Two freight cars, each with a mass of 3.9 105 kg, collide and stick together. One was initially moving at 3.2 m/s and the other was at rest. What is their final speed in m/s?
Conservation of momentum applies
momentum before= momentum after
3.9E5*3.2m/s= (2*3.9E5)V
To find the final speed of the two freight cars after the collision, we can use the principle of conservation of momentum.
The momentum before the collision is given by the sum of the individual momenta of the two cars:
Initial Momentum = (Mass of Car 1) x (Velocity of Car 1) + (Mass of Car 2) x (Velocity of Car 2)
Since the second car was initially at rest, the equation becomes:
Initial Momentum = (Mass of Car 1) x (Velocity of Car 1) + (Mass of Car 2) x 0
Now, let's calculate their initial momentum:
Initial Momentum = (3.9 x 10^5 kg) x (3.2 m/s) + (3.9 x 10^5 kg) x 0
= (3.9 x 10^5 kg) x (3.2 m/s)
= 1.248 x 10^6 kg*m/s
According to the principle of conservation of momentum, the total momentum before the collision should equal the total momentum after the collision:
Initial Momentum = Final Momentum
Since the cars stick together after the collision, their masses combine so that the mass of the two cars together is the sum of their individual masses:
Mass of two cars = Mass of Car 1 + Mass of Car 2
= (3.9 x 10^5 kg) + (3.9 x 10^5 kg)
= 7.8 x 10^5 kg
Let's denote the final velocity of the cars as V:
Final Momentum = (Mass of two cars) x V
Now, set the initial momentum equal to the final momentum:
Initial Momentum = Final Momentum
1.248 x 10^6 kg*m/s = (7.8 x 10^5 kg) x V
Now, solve for V:
V = (1.248 x 10^6 kg*m/s) / (7.8 x 10^5 kg)
≈ 1.6 m/s
Therefore, the final speed of the two freight cars after the collision is approximately 1.6 m/s.
To find the final speed of the two freight cars after the collision, you can use the principle of conservation of linear 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 calculated by multiplying its mass by its velocity. Let's denote the initial velocity of the first freight car as v1, the initial velocity of the second freight car as v2, and the final velocity of the two cars stuck together as vf.
Since the second freight car is initially at rest (v2 = 0), its momentum before the collision is zero.
The momentum of the first freight car before the collision is given by:
Initial Momentum 1 = mass 1 * initial velocity 1
= (3.9 * 10^5 kg) * (3.2 m/s)
The total momentum before the collision is the sum of the individual momenta of the two freight cars:
Total Initial Momentum = Initial Momentum 1 + Initial Momentum 2
Since the second freight car is initially at rest, the total initial momentum is equal to the momentum of the first freight car alone:
Total Initial Momentum = Initial Momentum 1
Now, according to the conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision. So,
Total Initial Momentum = Total Final Momentum
Therefore,
Initial Momentum 1 = Total Final Momentum
Now, let's calculate the total final momentum. Since the two freight cars stick together after the collision, we have:
Total Final Momentum = Total Mass of the two cars * Final Velocity
The total mass of the two cars is the sum of their individual masses:
Total Mass = mass 1 + mass 2
Therefore,
Initial Momentum 1 = Total Mass * Final Velocity
Rearranging the equation, we get:
Final Velocity = Initial Momentum 1 / Total Mass
Now we can substitute the known values into the equation and calculate the final velocity.
Note: Make sure to convert the masses to kg before plugging them into the equation.