Question

A roller coaster features a near vertical drop of 95 meters. If the initial velocity was zero, the mass of the cart and riders was 1,000 kg, and the velocity at the end of the drop was 35 m/s, how much of the potential energy was converted into thermal energy?319 kJ218 kJ342 kJ276 kJ

Answer 1

Given:

• Vertical drop = 95 meters

,

• Initial velocity = 0 m/s

,

• Mass of cart and riders = 1000 kg

,

• Final velocity = 35 m/s

Let's find the amount of potential energy converted to thermal energy.

For the potential energy, we have:

PE = mgh

Also thermal energy is a form of kinetic energy.

Thus, for the thermal energy, we have:

`KE=(1)/(2)mv^2`

Now, to find the difference, we have:

`\begin{gathered} PE-KE \\ \\ =(\text{mgh)}-((1)/(2)mv^2) \end{gathered}`

Where:

g is acceleration due to gravity = 9.8 m/s^2

v is the final velocity = 35 m/s

h is the height = 95 meters

m is the mass

Thus, we have:

`\begin{gathered} (1000*9.8*95)-((1)/(2)*1000*35^2) \\ \\ =931000-612500 \\ \\ =318500\text{ J }\approx319000\text{ }\approx319\text{ kJ} \end{gathered}`

Therefore, the amount of potential energy converted into thermal energy is 319 kiloJoules.

ANSWER:

319 kJ