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$\bullet$$\bullet$ In a rescue, the 73 kgpolice officer is suspendedby two cables, as shown inFigure 5.44 . (a) Sketch afree-body diagram of him.(b) Find the tension in eachcable.

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A. SEE STRUCTUREB. the tension are $\left[T_{1}=482 \mathrm{N}\right]$ and $\left[T_{2}=590 \mathrm{N}\right]$

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

Cyl R.

October 22, 2020

University of Washington

Hope College

University of Sheffield

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.

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$\bullet$$\bullet$ In a re…

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02:37

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10:01

For the plate of Prob. 2.8…

05:59

$\bullet$ Two weights are …

04:54

In Fig. $12-68,$ an 817 $\…

04:40

Knowing that the tension i…

03:14

In Fig. 13-27, an $817 \m…

All right, so we've got a police rescue our hands here. They're two cables by which this police officer is hanging and cables or not at the same angles from this hand. Same angle from the ceiling. One of them is a 35 degree angle. The other 42. Okay, so let's draw, girl everybody diagram of the situation and you really have tension and the weight of the police officers, your forces here. So, first of all, obviously, the weight of the police officer force of gravity acting downwards. And then you've tensions acting upwards. Uh, there is tension of this one string. Um, uh, let's call it t one. And then this tension I have this other string that's at a higher angle is calling. Sorry. Let's collect Teo too. Okay. And angle. Because there's a 48 degree angle between the ceiling and the, um, and cable we have that this angle is 48 degrees because of 35. The angle between the ceiling, the cable of attention. One you have at this angle. There's, um this angle is 35 degrees. So that's the free body diagram. The situation now to find the tensions I have. We simply resolve forces on DH. So let's start in the ex direction. This is basically just a virtually the second law. It's a great equilibrium in the extractions are net force is zero. So you have that t warns horizontal component, which would be co signed 35 t one coast, 35 minus T too, Coz 48 2 twos, horizontal component would add up to zero. Okay, so So you have that tea. One equals t too. Coast 48 over coast 35. And so tension warm is just 0.8169 times tension too. Okay, so this tells us the relationship between them, but not their values. So it's resolved forces in the white direction now. Same deal there. No net force. So now you have a vertical components of Marty. One sign signed 35 plus two two signed 35 because they're both acting up, which is a positive direction. I mean, t to side 40 eights. I, uh, will be subtracted from W to give zero w the weight of the police officer. Okay. And thankfully, we know the mass of the police officers away is just achieved mass times force of gravity s O that 73 cure O grams times 9.8 meters per second squared. Okay, so the weight of the police officer is 715. Don't better. 7 15 point for mutants. Okay. And so we can finish up the dissolving in the white direction we have. Okay, let's write down t one in terms of two, too. Because we found your one in terms too. So we have Wow, T two times point 8169 by 816 92. Time's sign. 35 plus Just tea to sign 48. Believe me, call to 715 for us. We just found. And so you have the sounds up to 1.21122 equal seven fifteen 15.4. They're 14 2 is 590 newts. And we know the relationship. 21 to 2. City one is, um, assault years, Uh, 482 mutants and and yeah, that's a

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