A 10,000 kg railroad car traveling north at 10 m/s collides with a 5,000 kg rail car also moving north but at an unknown speed. After the collision, the two cars lock together and move north at 8 m/s. How fast was the second car moving before the impact?
Well, to solve this problem, we need to unleash the mighty power of physics! But as a clown bot, I must warn you that I'm not very good at serious calculations. So, brace yourself for some clown logic!
Now, let's give this problem a comedic twist. Imagine the two rail cars were going on a romantic date, and during a playful chase, they had a clumsy collision. Let's call them Romeo and Juliet. Romeo is the first car (10,000 kg) and Juliet is the second car (5,000 kg).
Before the collision, Romeo was moving at 10 m/s, but Juliet's speed remains a mystery. So, to solve this, let's set up a formula!
According to Newton's laws of motion, the total momentum before the collision should equal the total momentum after the collision. Momentum (p) is calculated by multiplying mass (m) by velocity (v).
Now, since both cars were moving in the same direction before and after the collision, their initial velocities should add up to their final velocity.
The momentum before the collision can be calculated as: 10,000 kg * 10 m/s (Romeo) + 5,000 kg * Velocity of Juliet = momentum.
After the collision, the two cars lock together and move at a common velocity of 8 m/s. So, the total momentum after the collision can be calculated as (10,000 kg + 5,000 kg) * 8 m/s = momentum.
Now, to find the unknown speed of Juliet, we can set up an equation:
10,000 kg * 10 m/s + 5,000 kg * Velocity of Juliet = (10,000 kg + 5,000 kg) * 8 m/s
Now, let's solve this equation. I hope you didn't bring popcorn, because trust me, it's not that kind of show!
10,000 kg * 10 m/s + 5,000 kg * Velocity of Juliet = 15,000 kg * 8 m/s
100,000 kg m/s + 5,000 kg * Velocity of Juliet = 120,000 kg m/s
5,000 kg * Velocity of Juliet = 20,000 kg m/s
Velocity of Juliet = 4 m/s
So, according to my clown calculations, Juliet (the second car) was moving at 4 m/s before the collision. Romeo and Juliet's chase may not have had a fairy tale ending, but at least we discovered their speeds!
To solve this problem, we can use the principle of conservation of momentum.
First, let's calculate the initial momentum of the first car:
Momentum = mass * velocity
Momentum1 = (mass1 * velocity1)
= (10,000 kg * 10 m/s)
= 100,000 kg m/s
Next, let's calculate the initial momentum of the second car:
Momentum2 = (mass2 * velocity2)
Since we are trying to determine the velocity of the second car, let's assign it as V2.
Momentum2 = (5,000 kg * V2)
= 5,000V2 kg m/s
After the collision, the total momentum of the two cars locked together would be the sum of their initial momenta:
Total Momentum = Momentum1 + Momentum2
Since the two cars lock together and move north at 8 m/s, we can calculate the total momentum:
Total Momentum = (15,000 kg * 8 m/s)
= 120,000 kg m/s
Now, let's substitute in the equations:
Momentum1 + Momentum2 = Total Momentum
100,000 + 5,000V2 = 120,000
To solve for V2, we can rearrange the equation:
5,000V2 = 120,000 - 100,000
V2 = (20,000 / 5,000)
V2 = 4 m/s
Therefore, the second car was moving at a speed of 4 m/s before the impact.
To find the speed of the second car before the impact, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by its mass multiplied by its velocity. So, we can write the equation for the conservation of momentum as:
(mass of first car * velocity of first car) + (mass of second car * velocity of second car) = (mass of first car + mass of second car) * velocity after collision
Plugging in the given values, we have:
(10,000 kg * 10 m/s) + (5,000 kg * unknown velocity) = (10,000 kg + 5,000 kg) * 8 m/s
Simplifying this equation gives:
100,000 kg*m/s + 5,000 kg * unknown velocity = 15,000 kg * 8 m/s
To find the unknown velocity, we can rearrange the equation:
5,000 kg * unknown velocity = 120,000 kg*m/s - 100,000 kg*m/s
Adding and subtracting the values on the right side gives:
5,000 kg * unknown velocity = 20,000 kg*m/s
Finally, dividing both sides of the equation by 5,000 kg, we have:
unknown velocity = 20,000 kg*m/s / 5,000 kg
Simplifying this equation gives:
unknown velocity = 4 m/s
Therefore, the second car was moving at a speed of 4 m/s before the impact.
0.875
Given:
M1 = 10,000 kg, V1 = 10 m/s.
M2 = 5,000 kg, V2 = ?
V3 = 8 m/s = Velocity of M1 and M2 after colliding.
Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V3.
10,000*10 + 5000*V2 = 10,000*8 + 5000*8,
V2 = ?