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To transport a series of bundles of shingles $A$ to a roof, a contractor uses a motor-driven lift consisting of a horizontal platform $B C$ which rides on rails attached to the sides of a ladder. The lift starts from rest and initially moves with a constant acceleration a $_{1}$ as shown. The lift then decelerates at a constant rate $\mathbf{a}_{2}$ and comes to rest at $D$, near the top of the ladder. Knowing that the coefficient of static friction between a bundle of shingles and the horizontal platform is 0.30 determine the largest allowable acceleration $\mathbf{a}_{1}$ and the largest allowable deceleration a $_{2}$ if the bundle is not to slide on the platform.
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04:53
Eric Mockensturm
Physics 101 Mechanics
Chapter 12
Kinetics of Particles: Newton’s Second Law
Newton's Laws of Motion
Cornell University
University of Washington
University of Sheffield
McMaster University
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.
09:37
Isaac Newton (4 January 1643 – 31 March 1727) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.
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for the given problem. Both. What? A. To apply the maximum explosion we apply Newton's second law to figure B 12.23 a. Some of forces I mean, why direction is equal to m E times a exploration sign Cecka. Then we can write this expression in one minus w A. We should call to m a. A sign later from here and one will be cool. Teoh for me G plus p Sign that where w a physical to m A terms gene. So this is the weight over Must a then for horizontal motion some of forces in X axis direction. He's m a course EC solution year. Also course data. Then we can write this expression So 0.3 Newton So the normal force musical Teoh m a times A of course there. Then, um, we plugged the value for in one. So this will be 0.3 into um we will directly substitute the values so 0.3 times a year times is important. Three times sign theta minus scores that, uh, this is called The miners are appointed three times G Then the next step we solve for exploration a year. So this is for exploration. A, We get a is equal to minus 0.3 g divided by 0.3. Sign that more on this course that then we plug that that away Luong that we have 65 and g we have 9.81 We get exploration to be 19 point 5 to 6 meter per second squared for Ah, but be off the problem in order to Hermine the maximum exploration de solution. Sorry, we apply their Newton's second law. Do ah figure 12 point 23 b. This is p some off forces in vertical direction. If why is it called Teoh? Minus 2 May a sigh later. From here in two minus W A will be equal to minus M a time sign better so in two will be equal to m A into J minus a sign better So some of forces in the Y direction xx sorry x axis will be m a times a course data. So this will be 0.3 and to visit call two m a times a cost data then Ah, zero. So exploration time 0.3 sign. We pluck their value for into that, you often hear Would you sign that? Uh um minus course, that, uh is it called 0.3 times G. So expression we get here by playing the value for theta, which is 65 g. That is a 9.81 We get expression to be four 0.238 meter per second square. So this is our exploration for but be off the problem.
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