How Do You Calculate the Angle and Tension in a Rotating Ball System?

[puccafan]

Homework Statement

2 kg ball revolves in a horizontal circle with speed of 1.5 m/s. knowing that L= 600 mm, determine (a) the angle that cord forms withe vertical
(b) the tension in the cord
i don't know how to put the figure but this problem is similarly like people practice hammer throwing.
L= 600 mm is distance of the rope

Homework Equations

[a][n] = [v][2]/L

The Attempt at a Solution

i got this equation; 7.5+19.62cos θ = T
and 9.81 sin θ =[a][t]

please help me for the next step

 

[tiny-tim]

Hi puccafan!

(try using the X² tag just above the Reply box )

Homework Statement

2 kg ball revolves in a horizontal circle with speed of 1.5 m/s. knowing that L= 600 mm, determine (a) the angle that cord forms withe vertical
(b) the tension in the cord
i don't know how to put the figure but this problem is similarly like people practice hammer throwing.
L= 600 mm is distance of the rope

Homework Equations

[a][n] = [v][2]/L

The Attempt at a Solution

i got this equation; 7.5+19.62cos θ = T
and 9.81 sin θ =[a][t]

Yes, a = v²/L, where a of course is horizontal (there is no tangential acceleration).

But I don't follow your subsequent equations (you're not assuming that the acceleration is along the string, are you? … acceleration is a matter of geometry, not physics ) …

just resolve T into horizontal and vertical components, and leave g and a as they are.

What do you get? ​

 

[Mene]

I would approach this problem by first identifying the relevant equations and principles involved. In this case, we can use the centripetal force equation [a][n] = [v][2]/L and the equations for finding the components of force in a system (in this case, the horizontal and vertical components of the tension force).

Next, we can plug in the given values for the mass (2 kg), speed (1.5 m/s), and distance (600 mm) to solve for the centripetal acceleration and the total tension force in the system.

To find the angle that the cord forms with the vertical, we can use trigonometric ratios to determine the angle θ in the equation 9.81 sin θ =[a][t]. Once we have the angle, we can use it to solve for the horizontal and vertical components of the tension force using the equation 7.5+19.62cos θ = T.

It may also be helpful to draw a free body diagram to visualize the forces acting on the ball and the direction of the tension force.

Additionally, we can check our solution by making sure that the magnitude of the tension force (found by adding the horizontal and vertical components) matches the total tension force calculated using the centripetal force equation.

Overall, the key to solving this problem is to identify the relevant equations and concepts, plug in the given values, and carefully consider the direction of forces and angles involved.