An elementary student of mass is swinging on a swing

AP Physics 1 Aid » Newtonian Mechanics » Circular, Rotational, and also Harmonic Motion » Circular and Rotational Motion » Centripetal Force and Acceleration

A ball is attached to a string that is 1.5m long. It is spun so that it completes 2 full rotations eexceptionally second. What is the centripetal acceleration felt by the ball?


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Explanation:

We are sindicate asked to uncover the centripetal acceleration, which is given by:

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We were given

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 in the problem statement (radius will be equal to the length of the string), so we only must discover the velocity of the sphere.

You watching: An elementary student of mass is swinging on a swing

We are told that it travels in a circle with radius 1.5m and completes two complete rotations per second. The length of each rotation is simply the circumference of the circle:

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The velocity have the right to be found by multiplying that distance by the frequency:

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Now we have actually every one of our variables and also can plug right into our initially equation:

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Example Concern #2 : Centripetal Force And Acceleration


An amusement ride is provided to teach students around centripetal force. The ride is a circlular wall that you location your ago on. The wall and floor then begin to spin. Once it reaches a details rotational velocity, the floor drops, and also the students are pinned to the wall as an outcome of centripital force.


A student of mass 50kg decides to go on the ride. The coreliable of static friction in between the student and also wall is 0.8. If the diameter of the ride is 10m, what is the maximum period of the ride"s rotation that will certainly save the student pinned to the wall once the floor drops?

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Possible Answers:
Correct answer:

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Explanation:

Tbelow is a lot going on in this difficulty and also it will take a number of measures to get to the answer. However before, as soon as you boil the question down, we are pretty a lot asked exactly how quick should the ride spin so that the centripetal pressure on the student provides enough static friction to store the student from falling. Let"s job-related through this difficulty one step at a time.

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First, let"s number out what minimal static frictional force is required. This pressure will certainly be equal to the weight of the student; the student"s weight will certainly pull downward, while the friction of the wall pushes upward.

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Now we can calculate the normal pressure compelled to reach that magnitude of frictional pressure. Note that the vector for the normal force will be perpendicular to the wal, directed towards the facility of the circlel.

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This normal force is the minimum centripital force required to save the student pinned to the wall. We can convert this to centripital acceleration:

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We have the right to now convert centripital acceleration to a translational velocity making use of the equation:

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Rearvarying for velocity, we get:

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This is the velocity that the external wevery one of the ride need to be spinning at. Because we know the radius of the ride, we have the right to transform this velocity into a maximum duration, the final answer:

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If you weren"t sure just how to come around this equation, just think about your systems. You recognize you should get to units of seconds, and you have a value via units of m/s. Therefore, you should cancel out the meter and obtain the second on height.