A Ferris Wheel, 24.0 m in diameter, rotates once every 12.5s. What is the fractional change in a person's apparent weight: a) at the top, and b) at the bottom?
I need to know if I'm doing this right. Here's my work:
Equation Used:
Net Force = [(4(pi)^2)(R)(M)] / [T^2]
M=mass
T=Period
R=Radius
FN= Normal Force
mg = weight
Top:
mg - FN = [(4(pi)^2)(R)(M)] / [T^2]
FN = (6.77M) Newtons
Bottom:
FN - mg = [(4(pi)^2)(R)(M)] / [T^2]
FN = (12.8M) Newtons
This is what I got so far, but I'm not sure what it means by the fractional change in a person's apparent weight. So where do I go from here?
dad
To calculate the fractional change in a person's apparent weight, you need to find the difference between the normal force (FN) at the top and at the bottom of the Ferris Wheel, and then express that difference as a fraction of the person's actual weight.
Let's analyze your calculations:
At the top:
mg - FN = [(4(pi)^2)(R)(M)] / [T^2]
FN = (6.77M) Newtons
At the bottom:
FN - mg = [(4(pi)^2)(R)(M)] / [T^2]
FN = (12.8M) Newtons
Now, to find the fractional change in apparent weight, you can use the following formula:
Fractional Change = (Difference in Normal Force) / (Person's actual weight)
Therefore, the fractional change in apparent weight at the top would be:
Fractional Change (top) = (FN at the top - mg) / (mg)
Substituting the values:
Fractional Change (top) = (6.77M - mg) / (mg)
Similarly, the fractional change in apparent weight at the bottom would be:
Fractional Change (bottom) = (FN at the bottom - mg) / (mg)
Substituting the values:
Fractional Change (bottom) = (12.8M - mg) / (mg)
This will give you the fractional change in weight at the top and at the bottom of the Ferris Wheel.