Calculating Rotational Speed on a Giant Wheel

[Ishida52134]

Homework Statement

A giant wheel, 40m in diameter, is fitted with a cage and platform on which a man can stand.
The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by
the man on the platform is equal to his weight. The speed of the man is:
X is located at the top of the vertical wheel.
A. 14m/s
B. 20m/s
C. 28m/s
D. 80m/s
E. 120m/s

Homework Equations

Fn + Fg = ma

The Attempt at a Solution

Well it states the normal force is mg. So I got 2mg = m(v^2/r)
which I got that v = 28 m/s.
But the answer key says it's b.

 

[Ishida52134]

any ideas

 

[omiver4]

Homework Statement

A giant wheel, 40m in diameter, is fitted with a cage and platform on which a man can stand.
The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by
the man on the platform is equal to his weight. The speed of the man is:
X is located at the top of the vertical wheel.
A. 14m/s
B. 20m/s
C. 28m/s
D. 80m/s
E. 120m/s

Homework Equations

Fn + Fg = ma

The Attempt at a Solution

Well it states the normal force is mg. So I got 2mg = m(v^2/r)
which I got that v = 28 m/s.
But the answer key says it's b.

your method is correct I believe you just made a computational error.

 

[Saitama]

I see no image.

 

[Ishida52134]

your method is correct I believe you just made a computational error.

it's 2mg = mv^2/r
so v = sqrt (2gr) which is sqrt(784) = 28.

I don't know how to put an image up.
Basically it's just a vertical circle and point X is at the top of it.

 

[Ishida52134]

any ideas

 

[tehstone]

It appears to me that you are using the diameter in your calculation rather than the radius.

2mg = m*v^2/r
v = sqrt(2gr)
v = sqrt(2*(9.8m/s^2)*20m)
v = sqrt(392) = 19.798 which rounds up to 20 m/s

If you do the same math with r = 40 you get 28 m/s. However, the question states that the diameter is 40, so the radius must be 20.

 

[rl.bhat]

any ideas

Take g = 10 m/s^2. Then 2gr = ? ( 2r = diameter)

 

[omiver4]

it's 2mg = mv^2/r
so v = sqrt (2gr) which is sqrt(784) = 28.

I don't know how to put an image up.
Basically it's just a vertical circle and point X is at the top of it.

the reason you keep getting sqrt(784) is because you are using 40m for radius when you should be using 20m

 

[Ishida52134]

ohhhh lol thanks.