alculate the final speed of a 1500 kg roller coaster if it has an initial speed of 16 m/s but reduces its elevation by 8.6 m by coasting down a frictionless incline.
final KE=Intial KE+initial PE
1/2 m v^2= 1/2 m 16^2 + mg 8.6
solve for v
what mass do i use?
doesn matter, it divides out. If you want, use 1500kg
To calculate the final speed of the roller coaster, we can use the conservation of energy principle. The initial potential energy (due to the elevation) is converted into final kinetic energy (due to the motion) of the roller coaster.
1. Find the initial potential energy (PE_initial) of the roller coaster:
PE_initial = mass * gravitational acceleration * height
PE_initial = 1500 kg * 9.8 m/s^2 * 8.6 m
2. Find the final kinetic energy (KE_final) of the roller coaster:
KE_final = 0.5 * mass * final speed^2
3. Apply the conservation of energy principle:
PE_initial = KE_final
Substitute the values:
1500 kg * 9.8 m/s^2 * 8.6 m = 0.5 * 1500 kg * final speed^2
4. Solve the equation for the final speed (final speed = √(2 * PE_initial / mass)):
final speed = √(2 * (1500 kg * 9.8 m/s^2 * 8.6 m) / 1500 kg)
5. Calculate the final speed:
final speed = √(2 * 1500 kg * 9.8 m/s^2 * 8.6 m / 1500 kg)
= √(2 * 9.8 m/s^2 * 8.6 m)
= √(168.56 m^2/s^2)
≈ 12.99 m/s
Therefore, the final speed of the roller coaster is approximately 12.99 m/s.