Question

what is the TME of a 575 kg roller coaster car that is at rest 50 m above the lowest point on the ride? The maximum possible speed of the roller coaster is 31.3 m/s.

Answer 1

The total mechanical energy is $2.82\cdot 10^5 J$

Explanation:

The total mechanical energy (TME) of an object is equal to the sum of its gravitational potential energy (U) and its kinetic energy (K):

$TME = U + K$

When the car is at rest 50 m above the ground, its speed is zero, therefore its kinetic energy is zero as well:

K = 0

This means that the TME is just equal to the gravitational potential energy:

$TME=U=mgh$

where:

m is the mass of the car

$g=9.8 m/s^2$ is the acceleration of gravity

h is the height above the ground

For the car in the problem,

m = 575 kg

h = 50 m

Substituting,

$TME=(575)(9.8)(50)=2.82\cdot 10^5 J$

Learn more about gravitational potential energy:

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