A 10 kg cart was observed moving north with a speed of 15 m/s before it collided with an identical cart at rest. The collision was observed to cause the carts to couple and move together as one. What is in Joules the kinetic energy of the system of both carts after the collision?
To find the kinetic energy of the system of both carts after the collision, we need to first calculate the final velocity of the carts.
Let's assume that the final velocity of the carts after the collision is "v" (m/s).
Since the first cart is moving with a speed of 15 m/s and the second cart is at rest, the conservation of momentum tells us that the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity: momentum = mass × velocity.
For the first cart: momentum before = mass × velocity = (10 kg) × (15 m/s) = 150 kg·m/s.
For the second cart: momentum before = mass × velocity = (10 kg) × (0 m/s) = 0 kg·m/s.
After the collision, the carts move together as one, so they have a common final velocity "v".
The total momentum after the collision should be: momentum after = (10 kg + 10 kg) × v = 20 kg × v.
Using the conservation of momentum, we can equate the momentum before and after the collision:
momentum before = momentum after
150 kg·m/s = 20 kg × v
Solving for "v", we get:
v = 150 kg·m/s / 20 kg = 7.5 m/s
Now that we know the final velocity of the system of both carts after the collision (v = 7.5 m/s), we can calculate the kinetic energy of the system.
The kinetic energy of an object is given by the formula: kinetic energy = (1/2) × mass × velocity^2.
For the system of both carts:
kinetic energy = (1/2) × (10 kg + 10 kg) × (7.5 m/s)^2
Calculating this expression:
kinetic energy = (1/2) × 20 kg × (7.5 m/s)^2 = 562.5 J
So, the kinetic energy of the system of both carts after the collision is 562.5 Joules.