A railroad car with a mass of 2.33 × 104 kg moving at 3.71 m/s collides and joins with two railroad cars already joined together, each with the same mass as the single car and initially moving in the same direction at 1.44 m/s.
a) What is the final speed of the three joined cars after the collision?
Answer in units of m/s.
011 (part 2 of 2) 10.0 points
b) What is the decrease in kinetic energy during the collision?
conserve momentum. So,
2.33*10^4 * 3.71 + 4.66*10^4 * 1.44 = 6.99*10^4 * v
v = 2.20 m/s
So, now just figure
KE = 1/2 mv^2
for each car before, and the combo car after the collision.
2.20 m/s
To answer these questions, we need to use the conservation of momentum and the principle of conservation of energy.
a) To find the final speed of the three joined cars after the collision, we can use the conservation of momentum:
Momentum before the collision = Momentum after the collision
The momentum is given by the product of mass and velocity. Let's define the following variables:
m = mass of a single railroad car = 2.33 × 10^4 kg
v1 = initial velocity of the single car = 3.71 m/s
v2 = initial velocity of the two joined cars = 1.44 m/s
vf = final velocity of the three joined cars (which we need to find)
Since the two initially joined cars are moving in the same direction, their combined momentum is the sum of their individual momenta:
Initial momentum of the two joined cars = 2m * v2
The momentum before the collision is the sum of the momentum of the single car and the momentum of the two joined cars:
Initial momentum = m * v1 + 2m * v2
After the collision, the three cars are joined and move together with a final velocity vf. So the final momentum is:
Final momentum = 3m * vf
Using the conservation of momentum, we have:
Initial momentum = Final momentum
m * v1 + 2m * v2 = 3m * vf
Simplifying the equation:
v1 + 2v2 = 3vf
Now, plug in the given values for v1 and v2:
(3.71 m/s) + 2(1.44 m/s) = 3vf
Solve for vf to find the final velocity of the three joined cars.
b) To find the decrease in kinetic energy during the collision, we can use the principle of conservation of energy.
The initial kinetic energy (KE_initial) is the sum of the kinetic energies of the single car and the two joined cars:
KE_initial = 0.5 * m * v1^2 + 0.5 * 2m * v2^2
The final kinetic energy (KE_final) is the kinetic energy of the three joined cars:
KE_final = 0.5 * 3m * vf^2
The decrease in kinetic energy (ΔKE) is given by:
ΔKE = KE_initial - KE_final
Plug in the given values for m, v1, v2, and the final velocity vf to find the decrease in kinetic energy during the collision.