Question

A 36.0 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 11.00 m, she is moving at a speed of 7.80 m/s.

Calculate the mechanical energy lost due to friction (as heat, etc.).

Answer 1

E = 3495.96 J

Step-by-step explanation:

From the law of conservation of energy:

Total Mechanical Energy at h1 = Total Mechanical Energy at h2

Kinetic energy at h1 + potential energy at h1 = Kinetic energy at h2 + potential energy at h2 + Mechanical Energy Lost due to Friction

`K.E_(h1)+P.E_(h1) = K.E_(h2)+P.E_(h2) + E\\\\(1)/(2)mv_1^2\ J + mgh_1 = (1)/(2)mv_2^2 + mgh_2 + E\\\\(1)/(2)(36\ kg)(0\ m/s)_1^2\ J + (36\ kg)(9.81\ m/s^2)(24\ m)_1 = (1)/(2)(36\ kg)(7.8\ m/s)_2^2 + (36\ kg)(9.81\ m/s^2)(11\ m)_2 + E\\\\0\ J + 8475.84\ J = 1095.12\ J + 3884.76\ J + E\\E = 8475.84\ J - 1095.12\ J - 3884.76\ J\\`

E = 3495.96 J