PHY-150 Module 7 Project 3
Energy and Momentum
A&L Engineering: Roller Coaster Design Report
Height P1: 75m V1: 0m P2: 50m V2: 0m P3: 30m
Potential Energy 367,500 J 0J 245,000 J 0J 147,000 J
Kinetic Energy 0J 367,500 J 122,500 J 367,500 J 220,500 J
Velocity 0 m/s 38.34 m/s 22.14 m/s 38.34 m/s 29.70 m/s
Momentum 0 kg m/s 19,170 kg m/s 11,070 kg m/s 19,170 kg m/s 14,850 kg m/s
Calculating the Data
The total energy remains constant. There is no friction or air resistance. At the launch point, the
cart is at rest and all energy is potential energy. So, at this point, potential energy is equal to total
energy. We would use the same equation to find the potential energy at each additional valley
and peak.
PE = mgh
PE = 500 kg * 9.8 m/s2 * 75 m
PE = 367,500 J
Kinetic energy can be solved by remembering that Total Energy = Potential Energy + Kinetic
Energy (TE = PE + KE). Solve for KE by rearranging the equation to KE = TE – PE.
Velocity is unknown, but we can solve for it by using the equation MgH = mgh + ½mv2 where TE =
MgH and PE = mgh. The initial velocity is 0 but use the same steps to calculate the additional
velocities.
At the launch point:
367,500 J = 367,500 J + ½(500 kg)(v2)
367,500 = 367,500 + 250v2 Subtract 367,500 from both sides.
0 = 250v2 Divide 250 from both sides.
v =0
2 Square root both sides.
v = 0 m/s
Momentum is calculated by multiplying velocity by mass.
PHY-150 Module 7 Project 3 Energy and Momentum
Energy and Momentum
A&L Engineering: Roller Coaster Design Report
Height P1: 75m V1: 0m P2: 50m V2: 0m P3: 30m
Potential Energy 367,500 J 0J 245,000 J 0J 147,000 J
Kinetic Energy 0J 367,500 J 122,500 J 367,500 J 220,500 J
Velocity 0 m/s 38.34 m/s 22.14 m/s 38.34 m/s 29.70 m/s
Momentum 0 kg m/s 19,170 kg m/s 11,070 kg m/s 19,170 kg m/s 14,850 kg m/s
Calculating the Data
The total energy remains constant. There is no friction or air resistance. At the launch point, the
cart is at rest and all energy is potential energy. So, at this point, potential energy is equal to total
energy. We would use the same equation to find the potential energy at each additional valley
and peak.
PE = mgh
PE = 500 kg * 9.8 m/s2 * 75 m
PE = 367,500 J
Kinetic energy can be solved by remembering that Total Energy = Potential Energy + Kinetic
Energy (TE = PE + KE). Solve for KE by rearranging the equation to KE = TE – PE.
Velocity is unknown, but we can solve for it by using the equation MgH = mgh + ½mv2 where TE =
MgH and PE = mgh. The initial velocity is 0 but use the same steps to calculate the additional
velocities.
At the launch point:
367,500 J = 367,500 J + ½(500 kg)(v2)
367,500 = 367,500 + 250v2 Subtract 367,500 from both sides.
0 = 250v2 Divide 250 from both sides.
v =0
2 Square root both sides.
v = 0 m/s
Momentum is calculated by multiplying velocity by mass.
PHY-150 Module 7 Project 3 Energy and Momentum
