1) A 10.5-g bullet is fired into a stationary block of wood having mass m = 4.94

Question

1) A 10.5-g bullet is fired into a stationary block of wood having mass m = 4.94 kg. The bullet imbeds into the block. The speed of the bullet-plus-wood combination immediately after the collision is 0.591 m/s. What was the original speed of the bullet? (Express your answer with four significant figures.)

2) A car of mass m moving at a speed v1 collides and couples with the back of a truck of mass 4m moving initially in the same direction as the car at a lower speed v2. (Use any variable or symbol stated above as necessary.)

(a) What is the speed vf of the two vehicles immediately after the collision? Vf=

A 10.5-g bullet is fired into a stationary block of wood having mass m4.94 kg. The bullet imbeds into the block. The speed of the bullet-plus-wood combination immediately after the collision is 0.591 m/s. What was the original speed of the bullet? (Express your answer with four significant figures.) m/s Need Help?Read It Watch It Submit Answer Save Progress Practice Another Version 2 points SerPSE8 9.P.020. My Notes Ask Your Teach A car of mass m moving at a speed vi collides and couples with the back of a truck of mass 4m moving initially in the same direction as the car at a lower speed v2. (Use any variable or symbol stated above as necessary.) (a) What is the speed vf of the two vehicles immediately after the collision? (b) What is the change in kinetic energy of the car-truck system in the collision?

Explanation / Answer

1)

Momentum before = momentum after

(m_1)(v_1) = (m_1 + m_2)(v_2)

m_1 = mass of bullet
m_2 = mass of block
v_1 = speed of bullet
v_2 = speed of bullet-wood combination

(0.0105)(v_1) = (0.0105 + 4.94)(0.591)
v_1 = 278.6424 m/s

2)(a)

Conservation of momentum:
m * v1 + 4m * v2 = (m + 4m) * vf
m (v1 + 4 * v2) = 5m * vf
(v1 + 4 * v2) / 5 = vf

(b)
(1/2) * m * v1^2 + (1/2) * 4m * v2^2 = (1/2) * 5m * vf^2 + K
v1^2 + 4 * v2^2 = 5 * vf^2 + 2 * K / m

Substitute for vf
v1^2 + 4 * v2^2 = 5 * ((v1 + 4 * v2) / 5)^2 + 2 * K / m
v1^2 + 4 * v2^2 = (v1 + 4 * v2)^2 / 5 + 2 * K / m
v1^2 + 4 * v2^2 - (v1 + 4 * v2)^2 / 5 = 2 * K / m
v1^2 + 4 * v2^2 - (v1^2 + 8 * v1 * v2 + 16 v2^2) / 5 = 2 * K / m
5 * v1^2 + 20 * v2^2 - (v1^2 + 8 * v1 * v2 + 16 v2^2) = 10 * K / m
5 * v1^2 + 20 * v2^2 - v1^2 - 8 * v1 * v2 - 16 v2^2 = 10 * K / m
4 * v1^2 + 4 * v2^2 - 8 * v1 * v2 = 10 * K / m
m * (4 * v1^2 + 4 * v2^2 - 8 * v1 * v2) / 10 = K
2m/5 * (v1^2 + v2^2 - 2 * v1 * v2) = K
2m/5 * (v1^2 - 2 * v1 * v2 + v2^2) = K
2m/5 * (v1 - v2)^2 = K

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