The Giant Ferris Wheel has a radius of 30meters. Assuming that a time t= t_0 , the wheel rotates counterclockwise with a speed of 40m/min, and is slowing at a rate of 15m/min^2 . Find acceleration vector for a person seated in a car at the lowest point of the wheel.
How to find acceleration vector?
And i don't get what does it meant by acceleration vector is.
"confuse"
Please give a hand. Thank You.
To find the acceleration vector for a person seated in a car at the lowest point of the Ferris Wheel, we first need to understand what an acceleration vector is.
Acceleration refers to the rate at which an object's velocity is changing. It is a vector quantity because it has both magnitude and direction. In other words, it tells us how quickly the object is changing its velocity and in which direction.
In this case, we are looking for the acceleration vector at the lowest point of the Ferris Wheel. The acceleration vector will tell us the magnitude and direction of the acceleration experienced by the person in the car at that point.
To find the acceleration vector, we can use the centripetal acceleration formula, which is given by:
a = (v^2) / r
where "a" is the acceleration, "v" is the velocity, and "r" is the radius of the circle.
In this problem, we are given the radius of the Ferris Wheel (30 meters) and the speed at time t=t_0 (40 meters per minute). However, we also need to consider the deceleration (negative acceleration) of the Ferris Wheel, which is given as -15 meters per minute squared.
Since the Ferris Wheel is slowing down, the acceleration experienced by a person in the car at the lowest point will be the difference between the centripetal acceleration and the deceleration of the Ferris Wheel.
So, the acceleration vector can be calculated as follows:
a = [(v^2) / r] - deceleration
Substituting the given values:
a = [(40^2) / 30] - (-15)
Simplifying:
a = (1600 / 30) + 15
a ≈ 53.33 + 15
a ≈ 68.33 meters per minute squared
Therefore, the acceleration vector for a person seated in a car at the lowest point of the Ferris Wheel is approximately 68.33 meters per minute squared, directed towards the center of the Ferris Wheel.
I hope this explanation helps clarify the concept of acceleration vector and how to find it in this specific scenario. Let me know if you have any further questions!