Circular motion question - finding rpm

In summary, the question asks for the tension in the lower string and the rotation rate of a 0.60 kg sphere rotating around a vertical shaft supported by two strings. Using the equations v=2(pi)r/T, Fr= mv^2/r, and ω = v/R, the tension in the lower string is found to be 8.2 N and the rotation rate is calculated to be 89.3 rpm. There was some initial confusion about the first part, but it was resolved and the calculations were found to be correct.
  • #1
jgray
10
0

Homework Statement



A 0.60 kg sphere rotates around a vertical shaft supported by two strings, as shown. If the tension in the upper string is 18 N. Calculate
the tension in the lower string?
the rotation rate (in rev/min) of the system?

Homework Equations



v=2(pi)r/T
Fr= mv^2/r
ω = v/R

The Attempt at a Solution



I believe I have the first part correct, my question is really about the second part. For the second part of the question: I calculated the x components of each tension force to find the centripetal force = 20.96N. I then found the velocity by rearranging the equation: Fr = mv^2/r to get 3.74m/s. I used the equation ω = v/R to get 9.35 rads/sec and converted it to 89.3 rpm by multiplying 9.35 by 60s and dividing it by 2(pi). Am I on the right track?? Just seems like a small answer…
 

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  • #2
The upper string has to supply force for the mass to rotate and to stay afloat.
 
  • #3
[strike]Don't follow the 3.74 m/s. Did you divide by 6 or (0.6 x 9.81) instead of by 0.6 kg ?[/strike]

(Edit: Jgray is fully correct)
 
Last edited:
  • #4
I don't see any workings of the first part.
 
  • #5
@aziz: I think the poster is happy with the result of the first part (I support him/her in that) and now asks for help in the second part.

[strike]If I fill in v = 3.74m/s in mv^2/r I do not get the 21 N...[/strike]

(Edit: Jgray is fully correct)
 
Last edited:
  • #6
Hmm, maybe I do have an error in my first part then. I found the centripetal force:
T1x+T2x =
sin θ(T1) + sin θ(T2)=
sin53(18N) + sin53(8.2N) --8.2 N is the answer i found for the second tension force for part 1--
14.37+6.55
20.92N

For the velocity:
v^2= Fr(r)/m
(20.92N)(0.4m)/0.6kg=
square root of 13.95=
3.74m/s
 
  • #7
Fully correct, it was me that used r=4 (from the 3,4,5 triangle) instead of the 0.4 in the exercise. Sorry.

So the 3.74 is fine too. And the 9.35 and the 89.2.
 
  • #8
Thanks for the help! :)
 
  • #9
:redface:
 

FAQ: Circular motion question - finding rpm

What is circular motion and how is it related to rpm?

Circular motion is the movement of an object along a circular path. RPM, or revolutions per minute, is a unit of measurement used to describe the speed at which an object is rotating. In circular motion, an object is constantly changing direction and therefore also constantly changing its rotational speed, which is measured in rpm.

How do you calculate rpm?

RPM is calculated by dividing the number of revolutions completed by an object in a given time period by the duration of that time period. For example, if an object completes 10 revolutions in 2 minutes, its rpm would be 10/2 = 5 revolutions per minute.

What factors affect the rpm of an object in circular motion?

The rpm of an object in circular motion can be affected by several factors, including the size of the object, the speed at which it is moving, and the radius of the circular path it is following. Additionally, external forces such as friction and air resistance can also affect the rpm of an object.

How is rpm used in real life applications?

RPM is commonly used in various real life applications, such as measuring the speed of car engines, fans, and other rotating machinery. It is also used in sports to measure the speed of a spinning ball, and in physics experiments to study circular motion and rotational forces.

Can rpm be converted to other units of measurement?

Yes, rpm can be converted to other units of measurement such as radians per second (rad/s) or revolutions per hour (rpm). These conversions can be done by using conversion formulas or online converters.

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