Answer:
60008.4 J
Explanation:
The mass of each kid = 30 kg
mass of the cart = 20 kg
The speed of the cart down the hill = 30 km/hr = 30 x 1000/3600 = 8.33 m/s
The height of the hill = 80 m
The potential energy of the boys at the top of the hill = mgh
where
m is the total mass of the kids and the cart = (30 x 2) + 20 = 80 kg
g is the acceleration due to gravity = 9.81 m/s^2
h is their height above the ground = 80 m (on the top of the hill)
substituting, we have
potential energy PE = 80 x 9.81 x 80 = 62784 J
At an instance at the bottom of the hill
their kinetic energy = [tex]\frac{1}{2} mv^2[/tex]
where
v is their velocity = 8.33 m/s
m is their total mass = 80 kg
substituting, we have
kinetic energy KE = [tex]\frac{1}{2}*80*8.33^2[/tex] = 2775.6 J
Total work done on the cart is equal to the energy lost by the cart when it reached the bottom of the hill
work done by friction = PE - KE = 62784 - 2775.6 = 60008.4 J
