Name 3. (15 points) Ballistic Pendulum: A bullet with mass m is fired into a blo

Question

Name 3. (15 points) Ballistic Pendulum: A bullet with mass m is fired into a block of wood with mass M suspended like a pendulum, and makes a completely inelastic collision with it. After the impact of the bullet, the block swings up to a maximum height h. Given the values of h = 7.00 cm .0700 m, m = 5.75 g 0.00575 kg, and M-3.50 kg. (a) what is the initial velocity v_x of the bullet in m/s? (b) what is the velocity V_x of the bullet/block system right after impact? (c) what is the kinetic energy of the bullet right before impact? (d) what is the kinetic energy of the bullet/block system right after impact? Where did the initial energy of the bullet go? (Remember: Use Conservation of Linear Momentum to analyze the impact. Then, use Conservation of Total Mechanical Energy to see how high the bullet/block system swings.)

Explanation / Answer

a) h = V^2/(2*g)

0.07 = V^2/(2*9.81)

V = 1.72 m/sec is the speed of the bullet and block after impact

using law of conservation of momentum

(m*u) = (m+M)*V

(0.00575*u) = (0.00575+3.5)*1.72

u = 1048.67 m/s is the initial speed of the bullet

b) V_x = V = 1.72 m/s

C) kE_bullet = 0.5*m*u^2 = 0.5*0.00575*1048.67^2 = 3161.66 J

d) KE_system = (0.5*(m+M)*V^2 = 0.5*(0.00575+3.5)*1.72^2 = 5.19 J

initial energy energy of the bullet is gone as the internal energy of the system

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