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Show that $h$ must be greater than 0.60$\ell$ if the ball in Fig. 42 isto make a complete circle about the peg.
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Physics 101 Mechanics
Conservation of Energy
Moment, Impulse, and Collisions
Rutgers, The State University of New Jersey
University of Michigan - Ann Arbor
In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.
In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.
Shown below is a small bal…
Use the figure provided.
A ball is thrown at a spee…
Complete Swing show that, …
Go A ball is to be shot fr…
All right. So you have, um you want, uh, you want the ball to complete the circle with the string just going. Aah! Slack on the top of the circle. So, for in order for this to happen, the critical condition is that the force of gravity, you must balance the circular or centripetal force. Right? So eventually, force of gravity is equal to M V Square. Let's call it a secret. Squared over R. This is the critical velocity of which this will happen, and so critical velocity is critical. Velocity square is she are and are the radius of a circle is just l minus h from the diagram. So this is G times are minus h critical velocity squared. Next, we invoke energy conservation. So initially a top you have ngl the potential energy. That's all you have. Uh, and, um, But when this turn is completed, who have 1/2 em Time's critical velocity squared the kinetic energy, plus the potential energy of that point. So that is m two times two are because, uh, what goes up to twice the radius of a circle. So the diameter, In other words, um, we can cancel the masses. Then we have G L. It calls 1/2 times this times shoot times are minus H plus G to Judy Times l minus H. Because that's our so again. So now the G's canceled, too, And, um and we're left to it. One point, uh, two point we're left with 2.5. Uh, l is, uh is equal. Two, um is equal to 1.5 h river. That's how that one works out. So h is just, um, to fifth of 3/5 of l 0.6 times up. So this is the critical height. Therefore, H eyes greater than or equal to 0.6 l. So it must be at least points excel and, uh, has to be greater than points. Excel for this too. Uh, but then so this means there has to be greater than a nickel 2.6 l to complete the whole circle. That's it.
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