Circular motion of a tether ball

In summary, in this problem involving a ball tethered to a tall pole and thrown in a horizontal circle, you need to use the angle of 40 degrees between the rope and the pole to find the correct radius of the circular path. The tension in the rope can then be calculated using the weight of the ball and the angle, and its horizontal component can be found using the Pythagorean theorem. It is important to note that the total tension in the rope must be greater than the weight of the ball.
  • #1
in10sivkid
36
0
a .225 kg ball tethered to a tall pole on a 1.37m rope is thrown so that it travels in a horizontal circle with the rope making an angle of 40 with the pole
a) what is the speed of the ball
b) what is the tension in the rope

i am stuck on this problem because i do not have a unit time to be able to use any of the equations dealing with circular motion

i started out with knowing that the radius will be the cos40*1.37m = 1.05 m

but after that I'm always left with two unknowns for any equation. any hints on what i could be missing...thanks!
 
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  • #2
in10sivkid said:
a .225 kg ball tethered to a tall pole on a 1.37m rope is thrown so that it travels in a horizontal circle with the rope making an angle of 40 with the pole
a) what is the speed of the ball
b) what is the tension in the rope

i am stuck on this problem because i do not have a unit time to be able to use any of the equations dealing with circular motion

i started out with knowing that the radius will be the cos40*1.37m = 1.05 m

but after that I'm always left with two unknowns for any equation. any hints on what i could be missing...thanks!
You have to use the angle to determine the relative magnitudes of the centripetal (horizontal) and gravitational (downward) forces. That will give you the centripetal force from which you can easily determine the speed.

AM
 
  • #3
once again could you elaborate a little bit more on that...

how can I find the centripetal force if all I know is the radius, and mass

i don't have a velocity, or time, or angular velocity...what part am I failing to see here?
 
  • #4
Centripetal force=mv^2/r
but you need speed. My advice to you is that you draw a representative picture of the problem. Then show the forces acting on the particle. gravitational force is vertical to the horizontol. And the centripetal force is parallel to the horizontal. Try to use tan40... You already know the radius. v will be easy to find out then...
 
  • #5
hmmmm...ok 2 questions I'm not following

why would i use tan40...would i multiply that by .225 kg or the length of the rope...almost there i think
 
  • #6
i have this equation and it involves banking angles thos

tan(angle) =v^2/gr

would that be what you are referring to?
 
  • #7
exactly, you can find v now...
 
  • #8
last question dealing with this they then ask for the tension would that simply be
Mass * acceleration
mass * v^2/r??

if so...i'm getting a wrong answer or my book is wrong

so i got V = 2.94 m/s

from tan40 = v^2/(9.8 m/s)(1.05 m)

Ac = 8.23 m/s^2 = (2.94 m/s^2)/(1.05 m)
then T = (.225 kg)(8.23 m/s^2) = 1.85 N
 
  • #9
I didn't calculate v but I suppose you found it right
Anyway T is equal to the combination of the gravitational and centripetal forces... Try to use the pyhtagoras theorem... You have a right triangle.
 
  • #10
sooooo would that make tension the following?

T^2 = (mv^2/r)^2 + (mg)^2
 
  • #11
yup! congrats man :)
 
  • #12
ahhhh I guess there are just typos in the book then :)
 
  • #13
Well I'm quite sure I gave the correct solution
 
  • #14
yah it seems correct
 
  • #15
in10sivkid said:
a .225 kg ball tethered to a tall pole on a 1.37m rope is thrown so that it travels in a horizontal circle with the rope making an angle of 40 with the pole
a) what is the speed of the ball
b) what is the tension in the rope

i am stuck on this problem because i do not have a unit time to be able to use any of the equations dealing with circular motion

i started out with knowing that the radius will be the cos40*1.37m = 1.05 m

but after that I'm always left with two unknowns for any equation. any hints on what i could be missing...thanks!

You need to give this another try. The angle of 40 degrees is the angle the rope makes with the pole. The radius of motion is not cos40*1.37m. Furthermore, the tension cannot possibly be less than the weight of the ball, which is what you found.
 
  • #16
gah...you're right..I didn't even realize my calculated T was less than mass

i've been pondering over this...and I'm stumped..i can't figure out how i would calculate the radius...unless it really was 1.37m (actual length of the rope), but somehow i think that's not right.

was my line of thinking right in all the other aspects of the calculation once the radius was found?
 
  • #17
in10sivkid said:
gah...you're right..I didn't even realize my calculated T was less than mass

i've been pondering over this...and I'm stumped..i can't figure out how i would calculate the radius...unless it really was 1.37m (actual length of the rope), but somehow i think that's not right.

was my line of thinking right in all the other aspects of the calculation once the radius was found?

The 40 degree angle is between the rope and the pole. The radius of the circular path is the side opposite this angle, not adjacent to it. The vertical component of the tension has to equal the weight of the ball. With that and the correct angle you can find the tension, and then find its horizontal component. It looks like you were calculating just the horizontal component before, but you did not identify it as such. The horizontal component of the tension will be less than the weight of the ball, so that's OK, but the total tension has to be greater.
 

1. What is circular motion?

Circular motion is when an object moves in a circular path around a fixed point, called the center of rotation. It is a type of motion that is typically seen in objects attached to a string or tether, such as a tether ball.

2. How does a tether ball move in circular motion?

A tether ball moves in circular motion because it is attached to a string or tether that is fixed at one end, allowing the ball to swing around in a circular path. This motion is caused by the tension in the string and the ball's inertia, or tendency to continue moving in a straight line.

3. What factors affect the speed of a tether ball in circular motion?

The factors that affect the speed of a tether ball in circular motion include the length of the string, the force applied to the ball, and the mass of the ball. A longer string will result in a slower speed, while a shorter string will result in a faster speed. A greater force applied to the ball will also increase its speed, while a heavier ball will require more force to maintain a constant speed.

4. What is the difference between centripetal and centrifugal force in circular motion?

Centripetal force is the force that pulls an object towards the center of rotation, keeping it in its circular path. It is always directed towards the center of rotation. On the other hand, centrifugal force is the apparent outward force that is felt by an object in circular motion. It is not a real force, but rather a result of the object's inertia trying to keep it moving in a straight line.

5. How does the angle of the string affect the motion of a tether ball?

The angle of the string can affect the motion of a tether ball by changing the direction of the centripetal force. If the string is at a larger angle, the force will be directed more towards the horizontal direction, resulting in a more horizontal circular path. If the string is at a smaller angle, the force will be directed more towards the vertical direction, resulting in a more vertical circular path.

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