A children’s roller coaster is released from the top of a track. If its maximum speed at ground level is 8 m/s, find the height it was released from.
(1/2)MVmax^2 = M g H
Cancel out the M's and solve for H.
(This neglects friction and extra rotational kinetic energy of the wheels. It will give you an approximate answer that is an upper bound)
I’m tryna figure out what type of energy that problem is
To find the height the children's roller coaster was released from, we can apply the principle of conservation of energy.
The total energy of the roller coaster at the top of the track can be calculated as the sum of its potential energy (due to its height) and its kinetic energy (due to its velocity).
At the top of the track, when the roller coaster is released, its potential energy is maximum because it is at the highest point. At ground level, its potential energy is zero.
1. Calculate the kinetic energy at ground level using the maximum speed:
Kinetic energy = (1/2) * mass * velocity^2
Let's assume the mass of the roller coaster is 'm'.
Given velocity at ground level: 8 m/s
Kinetic energy at ground level = (1/2) * m * (8^2)
2. Equate the potential energy at the top of the track to the kinetic energy at ground level:
Potential energy at the top = Kinetic energy at ground level
Let's assume the height at the top of the track is 'h'.
Potential energy at the top = m * g * h (where g is the acceleration due to gravity, approximately 9.8 m/s^2)
Equating the two energies: m * g * h = (1/2) * m * (8^2)
3. Solve for the height 'h':
h = (1/2) * (8^2) / g
h = 32 / 9.8
h ≈ 3.27 meters
Therefore, the children's roller coaster was released from a height of approximately 3.27 meters.
To find the height at which the children's roller coaster was released, you can use the principle of conservation of energy.
The total mechanical energy of the roller coaster at the top is equal to the total mechanical energy at the bottom of the track. The total mechanical energy consists of the potential energy (PE) and the kinetic energy (KE) of the roller coaster.
At the top of the track, the roller coaster only has potential energy, which is given by the formula:
PE = m * g * h,
where m is the mass of the roller coaster, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height.
At the bottom of the track, the roller coaster has both potential energy and kinetic energy, which is given by the formula:
KE = 0.5 * m * v²,
where v is the maximum speed of the roller coaster at ground level.
Since the total mechanical energy is conserved, we can equate the potential energy at the top with the sum of potential and kinetic energy at the bottom:
m * g * h = 0.5 * m * v².
The mass of the roller coaster cancels out from both sides of the equation, simplifying it to:
g * h = 0.5 * v².
Now, we can solve for the height by rearranging the equation:
h = (0.5 * v²) / g.
Plugging in the given values, with v = 8 m/s and g = 9.8 m/s², we can calculate the height:
h = (0.5 * 8²) / 9.8 = 32 / 9.8 ≈ 3.27 meters.
Therefore, the roller coaster was released from a height of approximately 3.27 meters.