To determine the velocity of car #2 before the collision, we can use the conservation of momentum principle, which states that the total momentum before the collision should be equal to the total momentum after the collision.
From the given graph, we see that the momentum of car #1 before the collision is 8 Ns.
Let the initial velocity of car #2 be v2. Then, the initial momentum of car #2 is given by:
momentum_2_before = m2 * v2
Before the collision, the total momentum of the system is:
total_momentum_before = m1 * v1 + m2 * v2
After the collision, the cars are coupled together and move with a common velocity (vc). Then, the total momentum after the collision is:
total_momentum_after = (m1 + m2) * vc
From the given graph, we see that the total momentum after the collision is 20 Ns. Therefore,
total_momentum_after = 20 Ns
According to the conservation of momentum principle:
total_momentum_before = total_momentum_after
m1 * v1 + m2 * v2 = (m1 + m2) * vc
Using the given mass values, we can replace:
(18.0 kg) * 8 + (50.0 kg) * v2 = (18.0 kg + 50.0 kg) * 20
Solving for v2:
v2 = [(18.0 kg + 50.0 kg) * 20 - (18.0 kg) * 8] / (50.0 kg)
v2 = (68.0 kg * 20 - 144) / 50.0 kg
v2 = (1360 - 144) / 50.0 kg
v2 = 1216 / 50.0 kg
v2 = 24.32 m/s
Therefore, the initial velocity of car #2 before the collision is 24.32 m/s.
As shown in the figure below, cars #1 and #2 are sliding across a horizontal frictionless surface. The cars are equipped with a coupling arrangement similar to the one on railroad cars. Car #1 overtakes car #2 and they have a totally inelastic collision and become coupled together. You know the mass of each car;
m1 = 18.0 kg
and
m2 = 50.0 kg.
In addition, you are provided with the following graph, which shows the momentum of car #1 before, during and after the collision. Determine the velocity of car #2 before the collision.
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