A 63 kg child descends a slide 7.6 m high and reaches the bottom with a speed of 3.20 m/s. How much thermal energy (in joules) due to friction was generated in this process?
PE = M*g * h = 63*9.8 * 7.6 = 4692 J.
KE = 0.5M*V^2 = 0.5 * 63 * 3.2^2 = 323 J.
4692 - 323 = 4369 J. loss.
To calculate the thermal energy generated due to friction, you can use the conservation of mechanical energy. The child's potential energy at the top of the slide is converted to kinetic energy at the bottom, and the difference between these two energies represents the thermal energy generated.
The potential energy (PE) of the child at the top of the slide is given by the equation:
PE = mgh
Where:
m = mass of the child = 63 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height of the slide = 7.6 m
PE = 63 kg * 9.8 m/s^2 * 7.6 m
PE = 4632.24 J
The final kinetic energy (KE) of the child at the bottom of the slide is given by the equation:
KE = 1/2 mv^2
Where:
m = mass of the child = 63 kg
v = velocity of the child = 3.20 m/s
KE = 1/2 * 63 kg * (3.20 m/s)^2
KE = 3225.60 J
The thermal energy generated due to friction is given by the difference between the initial potential energy (PE) and the final kinetic energy (KE):
Thermal energy generated = PE - KE
Thermal energy generated = 4632.24 J - 3225.60 J
Thermal energy generated = 1406.64 J
Therefore, the amount of thermal energy (due to friction) generated in this process is approximately 1406.64 joules.
To calculate the amount of thermal energy generated due to friction, we need to use the principle of conservation of energy. The initial potential energy when the child starts sliding down the slide is converted into kinetic energy at the bottom. However, some energy is lost as thermal energy due to friction.
The formula for potential energy is: PE = m * g * h
where PE is the potential energy, m is the mass of the child, g is the acceleration due to gravity, and h is the height of the slide.
The formula for kinetic energy is: KE = 0.5 * m * v^2
where KE is the kinetic energy, m is the mass of the child, and v is the velocity of the child.
Using these formulas, we can calculate the initial potential energy (PE_initial), final kinetic energy (KE_final), and the change in thermal energy (ΔE_thermal).
First, let's calculate the initial potential energy:
PE_initial = m * g * h
= 63 kg * 9.8 m/s^2 * 7.6 m
≈ 4526.88 J
Next, let's calculate the final kinetic energy:
KE_final = 0.5 * m * v^2
= 0.5 * 63 kg * (3.20 m/s)^2
≈ 322.56 J
Now, let's calculate the change in thermal energy:
ΔE_thermal = PE_initial - KE_final
= 4526.88 J - 322.56 J
≈ 4204.32 J
Therefore, the amount of thermal energy due to friction generated in this process is approximately 4204.32 joules.