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A ball is attached to a horizontal cord of length $\ell$ whose other end is fixed, Fig. $42 .(a)$ If the ball is released, what will be its speed at the lowest point of its path? (b) A peg islocated a distance $h$ directly below the point of attachment of the cord. If $h=0.80 \ell,$ what will be the speed of the ball when it reaches the top of its circular path about the peg?

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A. $\sqrt{2 g \ell}$B. $v_{3}=\sqrt{1.2 g \ell}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

University of Sheffield

University of Winnipeg

McMaster University

Lectures

04:05

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.

04:30

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.

03:53

A ball is attached to a ho…

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04:03

06:31

03:58

01:47

03:54

ball is attached to horizo…

02:00

The string in Fig. $8-38$ …

07:01

A 0.50-kg ball that is tie…

04:37

A $0.50-\mathrm{kg}$ ball …

01:18

A ball attached to a strin…

You are to throw a ball wi…

04:55

A 1.0 -kg ball at the end …

01:31

Round your answers to two …

A ball is thrown at a spee…

So for this problem here you have an object spear which is attached to the horizontal string. Off length L other end is fixed and the ball is released. And when the ball is released, it will. You don't take this path and finally come to this location here water the speed of at the lowest point, which means me to calculate the speed at this point off this ball. So in this case, only gravity is doing the work on the boat. So gravity does work on the ball. If the gravity is doing work on the balls of mechanical energy is conserved in there. No non conservative forces. So we'll have of even our dislocation at zero and the height. Why one is equals to l. Because this whole distance exactly close to L and a dislocation we'll have by twos equals zero. Come on. And we need to find out the value of Vito. Where this location by the conservation of energy. So we have one and we have the location to So by the conservation of energy, we have even equals E too. So total energy, the top just drive official potential energy bitches mgl and at the bottom is only kinetic energy, which is half m V two squared. So therefore the velocity V two is in terms f l s studio. So that is the expression for a part. Now, for the be part in this scenario, we have a peg at this location. So Pakistan at that location. So what happens that this string there's an obstacle at this point. So at this point, when it comes, then there is a circular motion with starts and there's a big which is a hide edge. So circular motion starts around this big with radius equals to EJ minus help. So using conservation of energy for the points too. And for the point, This is the point, you know. And the points three. So circular motion, you know, starts had this location here. Then this is the center other circular motion. And when the ball faces this obstruction, the string faces this obstruction. Then the circular motion, you know, will be in this direction here with the radius of H minus. L So this is the location three here. And this is the location to so we can see here now. Ah, sorry. This location here. This location This is not X minus. L I just This is actually l minus, Ash, because Al is greater than so. This is a ll minus session because this whole distance, this whole distance was l and this was that. So they will Circle of motion is radios of l minus h. So when the object reaches dislocation from this location, the total height gained from this location to this location is two times l minus h. So therefore vied three with respect to the ground, there's two times minus h which is equals two, two times l minus 0.8 l because they're saying that the ratio is given as estrellas 0.8. So if you saw that, you will get to l minus 0.1 point six cell which should give you a point for l. So that is the white relocation. Now we set energies equals you two equals to be three by the law of conservation of energy. And then we'll have the equation for the law of conservation of energy. All right, here, have em beato squared. Less mg vie to should be equals to have m v three squared bless mg by three. So what we're doing a re equipping energy is that two and three. So now we'll just plugging in the equation. So we'll get half. And Vito squired was already proved to jail and right, Do you know a zero? Because this is Louis ground level here that should be equals 2/2 M v three squared, bless mg times height, riches point for ill. So if you saw that, you will get Vetri has square root off 1.2 g o. So that is the answer to

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