In the amusement park ride known as Magic Mountain Superman, powerful magnets accelerate a car and its riders from rest to 37.1 m/s in a time of 6.28 s. The mass of the car and riders is 8.88 × 103 kg. Find the average net force exerted on the car and riders by the magnets.
To find the average net force exerted on the car and riders by the magnets, you can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:
Net force = mass × acceleration
In this case, the acceleration can be found by using the equation of motion:
v = u + at
where,
v = final velocity (37.1 m/s)
u = initial velocity (0 m/s)
t = time (6.28 s)
Rearranging the equation, we can solve for acceleration:
a = (v - u) / t
Substituting the given values:
a = (37.1 m/s - 0 m/s) / 6.28 s
Next, calculate the acceleration:
a = 37.1 m/s / 6.28 s
Now that we have the acceleration, we can calculate the net force using the formula:
Net force = mass × acceleration
Substituting the given mass:
Net force = 8.88 × 10^3 kg × (37.1 m/s) / 6.28 s
Calculating the net force:
Net force = 5.27 × 10^4 N
Therefore, the average net force exerted on the car and riders by the magnets is 5.27 × 10^4 N.