Calculate the mechanical energy of the system [pendulum, Earth) at point GO. at the maximum angle 35 reached by the systemn after impact 1'5, Deduce the value of Vo and VE 5 If the bullet stranded in the wooden block in 50 ms, assume that only the forces charted by the bullet on the wooden Block Fory and that exerted by the wooden Block on the bullet Biyy are considerable during the Impati, all other external forces are nopligible and cancel each other. Calculate the force exerted by the bullet on the wooden Block In,w Calculate the force exerted by the wooden Block on the bullet For Deduce that principle of interaction is satisfied 7. Is the collision perfectly elastic? Justify your