In the amusement park ride known as Magic Mountain Superman, powerful magnets accelerate a car and its riders from rest to 33.9 m/s in a time of 6.02 s. The mass of the car and riders is 1.64 × 103 kg. Find the average net force exerted on the car and riders by the magnets.
Vo = 0
V = 33.9 m/s.
t = 6.02 s.
m = 1640 kg
F = ?
a = (V-Vo)/t = (33.9-0)/6.02 = 5.63 m/s^2.
F = m*a = 1640 * 5.63 = 9235 N.
To find the average net force exerted on the car and riders by the magnets, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, we need to find the acceleration of the car and riders. We can use the equation of motion:
v = u + at
Where:
v = final velocity = 33.9 m/s (given)
u = initial velocity = 0 m/s (since the car starts from rest)
a = acceleration (unknown)
t = time = 6.02 s (given)
Rearranging the equation, we have:
a = (v - u) / t
Substituting the given values:
a = (33.9 m/s - 0 m/s) / 6.02 s
a = 5.64 m/s^2
Now that we have the acceleration, we can calculate the average net force using Newton's second law:
F = m * a
Where:
F = net force (unknown)
m = mass of the car and riders = 1.64 × 103 kg (given)
a = acceleration = 5.64 m/s^2 (calculated)
Substituting the values:
F = (1.64 × 103 kg) * (5.64 m/s^2)
F = 9265.6 N
Therefore, the average net force exerted on the car and riders by the magnets is 9265.6 Newtons.
Step 1: Calculate the acceleration of the car and riders.
Acceleration can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (v0) = 0 m/s (since the car starts from rest)
Final velocity (v) = 33.9 m/s
Time (t) = 6.02 s
Acceleration (a) = (33.9 m/s - 0 m/s) / 6.02 s
= 33.9 m/s / 6.02 s
= 5.633 m/s²
Therefore, the acceleration of the car and riders is 5.633 m/s².
Step 2: Calculate the net force exerted on the car and riders.
Net force can be calculated using the equation:
net force = mass × acceleration
Given:
Mass (m) = 1.64 × 10³ kg
Acceleration (a) = 5.633 m/s²
Net force (F) = mass × acceleration
= 1.64 × 10³ kg × 5.633 m/s²
= 9.184 kg·m/s²
Therefore, the average net force exerted on the car and riders by the magnets is 9.184 kg·m/s².