A 32.8 kg child rides a 7.00 kg toboggan down a 12.0 m high snowy hill. If the child starts from rest and has a speed of 7.15 m/s at the bottom of the hill, what is the change in thermal energy of the child on their toboggan and the snow?
original PE=mgh=32.8*9.8*12
final KE=1/2 m v^2=.5*32.8*7.15^2
originalPE-finalKE-heatenergylost=0
solve for heatenergylost
To find the change in thermal energy of the child and the toboggan, we need to calculate the initial potential energy, final kinetic energy, and any potential energy that gets converted into thermal energy.
Step 1: Calculate the initial potential energy (PE_initial) of the child and the toboggan using the formula:
PE_initial = m * g * h
Where:
m = total mass of the child and toboggan = mass_child + mass_toboggan
g = acceleration due to gravity = 9.8 m/s^2 (approximately)
h = height of the hill = 12.0 m
mass_child = 32.8 kg
mass_toboggan = 7.00 kg
PE_initial = (32.8 kg + 7.00 kg) * 9.8 m/s^2 * 12.0 m
PE_initial = 39.8 kg * 9.8 m/s^2 * 12.0 m
Step 2: Calculate the final kinetic energy (KE_final) of the child and the toboggan using the formula:
KE_final = (1/2) * m * v^2
Where:
m = total mass of the child and toboggan = mass_child + mass_toboggan
v = final velocity of the child and toboggan at the bottom of the hill = 7.15 m/s
KE_final = (1/2) * (32.8 kg + 7.00 kg) * (7.15 m/s)^2
KE_final = (1/2) * 39.8 kg * (7.15 m/s)^2
Step 3: Calculate the change in thermal energy (ΔE_thermal) using the equation:
ΔE_thermal = PE_initial - KE_final
Now, let's substitute the calculated values into the formula:
ΔE_thermal = (39.8 kg * 9.8 m/s^2 * 12.0 m) - [(1/2) * 39.8 kg * (7.15 m/s)^2]