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$\bullet$ $\bullet$ $\bullet$ Pendulum. A small 0.12 kg metal ball is tied to a verylight (essentially massless) string 0.80 $\mathrm{m}$ long to form a pendu-lum that is then set swinging by releasing the ball from restwhen the string makes a $45^{\circ}$ angle with the vertical. Air dragand other forms of friction are negligible. What is the speed ofthe ball when the string passes through its vertical positionand what is the tension in the string at that instant?

the speed of the ball is $2.1 \mathrm{m} / \mathrm{s}$the tension is $1.9 \mathrm{N}$

Physics 101 Mechanics

Chapter 7

Work and Energ

Physics Basics

Applying Newton's Laws

Kinetic Energy

Potential Energy

Energy Conservation

Hope College

University of Sheffield

University of Winnipeg

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No, we're going to solve a problem. But 35 in this problem, it is given that Ah, metal ball, is it 45 degrees with the vertical is a dress at this position this Angula ce 45 degrees. And this is the position where we have to find the velocity off the metal ball, the metal balls, things like this in a circular part. The initial height off the metal ball from the based is at the total land off the string is l so by trigonometry, this land will become l cause what? Be fine. Does the height etch will become and minus l course 45 does metal ball is above the initial level by heart articles L minus L course 45 degrees No. Were given that the moss off the ball is equal to 0.12 Okay, Jeez, the land off The string is equal to zero point. Hey, makers. No, using energy conservation. The initial energy off the metal ball at 45 degree with the vertical is mm t that. Then we release this ball from this Then at the lowest position, it will have only kind of take energy which is half V square now substituting the values 9.81 is the value of X solution due to grab DJ into L minus l because 45 degrees good to have the square. This implies that 9.81 into zero pointed, which is the length of the string into one minus costs 45 which is 0.29 three sequel to have V squared Because we get we lost e at the lowest point, we close to wind one four meters 1st 2nd this is a velocity when we release is the murderball No, For the second part, we should see that had the lowest point. Yeah, the guilt is acting downwards and the tension force in the string is a ports. The metal ball is also tracing a circular pod So a year we will apply the concept off centripetal force. Also, as we know that FC centripetal force is always towards there Sender. So weekend day, the tension force minus the weight off the metal ball is equal to the centripetal force which is M v squared. But ah, in this case, are is the length of the string. So we can die. M v squared by l No plugging in the given values we can right? Deke was mg well, which is 0.12 into nine points. Yeah, one plus every square, well, 0.1 toe in tow. V We have already calculated the value of E, which is two point 14 He's square. Bye. Let off the string, which is zero point. This will give us zero one Born. Seven 1772 plus 0.6 Air seven On adding both these values be your pension is equal to one point it six Newton's. This is the record in Sile force in the spring when the metal ball is and the

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