A roller coaster car of mass 850 kg is released from the track at point a, calculate the velocity of the roller coaster car at point b assuming there is no friction and no air resistance
Answers
Explanation:
Assuming no friction between the roller coaster car and the hill, and neglecting air resistance, the kinetic energy the roller coaster car would have at the bottom of the hill would be equal to its gravitational potential energy at the top of the hill, by conservation of energy.
At the top of the hill, the roller coaster car only contains potential energy as it is perfectly still, so its total mechanical energy at the top of the hill would be in the form of only potential energy.
At the bottom of the hill, this potential energy would have converted all into kinetic energy, because there are, in this highly ideal situation, no energy losses due to friction.
The law of conservation of mechanical energy states that the total mechanical energy in a system is always conserved.
Let
K
E
denote Kinetic Energy
As an equation, the relationship would be:
m
g
h
=
1
2
m
v
2
OR
K
E
=
m
g
h
Assuming the acceleration due to gravity near the earth's surface is
9.81
m
s
, our equation becomes:
K
E
=
500
k
g
⋅
9.81
m
s
⋅
30
m
K
E
=
147150
Joules
Therefore, as the cart approaches the bottom of the hill where its gravitational potential energy is converted into kinetic energy, the amount of kinetic energy it would have would be equal to its potential energy at the start.
The cart would have 147150 Joules of Kinetic Energy at the bottom of the hill.