phy 121
Your 'cq_1_25.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Seed quest 25.1
A steel ball of mass 110 grams moves with a speed of 30 cm / second around a circle of radius 20 cm.
What are the magnitude and direction of the centripetal acceleration of the ball?
answer/question/discussion:
In QA 24 I learned that the magnitude of the acceleration of an object going at a constant speed around a circle is
A = v^2/r
Therefore:
A = 30^2 cm/s / 20cm = 45 cm/s^2
Good, but the calcuation would be expressed as
a = 30^2 (cm/s)^2 / 20cm = 45 cm/s^2.
The units as you express them would be1 / s^2, not cm/s^2.
However in query 24 I read about the centripetal acceleration being equal to the acceleration of gravity.
A = force of gravity
Which would simply be 9.8 m/s^2 or 980cm/s^2
This would be the case for a mass swinging in a vertical circle, if the string goes slack for an instant at the very top of the circle. At that instant there is no centripetal force and only gravity acts on the mass. Since the mass remains in the circular path, its centripetal acceleration at that instant comes only from gravity.
In QA 24 I also learned that the acceleration is directed toward the center of the circle, but then my notes say that the centripetal force is also directed toward the center of the circle.
since net force = mass * acceleration, an acceleration toward the center implies a net force toward the center.
In query 24 I figured that the motion of the object is perpendicular to the force maintaining it’s circular motion. Either way I’m not sure how you would determine the direction of a ball traveling in a circle. I might say that it is 360 degrees. But if it is perpendicular to the force then I might just assign it to be along the x axis and the force to be along the y axis.
the centripetal force is perpendicular to the velocity of an object moving on a circle. The direction of the velocity is tangent to the circle, while the direction of the acceleration, and therefore the force, is toward the center. The radial line from the center to the circle is perpendicular to the tangent line.
This applies at any point.
If the ball happens to be on the y axis then the tangent vector and therefore the velocity is in the x direction, while the acceleration is in the y direction.
What is the magnitude and direction of the centripetal force required to keep it moving around this circle?
answer/question/discussion:
If I go with acceleration being v^2/r then I will say that the centripetal force = mass * accel
110g = .110kg
.110kg * 45 cm/s^2 = 4950 kg * cm/ s^2.
kg * cm/s^2 is correct, but the units are neither MKS units nor CGS units. kg belongs to the former, cm to the latter.
This result converts to 49.5 kg * m/s^2, which is the same as 49.5 Joules.
I am sure it is directed in towards the center of the circle, but since the ball is constantly moving I hope I can just freeze it in time and designate it as being the y axis (90 degrees)
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30 mins
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&#This looks good. See my notes. Let me know if you have any questions. &#