Solving for Tension & Angles in Ball Mass Problem: Help Needed!

In summary, the conversation discusses finding the tension and angles in a system involving two balls with different masses attached to a tread with a length of 2R. It is determined that the angles must be different due to the different masses, and the equation m1*g*sinθ1 = m2*g*sinθ2 is used to solve for the angles. The final equation (θ1 + θ2) = 2R/R = 2 rad. is used to find the angles.
  • #1
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http://ruliweb6.nate.com:8080/ruliboard/gup/img_link7/436/435945_1.jpg

Ball A B
Mass m 2m

Length of tread is 2R where R is the radious of the Circle.
I have to find the tension on the tread and angles
I could have found the angles by assuming that the angle 1 and angle 2 are same
but as balls' masses are different, the angles must be different as well, and if they are different i don't think i can find the angle...
Any helps? Please TT
 

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  • #2
Ball comes rest when
m1*g*sinθ1 = m2*g*sinθ2.
It is given that m2 = 2m1
So sinθ1 = 2*sinθ2...(1)
Length of the thread is 2R and radius is R.
So (θ1 + θ2) = 2R/R = 2 rad.
Put θ2 = (2 - θ1) in the eq.1 and solve for θ1.
 

Related to Solving for Tension & Angles in Ball Mass Problem: Help Needed!

What is tension and how is it related to ball mass?

Tension is a force that is applied by a string, rope, or cable when it is pulled tight. In the context of a ball mass problem, it refers to the force exerted on a ball by a string or cable that is connected to it. This tension is directly related to the mass of the ball, as a heavier ball will require a greater tension force to keep it in motion.

How can I solve for tension and angles in a ball mass problem?

To solve for tension and angles in a ball mass problem, you will need to use the principles of Newton's Laws of Motion and basic trigonometry. First, draw a free body diagram to identify all the forces acting on the ball. Then, use Newton's Second Law to set up equations for the forces in the horizontal and vertical directions. Finally, use trigonometric functions to solve for the tension and angles.

What information do I need to solve for tension and angles in a ball mass problem?

To solve for tension and angles in a ball mass problem, you will need to know the mass of the ball, the acceleration due to gravity, the length of the string or cable, and any other forces acting on the ball (such as friction or air resistance). You may also need to know the initial velocity of the ball or the angle at which it is released.

What are some common mistakes when solving for tension and angles in a ball mass problem?

Some common mistakes when solving for tension and angles in a ball mass problem include not considering all the forces acting on the ball, forgetting to use the appropriate trigonometric functions, and not properly setting up the equations for the forces. It is important to carefully draw and label a free body diagram and use Newton's Second Law correctly to avoid these errors.

Can you provide an example of solving for tension and angles in a ball mass problem?

Sure, here is an example problem: A ball with a mass of 2 kg is attached to a string of length 1.5 meters. The ball is released from rest at an angle of 30 degrees above the horizontal. There is no air resistance, and the acceleration due to gravity is 9.8 m/s^2. What is the tension in the string? To solve this, we would draw a free body diagram and set up equations for the forces in the horizontal and vertical directions. Using trigonometric functions, we can solve for the tension to be approximately 19.6 N and the angle of the string to be 60 degrees above the horizontal.

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