A 21.0-kg child descends a slide 2.20m high and reaches the bottom with a speed of 1.40m/s . How much thermal energy due to friction was generated in this process?
To find the thermal energy due to friction, we need to calculate the work done by friction during the slide descent.
The potential energy (PE) of the child at the top of the slide is given by:
PE = m * g * h
where m is the mass of the child (21.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slide (2.20 m).
Substituting the given values:
PE = 21.0 kg * 9.8 m/s^2 * 2.20 m
= 456.12 J
At the bottom of the slide, the potential energy is converted into kinetic energy (KE). Therefore, we can equate the potential energy at the top to the sum of the kinetic energy (KE) and the work done by friction (Wf):
PE = KE + Wf
Rearranging the equation, we get:
Wf = PE - KE
The kinetic energy (KE) is given by:
KE = (1/2) * m * v^2
where v is the speed of the child at the bottom of the slide (1.40 m/s).
Substituting the given values:
KE = (1/2) * 21.0 kg * (1.40 m/s)^2
= 20.58 J
Now, substituting the values into the equation to calculate the work done by friction:
Wf = 456.12 J - 20.58 J
= 435.54 J
Therefore, the thermal energy due to friction generated in this process is 435.54 Joules.
To determine the thermal energy generated due to friction during the child's descent on the slide, we need to use the principle of conservation of energy.
The total mechanical energy at the top of the slide is equal to the sum of the gravitational potential energy and the kinetic energy at the bottom of the slide.
Gravitational potential energy (PE) is given by the formula: PE = mgh, where m is the mass of the child (21.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slide (2.20 m). So, PE = (21.0 kg)(9.8 m/s^2)(2.20 m) = 456.12 J.
The kinetic energy (KE) at the bottom of the slide is given by the formula: KE = (1/2)mv^2, where m is the mass of the child (21.0 kg), and v is the velocity at the bottom (1.40 m/s). So, KE = (1/2)(21.0 kg)(1.40 m/s)^2 = 20.58 J.
Since there is no external work done on the child during the descent, the total mechanical energy at the top of the slide should be equal to the total mechanical energy at the bottom of the slide, neglecting any energy losses due to friction.
Therefore, the thermal energy due to friction can be calculated as the difference between the initial mechanical energy and the final mechanical energy: Thermal Energy = Initial Mechanical Energy - Final Mechanical Energy.
Thermal Energy = (PE + KE) - KE = PE = 456.12 J
Hence, the thermal energy due to friction generated in this process is 456.12 Joules.