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A 0.20-kg ball on a stick is whirled on a vertical circle at a constant speed. When the ball is at the three o’clock position, the stick tension is 16 N. Find the tensions in the stick when the ball is at the twelve o’clock and at the six o’clock positions.

14$N$18$N$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

University of Michigan - Ann Arbor

Hope College

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

02:26

A $0.20-\mathrm{kg}$ ball …

0:00

A 0.16 kg ball on a stick …

04:34

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A $0.30-\mathrm{kg}$ ball …

04:20

(II) A ball on the end of …

01:25

A 0.72 -kg ball is swung v…

04:31

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01:26

in this problem, we have to find the attention mystic that's being world around in a circle at two different points. They're given as the hand positions on a clock in the problem 12 and six clock. But I've just labeled them one and three here for clarity. Now the only thing that were given is the attention in the stick at position to its 60 Newtons. No, we can use that information and our knowledge about how the centripetal force works to find the tension at the other points as well. Let's look at the free body diagram specifically half point to weaken. See that the only force pointing towards the centre of emotion here is teach you itself. FDA is pointing straight downward. It has no effect on the strip. It'll motion at all. That means that he, too, must be equal to FC. So we have a value for our centripetal force. No, now remember, since the since the velocity of the Abbott is constant and the radius is constant and its mass is constant as well. That means that the centripetal force is constant. Everywhere in the circle, F C is equal to em. The squared over R So no matter where we are on a circle, as long as those values air kept constant, RFC is going to stay the same. And that's gonna be the key to solving this problem. Let's look at, um, our 0.1 so we can see from the free body diagram that there are two forces pointing towards the centre of our circular motion t one and FT. That means that FC must be equal to those two forces added together. Now we also know the F C is equal to 60 Newton's, so we have 60 Newton's equals f G plus Thio one. Now we know the mass of the object as well 0.2 kilograms. So if we want to solve for the tension, we can rearrange to say that t one equals 16 n minus f g, which we can unplug in values, for it's 0.2 times 9.8 years per second squared, and this over here is gonna be equal to kilograms. But both are in units of mutants and then we can find that the attention at 0.1 must be equal to 14.4 Newtons, which we can just round to 14. Newton's approximately, and now we've already answered the first part of our problem. Now we're gonna use exactly the same approach for our second point that we have to calculate what I've labeled 0.0.3. All right, so at this point, we can see that our two forces air pointing in opposite directions. The attention is pointing inward toward the center, and the gravitational force is pointing directly outwards. So that means that at this point, are centripetal force is equal to our attention, minus our gravitational force at that point. So once again, we can isolate t three to make it you to sell for F C plus mg in this case. Now we can plug in for a centripetal Force 16 Newton's, as we figured out when we sort of the problem. And in this case, we're gonna be adding or 0.2 kilograms plus 9.8 meters, three seconds squared, and that is gonna give us a value of 17.96 or approximately 18 Newton's. And that's our answer to the second part of the problem.

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