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The two blocks are released from rest when $r=0.8 \mathrm{m}$ and $\mathrm{u}=$ $30^{\circ}$. Neglecting the mass of the pulley and the effect of friction in the pulley and between block $A$ and the horizontal surface, determine $(a)$ the initial tension in the cable, $(b)$ the initial acceleration of block $A,(c)$ the initial acceleration of block $B$

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Physics 101 Mechanics

Chapter 12

Kinetics of Particles: Newton’s Second Law

Newton's Laws of Motion

Cornell University

Rutgers, The State University of New Jersey

University of Washington

Hope College

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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The two blocks are release…

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The velocity of block $A$ …

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The two blocks shown are o…

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'The two blocks shown…

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The system shown is at res…

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Hello, everyone. Here it is. Given two blocks are released from rest. That is initial velocity is zero. When our is called 2.8 m on angle theater is called to 30 degrees. There is no friction anywhere. And massive duopoly is Nikola David. We have to calculate initial tension and that cable initial exploration of the block eight on initial exploration, The block B Let us start solving it in terms off polar coordinates. So, as you mean, let theater and our are polar coordinates off block a onda, let by the is traditional coordinate off block beat to define. It's a class lately motion using constraint, relation for cable Then we can write but are plus by we Toby Constant differentiating ever be questioned We can write terrible tive off our plus derivative off white which will be velocity off. We must be zero different shipping again the second derivative of our plus acceleration off the skull to zero. So from here you will get acceleration off these called toe negative off double derivative Off our say, this is the question. But now four block eight, we have to draw the free body I grab for block eight three Body diagram. This is a block eight. The weight off the block collect vertically downward. This is the normal reaction on here. It will be tension t at angle theater with her gentle on in this direction. It having exploration. So submission off Ethics four Block eight can be written as must off into acceleration off A which is given by he cause of theater. That is these cult Oh, Mass of the block A tow acceleration off a Surkov theater ce question number two now free body diagram Off block beat, suspension. Tick plus weight off the block is called toe Massa block into its acceleration. So for block beat submission off force along by access you made right, So you will get I'm BG minus t. It's called to mass off the block B into its acceleration. This is your 30 question adding equation run in tow or eliminating people. Listen, one plus two you will get Massa block and two G. It's called toe must off a in tow acceleration off a Seiko potato plus mass off block beat into its acceleration. This is your fourth actually 40 question No radio and transfers component off Acceleration. Eight. Radio and transfers components off Acceleration eight. Radio Bilby but Peter Daughter Square on it can be written as equal toe er in tow. Er, this is the direction back to emit factor for it, and it's Magluta can be written as a cost off theater ce question. Fight initially, Anguilla velocity zero So theater dot is zero. You think in equation. What toe? Eliminate adult and changing the side. We can write Acceleration off, Be blocked Toby Equal toe a course of potato substituting equations six and four and solving for acceleration off a and 24 and solving for acceleration off block A. We will get the well, um, we into G well, but I am a circus theater plus M B course. A potato Massa Block B is given 25 kg. Acceleration is 9.81 mass off block is Contiki. Angle is 30 degree toe acceleration off. You will get five point for it meter per second, squared on from Equation six. Acceleration off block B can be written. It's five point forage because off 30 that is 4.75 meter per second square. So answer off a part from equation toe tension in the table. We can find country in tow. Five point for it. Sec off 30. That is 1 26.6 new Get the acceleration off. Block eight is five point for it. Meter per second squared towards right. An acceleration off block beat is 4.75 meter per second square. Don't be a direction that's not for it.

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