A&L ENGINEERING
Roller Coaster Design Report
Coaster Design Diagram
Kinetic Energy, Potential Energy, and Momentum Calculations
Potential Energy:
Mass of cart: 500kg
Gravity:
Point 1: 75m, PE is 367500J
Point 2: 25m, PE is 122500J
Point 3: 55 m, PE is 269500J
Point 4: 20m, PE is 98000J
Kinetic Energy:
Kinetic Energy is determined with the following equation:
∆ h=Change∈height
Point 1:367500J
Point 2: 122500J
Point 3:269500J
Point 4:98000J
Velocity (because in order to find momentum we need the velocity):
Point 1: 38.34 m/s
Point 2: 22.41 m/s
Point 3:24.25 m/s
Point 4: 32.83 m/s
Momentum:
19170kg *m/s
11205kg*m/s
12125kg*m/s
16415kg*m/s
Energy Descriptions
At each of the identified points, how was kinetic energy transferred to potential
energy, and vice versa?
At the start of the track the cart is actually storing energy in the form of potential
energy. As the cart continues down the track the potential energy is then converted into
kinetic energy. So when the cart gets to the top of each valley it has more potential
energy and very little kinetic energy. So when the cart goes down into the bottom of a
valley and that potential energy is turned into kinetic energy leaves the cart with more
kinetic energy and very little potential energy once it is at the bottom.
What happens to the total energy of the cart as it moves along the track? Why?
As the cart moves through the track the energy is transferred between kinetic and
potential energy with very little energy lost due to friction. Which means that the
energy remains constant just fluctuating between the two kinetic and potential.
How is the principle of conservation of energy applied in this situation?
The principle of conservation is applied as the energy remains constant with no
creation or destruction of energy as the cart moves.
Collision Calculations
Given Information:
Mass of each cart: 500 kg
Velocity of first cart prior to collision:32.83m/s
Momentum prior to collision: (p=mv)
Cart 1: 500*32.83=16415 kg*m/s
Cart 2: 500*0=0 kg*m/s
Momentum combined prior to collision: 16415+0=16415 kg*m/s
Momentum post collision: (p=mv)
Going to assume that the carts stick together after they collide to make the total mass
1000kg
Total momentum post collision is: 16.42 m/s
Kinetic Energy prior to collision:
Cart 1: 98000
Cart 2:0J
Total: 98000J
Kinetic Energy post collision:
KE=
(
1
2
)
mv2
KE=
(
1
2
)
1000∗98002
=538904m/s
Collision Descriptions
What was the kinetic energy of each cart before and after the collision?
The kinetic energy prior to collision of cart 1 is 98000J and cart 2 is 0 as it is stationary
and unmoving meaning it is at rest with no kinetic energy. The cart is brought to 0
from the 98000J.
What happens to the total energy of the system, now including both carts, as a
result of the inelastic collision?
The total energy of the cart decreases as the kinetic energy is converted into other
forms of energy.
Describe how the principle of conservation of energy is applied in this situation.
In this situation I feel that when the cart comes to a halt the potential energy and
kinetic energy is lost losing the option of conservation of energy being applied.
References
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