Question

In the amusement park ride known as Magic Mountain Superman, powerful magnets accelerate a car and its riders from rest to 45 m/s (around 100 mi/h) in a time of 6.8 s. The mass of the car and riders is 5100 kg. Find the average net force exerted on the car and riders by the magnets.

Answer 1

The average net force exerted on the car and riders by the magnets is 33751.8 newtons.

Step-by-step explanation:

Let assume that car and its riders accelerate at constant rate, such that acceleration (
`a`), measured in meters per square second, can be found by using the following kinematic equation:

`a = (v_(f)-v_(o))/(t)` (Eq. 1)

Where:

`v_(o)`,
`v_(f)` - Initial and final speeds of the car and its riders, measured in meters per second.

`t` - Acceleration time, measured in seconds.

If we know that
`v_(o) = 0\,(m)/(s)`,
`v_(f) = 45\,(m)/(s)` and
`t = 6.8\,s`, the average acceleration of the car is:

`a = (45\,(m)/(s)-0\,(m)/(s))/(6.8\,s)`

`a = 6.618\,(m)/(s^(2))`

By the Second Newton's Law, we find that average force exerted on the car and riders by the magnets (
`F`), measured in newtons, is:

`F = m\cdot a` (Eq. 2)

Where
`m` is the mass of the car-riders system, measured in kilograms.

If we know that
`m = 5100\,kg` and
`a = 6.618\,(m)/(s^(2))`, the net force exerted on the car and riders is:

`F = (5100\,kg)\cdot \left(6.618\,(m)/(s^(2)) \right)`

`F = 33751.8\,N`

The average net force exerted on the car and riders by the magnets is 33751.8 newtons.