Jackie who is 20 kg slides down a playground slide that is 10 m high. If she comes to the bottom with a speed of 5.0 m/s, how much energy is lost as heat?
To calculate the amount of energy lost as heat, we need to determine the initial potential energy and the final kinetic energy of Jackie as she slides down the slide. The difference between these energies will give us the energy lost as heat.
First, let's calculate Jackie's initial potential energy at the top of the slide. The potential energy (PE) of an object is given by the formula:
PE = m * g * h
Where:
m is the mass of the object (20 kg)
g is the acceleration due to gravity (9.8 m/s^2)
h is the height of the slide (10 m)
So the initial potential energy (PE_initial) is:
PE_initial = m * g * h = 20 kg * 9.8 m/s^2 * 10 m = 1960 J
Next, let's calculate Jackie's final kinetic energy at the bottom of the slide. The kinetic energy (KE) of an object is given by the formula:
KE = (1/2) * m * v^2
Where:
m is the mass of the object (20 kg)
v is the velocity of the object at the bottom (5.0 m/s)
So the final kinetic energy (KE_final) is:
KE_final = (1/2) * m * v^2 = (1/2) * 20 kg * (5.0 m/s)^2 = 250 J
Finally, we can calculate the energy lost as heat by subtracting the final kinetic energy from the initial potential energy:
Energy lost as heat = PE_initial - KE_final = 1960 J - 250 J = 1710 J
Therefore, the amount of energy lost as heat is 1710 J.