An 84 kg child descends a slide 7.2 m high and reaches the bottom with a speed of 3.30 m/s. How much thermal energy (in joules) due to friction was generated in this process?
69 J
To calculate the amount of thermal energy generated due to friction, we need to use the principle of conservation of mechanical energy. The initial mechanical energy of the child at the top of the slide (potential energy) is converted into the final mechanical energy at the bottom (kinetic energy) and thermal energy due to friction.
First, let's calculate the potential energy of the child at the top of the slide:
Potential Energy = mass * gravity * height
Potential Energy = 84 kg * 9.8 m/s² * 7.2 m
Next, let's calculate the kinetic energy of the child at the bottom of the slide:
Kinetic Energy = 0.5 * mass * velocity^2
Kinetic Energy = 0.5 * 84 kg * (3.30 m/s)^2
Now, to find the thermal energy due to friction, we subtract the final mechanical energy (kinetic energy) from the initial mechanical energy (potential energy) because the difference is the energy lost to friction:
Thermal Energy = Potential Energy - Kinetic Energy
Substituting the values we calculated earlier:
Thermal Energy = (84 kg * 9.8 m/s² * 7.2 m) - (0.5 * 84 kg * (3.30 m/s)^2)
Solving this equation will give you the amount of thermal energy generated in joules.