Circular motion-what is the radius of the loop de loop in meters

[dani123]

Homework Statement

Snoopy is flying his vintage warplane in a "loop de loop" path being chased by the Red Baron. His instruments tell him the plane is level (at the bottom of the loop) and traveling at 180 km/hr. He is sitting on a set of bathroom scales that him he weighs four times what he normally does. What is the radius of the loop in meters?

Homework Equations

F_c=mv²/R
a_c=v²/R

The Attempt at a Solution

I am completely lost with this problem but this is what I attempted...

I started by converting 180km/hr into m/s and came up with 648 000 000m/s.

Then I used this value and plugged it into the centripetal acceleration equation and used a_c=9.8m/s² and then solved for R= 4.28*10¹⁶m

I know this must be the wrong answer but I am very lost as to what I should do or even how I should be looking at this problem... If anyone could help me out that would be greatly appreciated! Thank you so much in advance!

 

[tiny-tim]

hi dani123!

I started by converting 180km/hr into m/s and came up with 648 000 000m/s.

:rofl: :rofl: :rofl:

Then I used this value and plugged it into the centripetal acceleration equation and used a_c=9.8m/s² and then solved for R= 4.28*10¹⁶m

hint: what is the equation for the reaction force between snoopy and the scales?

 

[dani123]

im confused as to how that's going to help me find the radius..

 

[tiny-tim]

but the only information you have is the magnitude of that reaction force

 

[dani123]

so do i just convert 180km into meters?

 

[dani123]

nvm! scratch that last post ...

 

[tiny-tim]

yes, and hours into seconds

 

[dani123]

i tend to over think the problems that have the simplest answers! haha

 

[dani123]

after i converted it into m/s... that's the answer? really?

 

[gneill]

after i converted it into m/s... that's the answer? really?

That's the answer to his speed in m/s. It doesn't answer the question about the radius of the loop he's following.

Consider what his effective acceleration must be if he weighs 4x normal weight (when the usual acceleration due to gravity is just g). What additional acceleration is operating when he moves in circular motion?

 

[dani123]

im lost

 

[tiny-tim]

what is the equation for the reaction force between snoopy and the scales?

 

[dani123]

i don't know anymore,, I am really confused

 

[truesearch]

edit...delete

 

[Chestermiller]

If the radius were infinite, there would be a 1g upward force exerted by the scale on him. How many additional g's of force are required to keep him moving in a circle? That should be v²/R.

Chet

 

[tiny-tim]

well, how many forces are there, and what is the acceleration?

 

[Chestermiller]

The net force is 3g's.

 

[dani123]

how did you come up with these g's ?

 

[azizlwl]

The net force is 3g's.

What is the radius of the loop in meters?You draw a free body diagram. From this you can calculate the radius needed.
There are 3 forces exerted on the man.
1. Gravitional force.
2. Centripetal force.
3. Normal force. This force shown by the scale.

 

[vela]

There are 3 forces exerted on the man.
1. Gravitional force.
2. Centripetal force.
3. Normal force. This force shown by the scale.

There are only two forces on Snoopy: the gravitational force and normal force. The net force on Snoopy results in his centripetal acceleration.

 

[dani123]

ok i understand that, but to calculate the forces don't i need Snoopy's mass?

 

[tiny-tim]

ok i understand that, but to calculate the forces don't i need Snoopy's mass?

yes, but call it "m" …

when you calculate the speed or the radius, "m" will cancel out in the end

 

[dani123]

could someone show me which equations to use please? i have a list of them in front of me and I am lost as to which ones i should be focusing on

 

[tiny-tim]

i have a list of them in front of me …

show us

 

[dani123]

a_c=V²/R
a_c=4∏²R/T²
F_c=m*4∏²*R/T²=m*V²/T²
μ=F_f/F_n
average speed:V=2∏R/T
F_net=m*a
F_c=m*V²/T²
F_c=m*V²/R
F_ncos(θ)=m*g
F_c=F_n*sinθ

This is what I got...

 

[tiny-tim]

for the third time …

what is the equation for the reaction force between snoopy and the scales?​

 

[dani123]

Fnet=m*a?

 

[tiny-tim]

Fnet=m*a?

yes

and what forces is F_net made of?

 

[dani123]

mass and acceleration? which i don't have...

 

[vela]

That's not what Tim was asking for. Neither mass nor acceleration is a force. F_net is the sum of all of the forces exerted on Snoopy. Identify all the forces on Snoopy and add them up. That's the lefthand side of the equation. The righthand side is simply ma.

You should also be able to identify a relevant expression for Snoopy's acceleration since you were given that he's moving in a circle. Put this all together and you have the equation you need to solve.

 

[azizlwl]

There are only two forces on Snoopy: the gravitational force and normal force. The net force on Snoopy results in his centripetal acceleration.

Yes that is correct.
But I am looking at the force that had put the body in circular motion.
What can supply this force?
As OP has stated in one of his equations, F_c.
What are the sources that supply F_c

Surely one of the candidates is the spring of the scale.

 

[dani123]

if I got an answer R=255m... does this seem plausible?

 

[vela]

Show us your calculations.

 

[dani123]

v=180km/h=50m/s

a_c=v²/R
(9.8m/s²)=(50m/s)²/R

solved for R=255.10m... Probably wrong

 

[vela]

Close, but the value you used for a_c isn't correct. You need to find the acceleration using F=ma. Find the net force F on Snoopy and divide by his mass to find a. That will be the value of a you need in your calculation.