A 1000-kg car is moving east at 80 km/h collides head on with a 1500-kg car moving west at 40 km/h, and the two cars stick together. Which way does the wreckage move and with what initial speed?
a) 14m/s (conservation of momentum, 2200*60+1300*30=(2200+1300)*v )
b) 47500
c) 2.8 * 10^4
To determine the direction and initial speed of the wreckage after the collision, we can use the principle of conservation of momentum.
Step 1: Calculate the momentum of each car before the collision.
Momentum (P) is calculated by multiplying mass (m) by velocity (v).
Momentum of the first car (eastward): P1 = m1 * v1
= 1000 kg * 80 km/h
= 80,000 kg * km/h
Momentum of the second car (westward): P2 = m2 * v2
= 1500 kg * (-40 km/h) (since it is moving in the opposite direction)
= -60,000 kg * km/h
Step 2: Calculate the total momentum before the collision.
Total momentum before the collision (P_total) is the sum of the individual momenta of the cars.
P_total = P1 + P2
= 80,000 kg * km/h - 60,000 kg * km/h
= 20,000 kg * km/h
Step 3: Calculate the total mass of the wreckage.
After the collision, the two cars stick together, so the total mass of the wreckage is the sum of the masses of both cars.
Total mass (m_total) = m1 + m2
= 1000 kg + 1500 kg
= 2500 kg
Step 4: Calculate the initial velocity of the wreckage.
The initial velocity (V_initial) of the wreckage is the total momentum (P_total) divided by the total mass (m_total).
V_initial = P_total / m_total
= (20,000 kg * km/h) / 2500 kg
= 8 km/h
Therefore, the wreckage moves eastward with an initial velocity of 8 km/h.
To determine the direction and initial speed of the wreckage after the collision, we can apply the principles of conservation of momentum.
Momentum is the product of an object's mass and its velocity. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, provided that no external forces are involved.
Let's calculate the total momentum before the collision for both cars:
Momentum of the 1000-kg car moving east = mass * velocity
= 1000 kg * 80 km/h
Momentum of the 1500-kg car moving west = mass * velocity
= 1500 kg * (-40 km/h) (since westward motion is considered negative)
To calculate the total momentum, we add the individual momenta of the cars:
Total momentum before collision = Momentum of car 1 + Momentum of car 2
= (1000 kg * 80 km/h) + (1500 kg * (-40 km/h))
After the collision, the wreckage of the two cars sticks together, so we can consider them as one combined object. Let's denote the mass of the wreckage as M and the speed after the collision as V.
The total momentum after the collision is:
Total momentum after collision = Total mass of wreckage * Velocity of wreckage
= M * V
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Total momentum before collision = Total momentum after collision
Therefore, we can set up the equation:
(1000 kg * 80 km/h) + (1500 kg * (-40 km/h)) = M * V
Solving this equation will give us both the direction and initial speed of the wreckage after the collision.