Tape a string half a meter or so in length securely to a small rubber ball. Prac

Question

Tape a string half a meter or so in length securely to a small rubber ball. Practice whirling the ball in both horizontal and veritcal circles and make these observations:

a. For horizontal motion of the ball, how does the angle that the string makes with the horizontal vary with the speed of the ball?

b. If you let go of the string at a certain point in the circle, what path does the ball follow after release?

c. Can you feel differences in tension in the string for different speeds of the ball? How does the tension vary with speed?

d. For vertical circle, how does the tension in the string vary for different points in the circle? Is it greater at the bottom than at the top when the ball moves with constant speed?

ALSO, submit a lab report that includes objectives, procedure, and conclusions.

Explanation / Answer

You should understand the uniform circular motion of a particle so you can: a. Relate the radius of the circle and the speed or rate of revolution of the particle to the magnitude of the centripetal acceleration. You have this equation to work with: In this equation, v is the linear speed, so its fairly easy to relate it to the radius (r) or to the centripetal acceleration (ac). You just use the old equation as it is given. If r gets bigger, then the centripetal acceleration gets smaller, &tc. The rate of revolution is the rate that the thing rotates. This would be the number of rotations divided by the time it took to do them. This is called the angular velocity, . Unfortunately, you don’t got no equation for this. Just remember that any rate is simply a quantity divided by time, so the angular velocity is simply: Where ? is the angular displacement, which will most likely be the number of revolutions that have been made? What happens to the centripetal acceleration if the velocity is increased and you want to keep the same radius? If the radius increases, but the velocity stays the same, what happens to the centripetal acceleration? That kind of thing. You should be able to derive an equation that relates linear speed to angular velocity. We did that in your gravity handout. The Physics Kahuna showed you how to develop the equation: Basically, the velocity is proportional to the angular velocity. So whatever happens when the linear speed increases also happens if the angular velocity increases. You might be able to get away without developing the equation at all. Using this concept, it is a simple matter to relate the rate of revolution of the particle to the magnitude of the centripetal acceleration. b. Describe the direction of the particle’s velocity and acceleration at any instant during the motion. The acceleration is always towards the center. The velocity is always tangent to the object’s path.

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