Question

A 30-kg child sits at the top of a 3-meter slide. After sliding down, the child is traveling 4 m/s. How much PE does he start with? How much KE does he end with? How much energy is lost to friction?

Answer 1

Potential Energy: E=mgh
Kinetic Energy: E=1/2mv^2
m= mass
g= gravity constant (9.8)
h= height
v= velocity

882 J of potential energy at the top of the slide (stationary)240 J of kinetic energy at the bottom of the slide (constant acceleration)
882-240 J= 642J of energy is lost to friction as the child would slow down and eventually stop at the bottom of the slide using its feet or hands (friction) so there is less kinetic energy. The child would have its feet on the ground therefore there is no height value for the potential energy equation, therefore meaning there would be no potential energy.

Answer 2

Explanation:

It is given that,

Mass of the child, m = 30 kg

It sits at a height, h = 3 m

Speed of child, v = 4 m/s

1. The potential energy at the start is given by :

$P=mgh$

$P=30\times 9.8\times 3$

P = 882 J

2. Kinetic energy at the end is given by :

$K=\dfrac{1}{2}mv^2$

$K=\dfrac{1}{2}\times 30\times 4^2$

K = 240 J

3. Energy lost due to friction,

$\Delta E=P-K$

$\Delta E=882-240$

$\Delta E=642\ J$

Hence, this is the required solution.