Calculating Theta for Suspended Mass in Circle

  • Thread starter Thread starter Punchlinegirl
  • Start date Start date
  • Tags Tags
    Circle Mass Theta
Click For Summary
SUMMARY

The discussion focuses on calculating the angle theta (θ) for a mass of 9.3 kg suspended from a string of length 1.57 m, revolving in a horizontal circle with a tangential speed of 3.14 m/s. The user initially attempted to solve the problem using the equations Lsin(θ) = mv²/r and Lcos(θ) = mg, but misidentified the radius (r) as L/2. Correctly determining r as a function of θ is crucial for accurate calculations. The correct approach involves reevaluating the geometry of the system to derive the relationship between r and θ.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with trigonometric functions (sine, cosine, tangent)
  • Knowledge of Newton's laws of motion
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Review the geometry of circular motion to accurately define radius (r) in terms of angle θ
  • Study the derivation of tension in strings under circular motion
  • Learn about the relationship between centripetal force and gravitational force in rotating systems
  • Practice solving similar problems involving suspended masses and circular motion
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of rotating systems and forces acting on suspended masses.

Punchlinegirl
Messages
221
Reaction score
0
A mass m= 9.3 kg is suspended from a sting of length L=1.57 m. It revolves in horizontal circle. The tangential speed of the mass is 3.14 m/s. What is the angle theta between the string and the vertical in degrees?

I started off by using the equations Lsin theta= mv^2/ r and Lcos theta=mg
Solving the second one for L and plugging into the first gave me mgsin theta/ cos theta= mv^2/r. I then plugged in my numbers to get 91.14 sin theta/ cos theta = 116.8. Since sin/cos= tan, I simplified to get 91.14 tan theta= 116.8, using inverse tan to get an answer of 52 deg. This wasn't right... can someone help me?

Thanks
 
Physics news on Phys.org
First, I think you mean T (as in the tension of the string) when you wrote L.

Second, it looks like you decided that r=L/2; what made you decide that? r is the distance between the mass and the axis it rotates about. Look at the geometry again to find r as a function of θ.
 

Similar threads

Finding slip-off angle for mass off of sphere?
  • · Replies 7 ·
Replies
7
Views
1K
Deviation of Plumb Bob In Uniform Circular Motion
  • · Replies 11 ·
Replies
11
Views
3K
How can I find the velocity of a point on a disk rotating in a disc?
  • · Replies 16 ·
Replies
16
Views
2K
Finding the Work of a spring and friction with a changing angle
  • · Replies 21 ·
Replies
21
Views
2K
What is the Needed Coefficient of Static Friction for a Car on a Banked Curve?
  • · Replies 16 ·
Replies
16
Views
2K
Find Centre of Mass of Semi-Circle: Solving Integrals
  • · Replies 11 ·
Replies
11
Views
2K
Finding the period of an object moving in horizontal circle
  • · Replies 3 ·
Replies
3
Views
2K
Conic Pendulum Exercise: Tension and Velocity as Functions of Angle
  • · Replies 4 ·
Replies
4
Views
2K
Find Angle Theta for Mass Revolving in Horizontal Circle
  • · Replies 5 ·
Replies
5
Views
4K
How Do Forces Affect Particle Motion in Different Vertical Circle Scenarios?
  • · Replies 25 ·
Replies
25
Views
3K