Question

Assuming an ideal situation where no energy is lost, calculate the height of the ride at point W if the velocity of the roller coaster car is 23.0 m/s at point X and the mass is 1280 kg

Answer 1

Given data:

* The mass of the coaster car is 1280 kg.

* The velocity of the coaster car at the lowest point is 23 m/s.

Solution:

According to the law of conservation of energy, the potential energy of the car at the maximum height is equal to the kinetic energy of the car at the lowest point.

`U_(\max )=K_(\max )`

where U_max is the potential energy at the maximum height, and K_max is the maximum kinetic energy at the lowest height,

The maximum potential energy in terms of height is,

`U_(\max )=\text{mgh}`

where m is the mass, g is the acceleration due to gravity, and h is the maximum height,

The maximum kinetic energy of the car is,

`K_(\max )=(1)/(2)mv^2`

where m is the mass, and v is the maximum velocity of the body at the lowest point,

Substituting the known values in the conservation equation,

`\begin{gathered} \text{mgh}=(1)/(2)mv^2 \\ gh=(1)/(2)v^2 \\ h=(v^2)/(2g) \\ h=(23^2)/(2*9.8) \\ h=(529)/(19.6) \\ h=26.99 \\ h\approx27\text{ m} \end{gathered}`

Thus, the height of point W is 27 meters.