A 35.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 24.00 m. When she is partway down the slide, at a height h2 of 12.00 m, she is moving at a speed of 6.70 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.).

The mechanical energy loss is 3330.425 Joules.

Explanation:

The mechanical energy lost due to the work of non-conservative forces is given by:

Wncf = ΔEm = Emf - Emi

Where Emf is the final mechanical energy and Emi is the initial mechanical energy.

The mechanical energy i:

Em = Ek + Ep

where:

-The kinetic energy:

Ek = 0.5mv² (m is the mass and v is the speed)

-The gravitational potential energy:

Ep = mgh (m is the mass, g the acceleration of gravity and h is the height)

Therefore:

Emi = Eki + Epi

The initial kinetic energy is zero because she starts from rest.

Emi = Epi = mgh1

Emi = (35.0) (9.8) (24.00)

Emi = 8232 Joules.

Emf = Ekf + Epf = 0.5mv² + mgh2

Emf = 0.5 (35.0) (6.70) ² + (35.0) (9.8) (12.00)

Emf = 4901.575 Joules.

The variation of mechanical energy is:

Emf - Emi = 4901.575 - 8232 = - 3330.425 J

Therefore the loss is 33340.425 J