One glider with a mass 0.2 kg and a speed of 3.5 m/s traveling east collides with another glider with mass 0.5 kg and a speed of 2.0 m/s moving west. They collide and stick together.

Calculate the net mechanical energy and is it a loss or gain?

How do I calculate the momentum?

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To calculate the net mechanical energy after the collision and determine if it is a loss or gain, we need to calculate the initial mechanical energy and the final mechanical energy.

1. Calculate the initial mechanical energy:
The initial mechanical energy is the sum of the kinetic energy of both gliders before the collision. The equation for kinetic energy is given by KE = (1/2)mv^2, where m is the mass and v is the velocity.

For the first glider:
Mass (m1) = 0.2 kg
Velocity (v1) = 3.5 m/s
Kinetic energy (KE1) = (1/2) * (0.2 kg) * (3.5 m/s)^2

For the second glider:
Mass (m2) = 0.5 kg
Velocity (v2) = -2.0 m/s (since it is moving in the opposite direction)
Kinetic energy (KE2) = (1/2) * (0.5 kg) * (-2.0 m/s)^2

The initial mechanical energy (IME) = KE1 + KE2

2. Calculate the final mechanical energy:
After the collision, the two gliders stick together and move with a common velocity. We need to find this common velocity to calculate the final mechanical energy. The equation for finding the common velocity is given by the conservation of momentum:

(m1 * v1) + (m2 * v2) = (m1 + m2) * vf

Substituting the given values:
(0.2 kg * 3.5 m/s) + (0.5 kg * -2.0 m/s) = (0.2 kg + 0.5 kg) * vf

3. Calculate the net mechanical energy:
Once we find the common velocity (vf), we can calculate the final mechanical energy using the equation for kinetic energy.

Mass of the combined gliders after collision = m1 + m2
Final velocity (vf) = obtained from step 2

Final kinetic energy (KEF) = (1/2) * (m1 + m2) * vf^2

The net mechanical energy (NME) = KEF - IME

4. Determine if it is a loss or gain:
If the net mechanical energy is positive, it means there was a gain in mechanical energy after the collision. If the net mechanical energy is negative, it means there was a loss in mechanical energy.

So, calculate the net mechanical energy (NME) and determine if it is a loss or gain.

Use momentum conservation to get the final velocity. Then calculate the new mechanical energy. See for yourself if mechanical energy is lost or gained.