A Ferris wheel rotates 4 times each minute and has a diameter of 17 m.
The acceleration of gravity is 9.8 m/s2. What is the centripetal acceleration of a rider?
Answer in units of m/s2
You are driving down the road and hit a bump which causes your fishing tackle box to bounce out of the bed of your pickup. The box decelerates at a rate of 3 m/s¶ and skids 24 meters before coming to a stop. How fast were you traveling when the box fell out?
Ashley's answer has been posted elsewhere.
Anonymous's question does not belong here.
12
To find the centripetal acceleration of a rider on the Ferris wheel, we can use the formula for centripetal acceleration. The formula is:
ac = (v^2) / r
Where:
ac is the centripetal acceleration,
v is the linear velocity, and
r is the radius, which is half the diameter.
First, let's find the linear velocity. Since the Ferris wheel completes 4 rotations per minute, we can say it completes 4 * 2π radians in one minute. To convert this to seconds, we divide by 60. So the angular velocity, ω, is:
ω = (4 * 2π) / 60
Now, the linear velocity, v, is given by the formula:
v = ω * r
Using the given diameter of 17 m, we can find the radius, r, by dividing the diameter by 2:
r = 17 / 2
Finally, we can substitute the values into the formula for centripetal acceleration:
ac = (v^2) / r
Let's calculate it step by step.
First, calculate the angular velocity, ω:
ω = (4 * 2π) / 60
Next, find the radius, r:
r = 17 / 2
Then, calculate the linear velocity, v:
v = ω * r
Finally, calculate the centripetal acceleration, ac:
ac = (v^2) / r
Let's do the calculations.