Answer:
1081.9 J
Explanation:
In order to calculate how much energy is converted into thermal energy due to friction, we have to calculate the difference between the mechanical energy of the child at the top and at the bottom of the slide.
At the top of the slide, he is at rest, so its kinetic energy is zero, and so he only has gravitational potential energy. Therefore:
[tex]E_i = U = mgh = (24)(9.8)(5)=1176 J[/tex]
where
m = 24 kg is the mass of the child
g = 9.8 m/s^2 is the acceleration of gravity
h = 5 m is the height relative to the ground
At the bottom of the slide, the child has only kinetic energy, so its total energy is
[tex]E_f = K = \frac{1}{2}mv^2=\frac{1}{2}(24)(2.8)^2=94.1 J[/tex]
where
v = 2.8 m/s is the final speed of the child
Therefore, the therma energy generated due to friction is equal to the difference between the initial and final energy:
[tex]\Delta E = 1176 - 94.1=1081.9 J[/tex]
