Centripetal Force in an amusement park ride

[GoSS190]

In an amusement park ride called The Roundup, passengers stand inside a 18.0 m-diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane. Suppose the ring rotates once every 4.90 s. and the rider's mass is 58.0 kg.

A.) With how much force does the ring push on her at the top of the ride?

B.) With how much force does the ring push on her at the bottom of the ride?

C.) What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?

If anyone could help me with these questions that would be great. Thanks


I tried this using the equations to find v = (2pi(r)) / T

but then i realized that the velocity is different at the top than at the bottom. I am stumped as to how to find the velocity then find the force.

I think the equation for force at the top is (m(v_top)²) / R

Can anyone help me out with this though please

 

[rock.freak667]

At the top of the ring, what are the forces acting on the body? The resultant of those two forces is equal to the centripetal force.

 

[GoSS190]

The two forces are the normal force and gravity but i don't know how to find the normal force

 

[rock.freak667]

The two forces are the normal force and gravity but i don't know how to find the normal force

Yes, the are the two forces, the normal force (R) and the weight(W) <-I assumed that is what you meant by gravity.

The resultant of those two R+W=F_c where F_c is the centripetal force.

 

[GoSS190]

How do you find the R or the normal force cause the velocity is different at the top than at the bottom

 

[rock.freak667]

You don't need the velocity,the told you that "the ring rotates once every 4.90 s"

What does this tell you about the periodic time and hence the angular velocity?

 

[GoSS190]

it would be 1 / 4.9 right

 

[rock.freak667]

yes and how to relate that to angular velocity?


What formulas do you know to calculate centripetal force?

 

[GoSS190]

2pi / 4.9 is the angular velocity

 

[rock.freak667]

and centripetal force is therefore?

 

[GoSS190]

That is the part that I don't understand really

 

[GoSS190]

is it mw^2r

 

[rock.freak667]

yes it is, you can now solve part a and part b noting that Weight acts downwards and normal reaction acts upwards

 

[GoSS190]

i got an answer of 556177.07 but that doesn't seem correct to me and I don't know what i did wrong