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.
1 hour ago - 4 days left to answer.
To find the acceleration vector for a person seated in a car at the lowest point of the Ferris wheel, we can break down the problem into two components: radial acceleration and tangential acceleration.
1. Radial acceleration: Since the person is at the lowest point of the Ferris wheel, their position is at the maximum distance from the center. The radius of the Ferris wheel is given as 30 meters. The radial acceleration is always directed towards the center of the circle and can be calculated using the formula:
radial acceleration = (tangential speed)^2 / radius
Given that the tangential speed is 40 m/min, and the radius is 30 meters, we can substitute these values into the formula:
radial acceleration = (40 m/min)^2 / 30 m
Calculating this, we get:
radial acceleration = 1600 m^2/min^2 / 30 m
= 53.33 m/min^2
So the radial acceleration is 53.33 m/min^2 directed towards the center of the circle.
2. Tangential acceleration: The tangential acceleration is the rate at which the tangential speed changes. Given that the wheel is slowing down at a rate of 15 m/min^2, the tangential acceleration will be -15 m/min^2 (negative because it is slowing down).
So the tangential acceleration is -15 m/min^2.
The acceleration vector is the vector sum of these two components. Since the tangential acceleration is in the opposite direction of the radial acceleration, we subtract the magnitudes:
acceleration vector = radial acceleration - tangential acceleration
Plugging in the values:
acceleration vector = 53.33 m/min^2 - (-15 m/min^2)
= 53.33 m/min^2 + 15 m/min^2
= 68.33 m/min^2
Therefore, the acceleration vector for a person seated in a car at the lowest point of the Ferris wheel is 68.33 m/min^2 directed towards the center of the circle.
Note: The acceleration vector indicates the magnitude and direction of acceleration. In this case, it tells us how fast and in which direction the person's velocity is changing while they are on the Ferris wheel.