In a head-on, inelastic collision, a 4000 kg truck going 10 m/s east strikes a 1000 kg
car going 20 m/s west.
(a) What are the speed and the direction of the wreckage?
(b) How much kinetic energy is lost in the collision?
a) It is a head-on collision.
Momentum is conserved.
The final momentum (measured positive east) is 4000*10 -1000*20 = 20,000 kg m/s
Set that equal to (M1 + M2)*Vfinal
and solve for Vfinal.
b) Compute the (1/2)M1*V1^2 + (1/2)M2*V2^2 with
(1/2)(M1+M2)Vfinal^2
The latter will be less. The firrence will be the kinetic ene4rgy lost./
50,000
To find the speed and direction of the wreckage after the collision, you need to apply the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
Momentum is defined as the product of mass and velocity.
(a) Calculate the total momentum before the collision:
Initial momentum of the truck = mass of truck * velocity of truck = 4000 kg * 10 m/s = 40,000 kg·m/s (to the east)
Initial momentum of the car = mass of car * velocity of car = 1000 kg * (-20 m/s) = -20,000 kg·m/s (to the west)
Total initial momentum = 40,000 kg·m/s - 20,000 kg·m/s = 20,000 kg·m/s (to the east)
Now let's find the final momentum after the collision:
Let V be the final velocity of the wreckage.
Final momentum of the wreckage = (mass of truck + mass of car) * V
Because the truck and the car stick together after the collision (inelastic collision), their masses are combined.
Final momentum = (4000 kg + 1000 kg) * V = 5000 kg * V
According to the law of conservation of momentum:
Total initial momentum = Total final momentum
20,000 kg·m/s = 5000 kg * V
V = 20,000 kg·m/s / 5000 kg = 4 m/s
Therefore, the speed of the wreckage after the collision is 4 m/s to the east.
(b) To find the amount of kinetic energy lost in the collision, you need to compare the initial kinetic energy with the final kinetic energy.
Initial kinetic energy is given by:
Kinetic energy of the truck = 0.5 * mass of truck * (velocity of truck)^2
Kinetic energy of the car = 0.5 * mass of car * (velocity of car)^2
Initial kinetic energy = 0.5 * 4000 kg * (10 m/s)^2 + 0.5 * 1000 kg * (20 m/s)^2
= 200,000 J + 200,000 J
= 400,000 J
Final kinetic energy is given by:
Kinetic energy of the wreckage = 0.5 * (mass of truck + mass of car) * (final velocity of wreckage)^2
= 0.5 * 5000 kg * (4 m/s)^2
= 0.5 * 5000 kg * 16 m^2/s^2
= 40,000 J
The amount of kinetic energy lost in the collision is:
Kinetic energy lost = Initial kinetic energy - Final kinetic energy
= 400,000 J - 40,000 J
= 360,000 J
Therefore, 360,000 Joules of kinetic energy are lost in the collision.
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.
(a) Let's start by calculating the total momentum before the collision and after the collision. The momentum (p) of an object is given by the product of its mass (m) and velocity (v).
Before the collision:
Momentum of the truck = mass_truck * velocity_truck = 4000 kg * 10 m/s (east) = 40000 kg*m/s (east)
Momentum of the car = mass_car * velocity_car = 1000 kg * -20 m/s (west) = -20000 kg*m/s (west) [Negative sign indicates opposite direction]
Total momentum before the collision = Momentum of the truck + Momentum of the car
= 40000 kg*m/s (east) + (-20000 kg*m/s) (west)
= 40000 kg*m/s - 20000 kg*m/s
= 20000 kg*m/s (east-west)
Now, let's consider the total momentum after the collision. Since the collision is inelastic, the two objects stick together and move in the same direction.
Total momentum after the collision = Combined mass * Final velocity of wreckage
Given that the truck and car combine and move in the same direction, we can find the final velocity of the wreckage using the conservation of momentum.
Combined mass = mass_truck + mass_car = 4000 kg + 1000 kg = 5000 kg
Total momentum after the collision = Combined mass * Final velocity of wreckage
= 5000 kg * v (east or west)
Since the momentum before and after the collision must be the same, we can equate the two expressions:
20000 kg*m/s (east-west) = 5000 kg * v (east or west)
Simplifying the equation, we find: v = (20000 kg*m/s) / 5000 kg
Therefore, the speed of the wreckage is 4 m/s, and the direction is east (since the positive sign indicates east).
(b) To find the kinetic energy lost in the collision, we need to compare the initial and final kinetic energies.
Initial kinetic energy (KE) = 1/2 * mass_truck * (velocity_truck)^2 + 1/2 * mass_car * (velocity_car)^2
= 1/2 * 4000 kg * (10 m/s)^2 + 1/2 * 1000 kg * (20 m/s)^2
= 200000 J + 200000 J
= 400000 J
Final kinetic energy (KE) = 1/2 * combined mass * (final velocity of wreckage)^2
= 1/2 * 5000 kg * (4 m/s)^2
= 40000 J
Therefore, the kinetic energy lost in the collision is the difference between the initial and final kinetic energies:
Kinetic energy lost = Initial kinetic energy - Final kinetic energy
= 400000 J - 40000 J
= 360000 J
Hence, the kinetic energy lost in the collision is 360000 J.