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course Phy 241
7/14 2:24 am
024. Centripetal Acceleration
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Question: `q001. Note that this assignment contains 4 questions.
Note that this assignment contains 4 questions.
When an object moves a constant speed around a circle a force is necessary to keep changing its direction of motion. This is because any change in the direction of motion entails a change in the velocity of the object. This is because velocity is a vector quantity, and if the direction of a vector changes, then the vector and hence the velocity has changed. The acceleration of an object moving with constant speed v around a circle of radius r has magnitude v^2 / r, and the acceleration is directed toward the center of the circle. This results from a force directed toward the center of the circle. Such a force is called a centripetal (meaning toward the center) force, and the acceleration is called a centripetal acceleration.
If a 12 kg mass travels at three meters/second around a circle of radius five meters, what centripetal force is required?
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Your solution:
v^2 / r
= (3 meters/second) ^ 2/(5 meters)
= 1.8 meters/second ^ 2
Fcent = 12 kg * 1.8 meters/second ^ 2
Fcent = 21.6 Newtons
confidence rating #$&*:
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Question: `q002. How fast must a 50 g mass at the end of a string of length 70 cm be spun in a circular path in order to break the string, which has a breaking strength of 25 Newtons?
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Your solution:
r = .7 m m= .05 kg, F =25 Newtons
v = `sqrt( 25 N * .7 meters / (.05 kg) )
v = sqrt(350 m^2 / s^2)
v = 18.7 m/s
confidence rating #$&*:
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Question: `q003. What is the maximum number of times per second the mass in the preceding problem can travel around its circular path before the string breaks?
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Your solution:
r = 2 `pi * .7 m
r = 4.4 m
18.7m/s /4.4 m
= 4.25 s^-1
confidence rating #$&*:
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Question: `q004. Explain in terms of basic intuition why a force is required to keep a mass traveling any circular path.
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Your solution:
The direction of motion of a massive object can't change without giving it some sort of a push, in which without a large amount of force an object in motion will stay in motion along a straight line and without change in speed.
confidence rating #$&*:
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If you understand the assignment and were able to solve the previously given problems from your worksheets, you should be able to complete most of the following problems quickly and easily. If you experience difficulty with some of these problems, you will be given notes and we will work to resolve difficulties.
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Question: `q004. The centripetal force on a 0.2 kg mass, as it travels around a circle of radius 80 cm, is 12 Newtons. How fast is it moving?
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Your solution:
m =0.2 kg, r = 80 cm =.8 m, Fnet = 12 Newtons
v = sqrt(12 Newtons * .8 cm/(0.2 kg))
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You wrote the radius as .8 cm rather than .8 m. You corrected this below.
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v = sqrt(9.6 N*m/0.2 kg)
v = sqrt(48 m^2/s^2)
v = 6.92 m/s
confidence rating #$&*:
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Self-critique (if necessary):
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&#Good work. See my notes and let me know if you have questions. &#