A 32.0 kg child descends a slide 4.00 m high. She reaches the bottom with a speed of 2.40 m/s, was the mechanical energy conserved? Explain your reasoning and identify the energy transformations involved.

ΔPE =m•g•Δh-0 = 32•9.8•4 =1254 J,

ΔKE =0 - m•v²/2 = - 32•(2.4)²/2 = -92.15J.
If the energy is conserved, ΔPE = - ΔKE.
They are not equal; therefore, the part of energy was lost, most likely, for friction.

To determine whether mechanical energy was conserved, we need to analyze the energy transformations involved in the situation.

Mechanical energy is the sum of potential energy and kinetic energy. In this case, the potential energy at the top of the slide is given by the formula PE = mgh, where m is the mass (32.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (4.00 m). Substituting the values, we find that the potential energy at the top is PE = (32.0 kg)(9.8 m/s^2)(4.00 m) = 1254.4 J.

At the bottom of the slide, the child has a speed of 2.40 m/s. The kinetic energy is given by the formula KE = (1/2)mv^2, where m is the mass and v is the velocity. Substituting the values, we find that the kinetic energy at the bottom is KE = (1/2)(32.0 kg)(2.40 m/s)^2 = 92.16 J.

Now let's compare the initial potential energy to the final kinetic energy. The potential energy at the top was 1254.4 J, while the kinetic energy at the bottom is 92.16 J. As we can see, the final kinetic energy is significantly lower than the initial potential energy.

Therefore, mechanical energy was not conserved in this situation. The energy transformation involved in this scenario is the conversion of potential energy to kinetic energy as the child descends the slide. The loss of mechanical energy can be attributed to various factors such as friction, air resistance, and sound.