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

Answer:

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

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:

$a = \frac{v_{f}-v_{o}}{t}$ (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 $v_{o} = 0\,\frac{m}{s}$, $v_{f} = 45\,\frac{m}{s}$ and $t = 6.8\,s$, the average acceleration of the car is:

$a = \frac{45\,\frac{m}{s}-0\,\frac{m}{s}}{6.8\,s}$

$a = 6.618\,\frac{m}{s^{2}}$

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 $a = 6.618\,\frac{m}{s^{2}}$, the net force exerted on the car and riders is:

$F = (5100\,kg)\cdot \left(6.618\,\frac{m}{s^{2}} \right)$

$F = 33751.8\,N$

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