Question

A 31.0kg child slides down a long slide in a playground. She starts from test at a height of 18.00m. When she is partway down the slide, at a height of 8.00m, she is moving at a speed of 7.70m/s. Calculate the mechanical energy lost due to friction

Answer 1

Given:

Mass = 31.0 kg

Height = 18.00 m

FInal height = 8.00 m

Speed, v = 7.70 m/s

Let's find the mechanical energy lost due to friction.

Apply the conservation of mass:

`(1)/(2)mv^2=mg\Delta h`

Total mechanical energy at the point 1.

E = PE + KE

`\begin{gathered} E=\text{mgh}+(1)/(2)mu^2 \\ \\ E=(31*9.8*18)+((1)/(2)*21*0) \\ \\ E_1=5468.4\text{ J} \end{gathered}`

Total mechanical energy at point 2:

`\begin{gathered} E=mgh_2+(1)/(2)mv^2 \\ \\ E=(31*9.8*8)+((1)/(2)*31*7.7^2) \\ \\ E=2430.4+918.995 \\ \\ E_2=3349.395\text{ J} \end{gathered}`

To find the energy lost due to friction , apply the formula:

Energy lost = E1 - E2

Energy lost = 5468.4 - 3349.395 = 2119.0 J

Therefore, the mechanical energy lost due to friction is 2119 J

ANSWER:

2119 J