Ball on a String: Tension and Speed Formulas for Circular Motion

  • Thread starter Thread starter vl108
  • Start date Start date
  • Tags Tags
    Ball String
AI Thread Summary
The discussion focuses on deriving formulas for tension and speed in a tether ball system. The tension T in the rope can be expressed as Tcos(θ) = mg, which accounts for vertical forces. For the horizontal forces, the centripetal force equation F = mv²/r is utilized to find the speed v of the ball. Participants emphasize the need to separate vertical and horizontal forces to solve the problem accurately. Overall, the thread provides insights into the physics of circular motion involving tension and speed calculations.
vl108
Messages
2
Reaction score
0
A tether ball of mass m is suspended by a rope of length L from the top of a pole. A youngster gives it a whack so that it moves with some speed v in a circle of radius r = L sin(θ) < L around the pole.
a) Find an expression for the tension T in the rope as a function of m, g, and θ.
b) Find an expression for the speed v of the ball as a function of θ.



F = mv^2 / r



I do not know what to do. All I have is Tcosx = mv^2/r - mg
any help please??
 
Physics news on Phys.org
+ mg sorry
 
That's not right. There are essentially two equations. One for the vertical forces and one for the horizontal forces.

You've written the equation for the vertical forces, but the centripetal force shouldn't be in it. You should have: Tcos(\theta) = mg For the vertical forces.
From this you get the tension in the rope.

Then you can use the equation for the horizontal forces to get the speed of the ball.
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »
Thread 'Trying to understand the logic behind adding vectors with an angle between them'

Thread 'Trying to understand the logic behind adding vectors with an angle between them'

My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
View full post »
Thread 'Correct statement about a reservoir with an outlet pipe'

Thread 'Correct statement about a reservoir with an outlet pipe'

The answer to this question is statements (ii) and (iv) are correct. (i) This is FALSE because the speed of water in the tap is greater than speed at the water surface (ii) I don't even understand this statement. What does the "seal" part have to do with water flowing out? Won't the water still flow out through the tap until the tank is empty whether the reservoir is sealed or not? (iii) In my opinion, this statement would be correct. Increasing the gravitational potential energy of the...
View full post »

Similar threads

Ball on a string thrown around a spool
Replies
3
Views
892
Determine the speed and tension of keys swinging in a circular path
Replies
8
Views
2K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
2K
Vertical Circle (Circular Motion)
Replies
5
Views
2K
What minimum speed do we need to give a charged ball?
Replies
12
Views
1K
Conic Pendulum Exercise: Tension and Velocity as Functions of Angle
Replies
4
Views
2K
A ball is thrown w/initial speed vi at an angle 𝜃i with the horizontal
Replies
5
Views
1K
Tangential Acceleration Problem, UCM
Replies
2
Views
1K
Tension and speed of bowling ball pendulum passing the equilibrium position
Replies
2
Views
1K
For a Pendulum: Knowing Acceleration Find Maximum Angle
Replies
26
Views
3K

Hot Threads

Recent Insights

Back
Top