A 6,000 kg train car is moving to the right at 10 m/s and connects to a 4,000-kg train car that wasn't moving. What is the veloc
1 answer:
1) The final velocity of the two trains is 6 m/s to the right
2) It is an inelastic collision
Explanation:
1)
We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two trains must be conserved before and after the collision.
Therefore we can write:
where:
is the mass of the first train
is the initial velocity of the first train
is the mass of the second train
is the initial velocity of the second train (initially at rest)
is the final combined velocity of the two trains
Solving the equation for v, we find the final velocity of the two trains:
2)
There are two types of collisions:
- Elastic collision: in an elastic collision, both the total momentum and the total kinetic energy of the system are conserved
- Inelastic collision: in an inelastic collision, only the total momentum is conserved, while the total kinetic energy is not (part of it is converted into thermal energy due to internal frictions)
To verify what type of collision is this, we can compare the total kinetic energy before and after the collision:
Before:
After:
As we can see, the kinetic energy is not conserved, so this is an inelastic collision.
Learn more about momentum here:
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The time needed for the 7th car to pass is 13.2 s
Explanation:
The motion of the train is a uniformly accelerated motion, therefore we can use suvat equations.
We start by analzying the motion of the first car, by using the equation:
where
s is the distance covered by the first car in a time t, which corresponds to the length of one car
u = 0 is the initial velocity
a is the acceleration
t = 5.0 s is the time
The equation can be rewritten as
where L is the length of one car.
The same equation can be written considering the first 7 cars:
where
7L is the distance covered by the 7 cars
t' is the time needed
We still have
u = 0
And the acceleration is constant so it is
Substituting into the equation, we can find t':
In attachment the graph of the distance covered versus the time taken: since the motion is uniformly accelerated, the relationship between the two variables is quadratical.
Learn more about accelerated motion:
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