My Math Forum Questions about kinetic energy

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 July 24th, 2016, 05:26 PM #1 Member   Joined: Jan 2016 From: United States Posts: 61 Thanks: 7 Questions about kinetic energy These are a few end of chapter questions to see if you understood the theory. Unfortunately there's no answers for these in the book could someone double check my answers? It shouldn't be too much trouble, I appreciate the help as always ^.^ 1) An elevator is hoisted by its cables at constant speed. Is the total work done on the elevator positive, negative, or zero? The work done on the elevator is positive since the direction of motion is the same as the direction of force from the pull of the cables. (assuming the elevator is moving up) 2) If it takes total work W to give an object a speed v and kinetic energy K, starting from rest, what will be the objectâ€™s speed (in terms of v) and kinetic energy (in terms of K) if we do twice as much work on it, again starting from rest? Since the object starts at rest then the initial kinetic energy is zero. In terms of v, since K = 1/2(m * v^2) then 2K = m * v^2 and sqrt(v) = 2K / m 3) If there is a net nonzero force on a moving object, can the total work done on the object be zero? Explain, using an example. Yes. if the force is perpendicular to the object the work done will be zero. If an object is being pushed along an even floor, then it will have the constant downwards perpendicular force of gravity acting on it, but the work done on the object by this force is zero since it's perpendicular to the motion. Although if the object were being pulled upwards then gravity would be anitiparallel and apply negative work. 4) A falling brick has a mass of 1.5 kg and is moving straight downward with a speed of 5.0 m>s. A 1.5-kg physics book is sliding across the floor with a speed of 5.0 m>s. A 1.5-kg melon is traveling with a horizontal velocity component 3.0 m>s to the right and a vertical component 4.0 m>s upward. Do all of these objects have the same velocity? Do all of them have the same kinetic energy? For both questions, give your reasoning. For velocity they all have 5 m/s (including the melon 3-4-5 triangle), but they are not the same for kinetic energy. The fall bricks motion is parallel to the force of gravity which does positive work on it. The book sliding across the floor has movement perpendicular to the force of gravity so gravity does zero work, and lastly the melon which is travelling at an upward angle is antiparallel to the force of gravity, therefore gravity does negative work on it. 5)When a certain force is applied to an ideal spring, the spring stretches a distance x from its unstretched length and does work W. If instead twice the force is applied, what distance (in terms of x) does the spring stretch from its unstretched length, and how much work (in terms of W) is required to stretch it this distance? This answer is almost all guess work (by that I mean I'm not very sure if it's right or not), but if you stretch the spring a certain distance, then by newtons laws there will be an antiparallel force with equal magnitude. To further stretch the spring by some base unit of distance you will have to overcome the negative work done by this force, and every time you stretch the spring by another of these base units of distance the negative work you have to overcome will grow. If there's some formula for this I really have no idea.
July 25th, 2016, 05:20 AM   #2
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Joined: Jun 2015
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These are tricky and definitely designed to test your understanding.

Look carefully at my notes and ask any questions you have about them, they are rather brief since there are 5 questions.

I have done thme in an attachment since there is some maths involved.

Trust the maths and be careful to get to the end of the calculation, you dod not do this.

Also trust the maxim

No work is done if a system of forces in equilibrium moves its point of application.
Attached Images
 mech1.jpg (51.0 KB, 10 views)

Last edited by studiot; July 25th, 2016 at 05:22 AM. Reason: add missing attachment.

 July 26th, 2016, 02:42 AM #3 Member   Joined: Jan 2016 From: United States Posts: 61 Thanks: 7 Thanks! and yea number 2 was a typo

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# if it takes total work w to give an object a speed

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