Question

A 24kg child descends a slide 5m high and reaches the bottom with a speed of 2.8m/s. How much thermal energy due to friction was generated in this process?

Answer 1

To calculate the thermal energy due to friction generated during the child's descent down the slide, we need to calculate the potential energy and kinetic energy of the child. The thermal energy due to friction can be found by subtracting the kinetic energy from the potential energy.

Step-by-step explanation:

To calculate the thermal energy due to friction generated during the child's descent down the slide, we need to first calculate the potential energy the child had at the top of the slide and then subtract the kinetic energy the child had at the bottom of the slide. Potential energy is given by the formula PE = mgh, where m is the mass of the child, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the slide. Kinetic energy is given by the formula KE = (1/2)mv², where v is the velocity of the child at the bottom of the slide.

First, calculate the potential energy: PE = (24 kg)(9.8 m/s²)(5 m) = 1176 J

Next, calculate the kinetic energy: KE = (1/2)(24 kg)(2.8 m/s)² = 117.6 J

Finally, subtract the kinetic energy from the potential energy to find the thermal energy due to friction: 1176 J - 117.6 J = 1058.4 J.

Answer 2

1081.9 J

Step-by-step 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:

`E_i = U = mgh = (24)(9.8)(5)=1176 J`

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

`E_f = K = (1)/(2)mv^2=(1)/(2)(24)(2.8)^2=94.1 J`

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:

`\Delta E = 1176 - 94.1=1081.9 J`