Magnitude/direction of the ball's acceleration

In summary, a 2.0 kg ball is swinging in a vertical circle on an 80 cm-long string with a tension of 20 N at theta = 30 degrees. The ball's speed at theta = 30 is 3.8 m/s, and to find its acceleration and direction, you can use the equations f=ma and a=v^2/r. By drawing a force diagram at 30 degrees, you can determine that the ball's acceleration will always be directed radially outward. To find the magnitude of acceleration, square each component, add them, and then square root the sum.
  • #1
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Homework Statement



A 2.0 kg ball swings in a vertical circle on the end of an 80 cm-long string. The tension in the string is 20 N when its angle from the highest point on the circle is theta = 30.

A) What is the ball's speed when theta = 30?
B) What is the magnitude of the ball's acceleration when theta = 30?
C) What is the direction of the ball's acceleration when theta = 30? Give the direction as an angle from the r-axis.

Homework Equations


f=ma; a = v2/r

The Attempt at a Solution



A) T-mgcos(theta)=mv2/r; v=sqrt((t-gcos(theta))*r) which is 3.8 m/s (the correct answer)

I have no idea how to go about finding part b and c. The only thing I may know about part c is that I'll have to use arctan at some point.

Thanks for all the help, I really appreciate it :)
 
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  • #2
It may be easier to solve for part c first, and then part b. Finding the acceleration vector may be the best thing you can do for yourself right now. I recommend drawing a picture of the force diagram when the ball is at 30 degrees. Will the ball's acceleration always be radially directed outward, always directed along the circular path of the pendulum's motion, or always down with the gravitational force?
 
  • #3
And then after finding the direction, square each component, add them, and then square root the sum for magnitude! Hope this helps!
 

What is the magnitude of the ball's acceleration?

The magnitude of the ball's acceleration is a measure of the rate at which the ball's velocity is changing. It is typically measured in units of meters per second squared (m/s^2) and can be calculated by dividing the change in velocity by the change in time.

What is the direction of the ball's acceleration?

The direction of the ball's acceleration is the direction in which the ball is moving as its velocity changes. This can be determined by looking at the change in the ball's velocity over a specific time interval. If the velocity is increasing, the acceleration is in the same direction as the velocity. If the velocity is decreasing, the acceleration is in the opposite direction.

How does the magnitude of the ball's acceleration affect its motion?

The magnitude of the ball's acceleration determines how quickly its velocity is changing. A larger magnitude of acceleration means the ball's velocity is changing at a faster rate, resulting in a more rapid change in its position and direction of motion. This can lead to a more dramatic or faster motion of the ball.

Can the direction of the ball's acceleration change?

Yes, the direction of the ball's acceleration can change. This can occur if the ball changes direction or if there is a force acting on the ball that causes it to accelerate in a different direction. The direction of the ball's acceleration will always be in the same direction as the net force acting on the ball.

How is the magnitude and direction of the ball's acceleration related to its velocity?

The magnitude and direction of the ball's acceleration are directly related to its velocity. As the ball accelerates, its velocity changes in both magnitude and direction. The magnitude of the acceleration is directly proportional to the rate of change in velocity, while the direction of the acceleration is always in the same direction as the change in velocity.

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