What is the centripetal acceleration?

[laladude]

Homework Statement

If a ball is being twirled in a circle with a radius of 0.5m, and then is let go such that the balls velocity makes an angle 30 degrees from the horizontal and then covers a distance of 1,000m before it hits the ground. What was the centripetal accelertaion provided by the string??

Picture provided

Homework Equations

Ac = v^2 / r

The Attempt at a Solution

I don't really understand how to get the velocity in order to just plug in everything else into the equation.

 

[QuarkCharmer]

Work backwards. What velocity would you need to make the ball arc 30 and cover 1000m for instance.

 

[laladude]

Work backwards. What velocity would you need to make the ball arc 30 and cover 1000m for instance.

I'm still not understanding it.

 

[JHamm]

He's saying pretend there was just a projectile fired at a 30 degree angle that covered 1000m, from that you can find the velocity of the projectile, that velocity is the same as the velocity the object was moving as it spun around the circle.

 

[asteriatic]

The centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. It is given by the equation Ac = v^2 / r, where v is the velocity of the object and r is the radius of the circle.

In this scenario, the ball is being twirled in a circle with a radius of 0.5m. When it is let go, its velocity is not given directly, but we can calculate it using the distance it covers and the angle at which it is released. This can be done using trigonometry:

v = d/t = 1000m / t

Where t is the time taken for the ball to travel 1000m. To find t, we can use the fact that the angle between the ball's initial velocity and the horizontal is 30 degrees, and the distance traveled is the arc length of the circle. This gives us:

t = (theta * r) / v = (30 degrees * 0.5m) / v = 0.2618 / v

Now we can substitute this value of t into the equation for velocity to get:

v = 1000m / (0.2618 / v) = 3823.7 m/s

Now we can plug this value into the equation for centripetal acceleration to get:

Ac = (3823.7 m/s)^2 / 0.5m = 2,919,379 m/s^2

Therefore, the centripetal acceleration provided by the string is approximately 2,919,379 m/s^2.