Rotation at an angle - Tether ball (Finding length)

AI Thread Summary
A tether ball is attached to a 3m tall pole and is swung at a speed of 9.5 m/s, creating an angle of 32° with the vertical. The initial calculations for the radius of rotation yielded an impractically large value, raising concerns about the problem's setup. The discussion revealed that the radius of 14.7m implies a string length of approximately 27.7m, which contradicts the pole height. Participants acknowledged the discrepancy and suggested that the issue lies within the problem itself rather than the calculations. The conversation concluded with a sense of camaraderie among the contributors as they navigated the complexities of the problem.
testme
Messages
68
Reaction score
0

Homework Statement


A tether ball is a ball at the end of a rope tied to a pole 3m tall. A player whips the ball around with a speed of 9.5 m/s and the string rises to an angle of 32°. Find the length of the string.

length of pole = 3m
v = 9.5
angle θ = 32°

Homework Equations


Fnet = ma



The Attempt at a Solution


I drew the FBD on the diagram itself

http://sadpanda.us/images/857602-GFGQJ1G.jpg

I know I did something wrong because the radius I got is way too big.
 
Last edited by a moderator:
Physics news on Phys.org
testme said:

Homework Statement


A tether ball is a ball at the end of a rope tied to a pole 3m tall. A player whips the ball around with a speed of 9.5 m/s and the string rises to an angle of 32°. Find the length of the string.

length of pole = 3m
v = 9.5
angle θ = 32°

Homework Equations


Fnet = ma



The Attempt at a Solution


I drew the FBD on the diagram itself

http://sadpanda.us/images/857602-GFGQJ1G.jpg

I know I did something wrong because the radius I got is way too big.

Actually, your value matches the given information of angle and velocity. It doesn't accord very well with the supposed 3m height of the pole though! And it gets worse when you consider that 14.7m is just the radius of rotation; the string length h will be about twice that!

Looks like a problem with the problem itself, not your work :smile:
 
Last edited by a moderator:
Oh, damn.. I left the next question cause it was the same idea.

So to calculate h ot wpi;d ne

Fx = 14. 7m

14.7 h
----- = ----
sin32 sin 90

h = 27.7 m?
 
testme said:
Oh, damn.. I left the next question cause it was the same idea.

So to calculate h ot wpi;d ne

Fx = 14. 7m

14.7 h
----- = ----
sin32 sin 90

h = 27.7 m?

That looks about right :wink:
 
Thanks a lot, that damn question threw me off.

Anyways, I'm off to bed. G'night everyone who reads this :)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Finding the Length and Velocity of a Spring in Circular Motion
Replies
4
Views
2K
Circular Motion and Gravitation of tether ball
Replies
15
Views
4K
Conservation of energy and tether ball
Replies
1
Views
3K
Finding Charge & Tension of a Suspended Cork Ball
Replies
3
Views
4K
Rod swinging and hitting a ball
Replies
31
Views
4K
Finding Angle of String with Two Charged Balls
Replies
1
Views
2K
How Is Torque Equilibrium Applied to a Sphere Tethered to a Wall?
Replies
5
Views
6K
Tension and net torque in a cable
Replies
10
Views
5K
Analyzing the Tether Ball Problem: Forces and Motion
Replies
7
Views
3K
Ball on a String: Tension and Speed Formulas for Circular Motion
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top