An object of mass 3.06 kg is released from rest and drops 1.75 m to the floor. The collision is completely inelastic. How much kinetic energy is lost during the collision?

To determine the amount of kinetic energy lost during the collision, we first need to calculate the initial kinetic energy and the final kinetic energy.

1. Calculate initial kinetic energy:
The object is released from rest, so its initial velocity is 0 m/s. The formula for kinetic energy is given by:
Kinetic Energy = 0.5 * mass * velocity^2

Since the initial velocity is 0, the initial kinetic energy will be 0 as well.

2. Calculate final kinetic energy:
The object drops 1.75 m to the floor, and the collision is completely inelastic. In an inelastic collision, kinetic energy is not conserved and is converted into other forms of energy, such as heat or sound.

As the object drops, its potential energy is converted into kinetic energy. The formula for potential energy is given by:
Potential Energy = mass * gravity * height

Using the given values:
Potential Energy = 3.06 kg * 9.8 m/s^2 * 1.75 m

Simplifying:
Potential Energy = 49.2435 Joules

Since the collision is completely inelastic, we assume that all the initial potential energy is converted into final kinetic energy. Therefore, the final kinetic energy will be equal to the potential energy just before the collision.

3. Calculate the kinetic energy lost during the collision:
The kinetic energy lost during the collision will be the difference between the initial kinetic energy and the final kinetic energy.

Kinetic Energy Lost = Initial Kinetic Energy - Final Kinetic Energy
= 0 - Potential Energy
= -49.2435 Joules

The kinetic energy lost during the collision is -49.2435 Joules. The negative sign indicates that energy is lost during the collision.