A girl on a sled with a total mass of 90kg starts from an elevation of 100meters. At the bottom of the run her speed is 30m/s. How much energy in joules was lost due to
friction?
Potential energy drop = m g h =90*9.81*100
= 88,290 Joules
Kinetic energy = (1/2) m v^2 = 45(900) = 40,500 Joules
so
loss to heat = difference = 47,790 Joules
To calculate the energy lost due to friction, we need to find the potential energy at the starting point and the kinetic energy at the bottom of the run, and then calculate the difference.
1. Calculate the potential energy (PE) at the starting point:
PE = mgh
where m is the mass (90 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (100 meters).
PE = (90 kg) x (9.8 m/s^2) x (100 m)
PE = 88,200 joules
2. Calculate the kinetic energy (KE) at the bottom of the run:
KE = 0.5mv^2
where m is the mass (90 kg) and v is the velocity (30 m/s).
KE = 0.5 x (90 kg) x (30 m/s)^2
KE = 40,500 joules
3. Calculate the energy lost due to friction:
Energy Lost = PE - KE
Energy Lost = 88,200 joules - 40,500 joules
Energy Lost = 47,700 joules
Therefore, the amount of energy lost due to friction is 47,700 joules.