Question

A child and sled with a combined mass of 50 kg, start from rest and slide down a frictionless hill that is 7.5 meters high. what is the mechanical energy of the sled at the top? what is the mechanical energy of the sled at the bottom? what is the speed of the sled at the bottom of the hill

Answer 1

The mechanical enegia is the sum of the kinetic energy plus the potential energy
 Kinetic energy = (1/2) * m * v ^ 2
 Potential energy = m * g * h
 Mechanical energy = (1/2) * m * v ^ 2 + m * g * h
 What is the mechanical energy of the sled at the top? 
 Mechanical energy = (1/2) * m * v ^ 2 + m * g * h
 Mechanical energy = (1/2) * (50) * (0) ^ 2 + (50) * (9.8) * (7.5) = 3675
 Mechanical energy = 3675J
 What is the mechanical energy of the sled at the bottom? 
 By conservation of energy we have that the energy in point 1 is equal to the energy in point 2
 Mechanical energy = 3675J
 What is the speed of the sled at the bottom of the hill?
 Mechanical energy = 3675J = (1/2) * m * v ^ 2
 clearing up v we have
 (1/2) * (50) * v ^ 2 = 3675
 v ^ 2 = 3675 * (2) * (1/50)
 v = root (3675 * (2) * (1/50)) = 12.12 m / s
 answer
 3675J
 3675J
 12.12 m / s