Question

a 4768-kg roller coaster train full of riders approaches the loading dock at a speed of 17.1 m/s. It is abruptly decelerated to a speed of 2.2 m/s over a distance of 13.6m. Determine the magnitude of the restraining force that acts upon the roller coaster cars.

Answer 1

Step-by-step explanation:

To determine the magnitude of the restraining force acting on the roller coaster cars, we can use the equation:

Force = Mass * Acceleration

1. Calculate the initial velocity:

Initial velocity (u) = 17.1 m/s

2. Calculate the final velocity:

Final velocity (v) = 2.2 m/s

3. Calculate the change in velocity:

Change in velocity (Δv) = v - u = 2.2 m/s - 17.1 m/s = -14.9 m/s (negative because the roller coaster is decelerating)

4. Calculate the distance traveled:

Distance (d) = 13.6 m

5. Calculate the acceleration:

Acceleration (a) = Δv / t

We need to calculate the time (t) first. To do this, we can use the equation of motion:

v = u + at

Rearranging the equation, we have:

t = (v - u) / a

Substituting the values, we have:

t = (-14.9 m/s) / a

6. Now, substitute the values into the equation to calculate the acceleration:

a = (v - u) / t

a = (-14.9 m/s) / (-14.9 m/s / a)

a = 1 m/s^2

7. Calculate the magnitude of the restraining force:

Force = Mass * Acceleration

Mass = 4768 kg

Force = 4768 kg * 1 m/s^2

Force = 4768 N

Therefore, the magnitude of the restraining force that acts upon the roller coaster cars is 4768 Newtons.