if the cart in the last question collides INELASTICALLY with a stationary cart of mass 150 g, what is the kinetic energy of the carts after the collision (LEAVE OUT units of J)?
1/2(100)(2)^2 + 1/2(150)(0)^2 = 200
To calculate the kinetic energy of the carts after an inelastic collision, you need to determine the final velocity of the two carts.
Using the principle of conservation of momentum in an inelastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The initial momentum is given by the equation:
Initial momentum = (mass of cart 1) x (velocity of cart 1) + (mass of cart 2) x (velocity of cart 2)
Since the second cart is initially stationary, its initial velocity is zero:
Initial momentum = (mass of cart 1) x (velocity of cart 1) + (mass of cart 2) x (0)
After the collision, the two carts stick together and move with a final combined velocity. Let's call this final velocity V.
The final momentum is given by the equation:
Final momentum = (mass of combined carts) x (final velocity) = (mass of cart 1 + mass of cart 2) x (final velocity)
Since the two carts stick together, their masses add up:
Final momentum = (mass of cart 1 + mass of cart 2) x (final velocity)
By conserving momentum, we know that the initial momentum is equal to the final momentum:
(mass of cart 1) x (velocity of cart 1) + (mass of cart 2) x (0) = (mass of cart 1 + mass of cart 2) x (final velocity)
Now, we can rearrange the equation to solve for the final velocity:
(mass of cart 1) x (velocity of cart 1) = (mass of cart 1 + mass of cart 2) x (final velocity)
(mass of cart 1) x (velocity of cart 1) = (mass of cart 1 x final velocity) + (mass of cart 2 x final velocity)
(mass of cart 1) x (velocity of cart 1) - (mass of cart 1 x final velocity) = (mass of cart 2 x final velocity)
(mass of cart 1) x (velocity of cart 1) - (mass of cart 1 x final velocity) = (mass of cart 2 x final velocity)
(mass of cart 1) x (velocity of cart 1) = (final velocity) x [(mass of cart 1) + (mass of cart 2)]
(final velocity) = [(mass of cart 1) x (velocity of cart 1)] / [(mass of cart 1) + (mass of cart 2)]
Substituting the given values:
(final velocity) = [(124 g) x (3 m/s)] / [(124 g) + (150 g)]
(final velocity) = (372 g × m/s) / (274 g)
(final velocity) ≈ 1.36 m/s
Now, to calculate the total kinetic energy after the collision, we can use the formula:
Total kinetic energy = (1/2) x (mass of combined carts) x (final velocity)^2
Substituting the given values:
Total kinetic energy = (1/2) x [(124 g) + (150 g)] x (1.36 m/s)^2
Now you can calculate the total kinetic energy using the given values.
To find the kinetic energy of the carts after an inelastic collision, we need to know the initial kinetic energy of the moving cart (from the last question) and calculate the final kinetic energy.
1. Recall the mass and initial velocity of the moving cart from the last question. Let's say the mass is m and the initial velocity is v.
2. The kinetic energy of the moving cart before the collision is given by the formula: KE = (1/2)mv^2.
3. Now, let's consider the collision. Since it is inelastic, the two carts stick together after the collision. We need to calculate the final velocity of the carts together.
4. To do this, let's assume the final velocity of the combined carts is V. We can apply the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
5. The momentum before the collision is given by the formula: momentum = mass x velocity. So the total momentum before the collision is (m x v) + (150 g x 0) since the stationary cart has zero initial velocity.
6. The total momentum after the collision is the mass of the combined carts (m + 150 g) multiplied by the final velocity V.
7. Setting the two momentum equations equal to each other, we get: (m x v) + (150 g x 0) = (m + 150 g) x V.
8. Solving for V, we have V = ((m x v) / (m + 150 g)).
9. Now that we have the final velocity, we can calculate the final kinetic energy of the combined carts using the formula: KE = (1/2) x (m + 150 g) x (V^2).
10. Substitute the values of mass (m), initial velocity (v), and final velocity (V) into the formula to calculate the final kinetic energy.
11. The result will be the kinetic energy of the carts after the inelastic collision, leaving out the units.