Calculating Centripetal Force in The Roundup Amusement Ride

[SherBear]

Homework Statement

In an amusement park ride called The Roundup, passengers standinside a 16 m diameter rotating ring.After the ring has acquired sufficient speed, it tilts into avertical plane, as shown in Figure

Part A

Suppose the ring rotates once every 4.70 s. If a rider's mass is 53.0 kg,with how much force does the ring push on her at the top of the ride?

There are several parts, but I want to do one piece at a time please

Homework Equations

I think V(top)=r w = 2 pie r/ T

T(top)=(m/r)(v^2 top)-mg

The Attempt at a Solution

I tried V(top)=r w = 2 pie r/ T
=(2 pie (16)/(2(4.70s)=10.69 m/s
then
T(top)=(m/r)(v^2 top)-mg
=(53/16)(10.69 m/s)^2-53(9.8 m/s^2)=
-140.86 N ?

 

[SherBear]

Also to get the radius aka r, is it diameter/ 2 ? For my problem it would be 16/2=8=r?

 

[SherBear]

Also for the mass it would be .53m instead of 53 kg?

 

[SherBear]

With those two changes made my final answer is -3.2978N, is this correct?

 

[PeterO]

Homework Statement

In an amusement park ride called The Roundup, passengers standinside a 16 m diameter rotating ring.After the ring has acquired sufficient speed, it tilts into avertical plane, as shown in Figure

Part A

Suppose the ring rotates once every 4.70 s. If a rider's mass is 53.0 kg,with how much force does the ring push on her at the top of the ride?

There are several parts, but I want to do one piece at a time please

Homework Equations

I think V(top)=r w = 2 pie r/ T

T(top)=(m/r)(v^2 top)-mg

The Attempt at a Solution

I tried V(top)=r w = 2 pie r/ T
=(2 pie (16)/(2(4.70s)=10.69 m/s
then
T(top)=(m/r)(v^2 top)-mg
=(53/16)(10.69 m/s)^2-53(9.8 m/s^2)=
-140.86 N ?

Have you heard of the other formula for centripetal acceleration?

a = 4∏².R / T²

this enables you to calculate the acceleration from the period and radius [quantities you were given, without having to calculate the speed.

 

[SherBear]

Have you heard of the other formula for centripetal acceleration?

a = 4∏².R / T²

this enables you to calculate the acceleration from the period and radius [quantities you were given, without having to calculate the speed.

Does that give you the T(top)? I have 14.30 for that equation
then do I plug it into the second equation i listed?

 

[PeterO]

Does that give you the T(top)? I have 14.30 for that equation
then do I plug it into the second equation i listed?

This device travels at constant speed - with a period of 4.70 seconds.
The centripetal acceleration is the same at all times/positions.

The only thing that changes is that at the top, the ring supplies force to supplement gravity in producing that acceleration, whereas at the bottom, the ring has to apply a force to overcome gravity as well as providing the acceleration.

At all other places, friction comes into play and it is just too hard to work out - so we are never asked.

 

[SherBear]

This device travels at constant speed - with a period of 4.70 seconds.
The centripetal acceleration is the same at all times/positions.

The only thing that changes is that at the top, the ring supplies force to supplement gravity in producing that acceleration, whereas at the bottom, the ring has to apply a force to overcome gravity as well as providing the acceleration.

At all other places, friction comes into play and it is just too hard to work out - so we are never asked.

The answer at the top and bottom are 14.30N?

 

[PeterO]

The answer at the top and bottom are 14.30N?

No,

That formula calculates acceleration - after substituting in Radius (R) and Period (T)

 

[SherBear]

That's what I thought but I don't know what to do afterward.

 

[SherBear]

Well i'll post B if anyone wants to help, for B Suppose the ring rotates once every 4.70s . If a rider's mass is 53.0kg , with how much force does the ring push on her at the bottom of the ride?

 

[SherBear]

I got this now...i used 2 pie r / T to get the speed
then to get the force i used F=mv^2/(r)-wg and got 237.68 N which is correct
Thank you!

 

[PeterO]

That's what I thought but I don't know what to do afterward.

having found the acceleration is 14.3, the next step is to realize that acceleration is down. Gravity contributes enough force to create an acceleration of 9.8, but we need an extra 4.5 if we are to get the 14.3.

F = ma

F = 53 x 4.5 = 238.5 N

Centripetal acceleration can be given by a = v²/R , meaning the Centripetal force needed is F = mv²/R

The alternative formula is

a = 4∏²R / T² meaning F = 4∏²Rm / T²

subtract wg from that force - as you did and the answer is there.

 

[SherBear]

having found the acceleration is 14.3, the next step is to realize that acceleration is down. Gravity contributes enough force to create an acceleration of 9.8, but we need an extra 4.5 if we are to get the 14.3.

F = ma

F = 53 x 4.5 = 238.5 N

Centripetal acceleration can be given by a = v²/R , meaning the Centripetal force needed is F = mv²/R

The alternative formula is

a = 4∏²R / T² meaning F = 4∏²Rm / T²

subtract wg from that force - as you did and the answer is there.

Thank you PeterO for all your help and hard work!