El Toro is the third tallest wooden roller coaster in the world. It has a drop of 55 meters. One empty cart has a mass of 958 kg and 511,000 J of kinetic energy when it reaches the base level of the track.

How much energy is converted into heat when the cart is at the base level of the track?

Show your work and give your answer with the correct units.

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Steps:

1. Calculate the gravitational potential energy (GPE) at the top of the drop using the formula:
[tex]\[ \text{GPE} = mgh \][/tex]
where:
- \( m \) is the mass of the cart (958 kg)
- \( g \) is the acceleration due to gravity (\(9.8 \, \text{m/s}^2\))
- \( h \) is the height of the drop (55 meters)

2. Calculate the kinetic energy (KE) at the base level given as 511,000 J.

3. Determine the energy converted into heat by subtracting the kinetic energy from the gravitational potential energy.

[tex]\[ \text{Energy converted to heat} = \text{GPE} - \text{KE} \][/tex]

Note: Show all calculations step-by-step for full credit.



Answer :

Final answer:

The conversion of kinetic energy to heat energy in a roller coaster cart is determined by using the conservation of energy principle.


Explanation:

Kinetic energy is converted into heat when the roller coaster cart reaches the base. Using the principle of conservation of energy, the initial kinetic energy is equal to the sum of potential energy at the top and the kinetic energy at the base level.

This can be calculated as: Potential Energy at the top = Kinetic Energy at the base + Heat Energy

Substitute the values given and solve for Heat Energy to find out the energy converted into heat.


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