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$\bullet$$\bullet$ A block with mass $m_{1}$ is placed on an inclined plane withslope angle $\alpha$ and is connected to a second hanging block withmass $m_{2}$ by a cord passing over a small, frictionless pulley(Fig. 5.68 ). The coefficient of static friction is $\mu_{3}$ and the coef-ficient of kinetic friction is $\mu_{\mathrm{k}}$ (a) Find the mass $m_{2}$ for whichblock $m_{1}$ moves up the plane at constant speed once it is set inmotion. (b) Find the mass $m_{2}$ for which block $m_{1}$ moves downthe plane at constant speed once it is set in motion. (c) Forwhat range of values of $m_{2}$ will the blocks remain at rest if theyare released from rest?

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Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

McMaster University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

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.

03:25

A block with mass $m_{1}$ …

12:02

05:28

06:16

A block with mass $m_1$ is…

03:55

07:22

A block of mass $m_{1}=21.…

05:27

$\bullet 4.60$ A block of …

02:17

Two blocks of mass $M_{1}$…

03:51

Block $A$ in Fig. 6-56 ha…

02:57

Block $A$ in Fig. $6-56$ h…

19:28

Two blocks made of differe…

17:09

A marble block of mass $m_…

all right. So not a free body diagram. But here is the situation that were presented. Uh, you have a bank of Aram and Kleiner Alfa to these two, the horizontal. And so And then you have two masses connected by a hole in one on the ramp and won pain from the from string of the streams. Tension T intention of acting toe wants to pull our extra members on. But we're calling this mass on the right one. Oops. I was hanging on to OK, and so in part, your velocity is acting uphill. So you're friction Force will be acting officer. Back it down so you can resolve forces when second law and And the note, first of all that hear from them too. Tea isn't called em to rate. The rate of the second mass is equal to detention in st okay themselves, then, looking at, uh, looking at the, uh why so our slips the extraction? Uh, you want to know the force? So this Can't you see this? The attention team vertical tend to chief is equal to the ex component heart. Wait one. So it's someone she signed after. That's the ex coupon of Amon G. Uh, plus, I have some care. She's also hacking downwards in this case. And, uh, except K is just music Cara Times. Yeah, use of character times and maybe. And oops. And we can figure out you can figure out from dissolving forces in the why direction that lost zero. And where is just this? This force here, normal force on DSO and uh will be equal to m one. She co sign off. That's the white component of Mong. So we can write that down. As you said, care and sorrow after taking me on downers OK, turns on one she insight No play selves quick. So M too is equal to we can you know. And two, take them One common, uh, sign ofthe bus, music care, coastline this case and part B your velocity acting down the hill So a fictional force must be acting uphill straight himself and remains the same. But what changes is the net force in the end then and the extraction. And so you get to you calls I'm too to you again. Izzy called tio again m one Teo site Alfa minus of so can. So we can we can infer that everything will be the same except for for him too. Except for this side here, right into his M one time side, Alfa minus use of care cosign Alfa Because that's what I've said Carrion live in is a little minus sign before it. All right, And then and then in part, see curtsy. We simply want a range of them too. And the range is given by these two extremes, actually, and parts and be so the rains will be the minimum is someone sign off minus music care cosign alpha and so too will be less than or equal to or greater memory. Call to that. And I'm too will be less generous. Call to the maximum, which is his part. And one sign time. Sign up, up plus care Casanova and that's it.

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