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(II) Two masses $m_{A}=2.0 \mathrm{kg}$ and $m_{B}=5.0 \mathrm{kg}$ are oninclines and are connected together by a string as shown inFig. $37 .$ The coefficient of kinetic friction between each massand its incline is $\mu_{\mathrm{k}}=0.30 .$ If $m_{\mathrm{A}}$ moves up, and $m_{\mathrm{B}}$ movesdown, determine their acceleration.

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$=-2.2 \mathrm{~m} / \mathrm{s}^{2}$

Physics 101 Mechanics

Chapter 5

Using Newton's Laws: Friction, Circular Motion, Drag Forces

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

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Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

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So let's assume that the direction off Ah, the emotion off each block is the positive extraction. So here Ah, we're denoting with denoting box A as with gluing and do nothing box be with reading and also why is basically particle to the slope or vertical tow? The XX is now I've already drawn the free body diagram. Is there exactly similar? The only difference is for blockade of friction forces acting Ah, in the opposite direction. Off blocky and four block B. It's again acting in the opposite direction. But the tension force and ah friction force in Block B are in the same different direction, whereas in blockade, the tension force and the friction force are acting in the opposite direction. So as you can see that the questions will be quite similar, the only thing will be the change in sign for the Friction forces. So let's write the questions down for Block A and then we'll do the same thing for plumpy. So I'm using blue ing for block block A so it's gonna be f off in. It's in the wind direction minus and a G cool science Ada Hey, which is equal to zero. And from here we can we see that, if any is equal to M A G co signed did I? And in the extraction we have f off X Day that is equal dough F D minus and a G scientist up. It's actually shrink the picture a little bit so that it would have more room, toe buried equations so and a decide theta minus if off. If, um, let's see. We have f f r a. That's equal to M eight times so similarly in in, we'll write the same similar questions for dog be Israel. So why easy? Will do. Um, if and b minus and b g co sign, they don't be which is equal to zero. And then if off Expedia that's gonna be for big species, it will do and be signed data minus F off f r B minus f t with sequel toe M B times A. So what we can do here is first awfully can substitute this frictional friction force time. So, for the first case we have will have if off f r A, which is equal to new eight times. Um, if off any where Mew is deprivation of kind of friction so we can combine these two equations and substitute that here. Similarly, in Box B, we have f off F R B, which is equal to new B F off N B. So we'll add this question will relate this equation with this and with wybie wybie and then substitute that in the friction equation part. So if we do so, we will end up having to questions. One is in terms off m A and the other is in terms off m b a. So here on the solutions for those questions. So here I am. Hey, this is for the block A and ah for block B, it's m b times eight, so we can add them up and then solve for the ex elation from there. So when we added the questions, we had this league expression and we divided m a place and be on both sides to get rid off limitless and being from the left. And this is what we got here now. Ah, The given values for Amy and and be are two and five cages respectively. Then angles are 51 in 21 cage 21 degrees for its 51 for B. It's 21 mu. And maybe these are the coefficient of planet friction there. Same. Ah, there's essentially the same thing. It's 210.3. So if we use all the numbers we see that ex elation becomes negative. 2.2 Media over second squid. Thank you.

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