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$\bullet$$\bullet$ A man pushes on a piano of mass 180 $\mathrm{kg}$ so that it slides ata constant velocity of 12.0 $\mathrm{cm} / \mathrm{s}$ down a ramp that is inclinedat $11.0^{\circ}$ above the horizontal. No appreciable friction is actingon the piano. Calculate the magnitude and direction of thispush (a) if the man pushes parallel to the incline, (b) if the manpushes the piano up the plane instead, also at 12.0 $\mathrm{cm} / \mathrm{s}$ paral-lel to the incline, and (c) if the man pushes horizontally, butstill with a speed of 12.0 $\mathrm{cm} / \mathrm{s}$ .

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a. 336.6 $\mathrm{N}$b. 3366$N$c. 343 $\mathrm{N}$

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

University of Michigan - Ann Arbor

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.

04:55

A man pushes on a piano of…

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A man pushes on a piano wi…

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03:21

04:20

08:04

07:31

(II) A 380-kg piano slides…

05:30

(II) A 380 -kg piano slide…

06:42

(II) A 330 -kg piano slide…

04:09

A $380-\mathrm{kg}$ piano …

02:24

A force of $1600 \mathrm{N…

03:00

A 450 -kg piano is being u…

01:33

Ramp Angle Billy stops whi…

Okay, so here, before we get to solving anything about the problem, let's identify what we're working with you, right? So you have a ramp that's inclined at 11 degrees to the horizontal appear. Now, that's all. It has to go down. Any constant speed off 12 centimeters. Sickness is very, very important to constant speed. So there is no acceleration here. A constant reid means acceleration zero on an acceleration of the parents, and it is going down. So, uh, we have a force of gravity that's after down Fritz all of its way. So gravity is acting downwards. And so you want no net force that no acceleration. You want no net force? Well, that means is gravity's actually got word, some other force. Let's call that F must be acting up words. Right. So that is what would cause it to go down at a constant velocity. So you need a force that can you need a force that can balance out the effect. Is that sort of push? This All this means is that the push the man exerts must be upwards. That is critical. Um, Quint of this whole thing of this whole problem. So Let's start with problems and especially part and that's actually dropped. Three bodies diagram for this. So man Kush is parallel to the plane. So here. Okay, so you have. So that's the not so Graham. You have the force of gravity acting downwards. W and this would be and an angle 11 degrees from the the the vertical. Great. So we choose us to their vertical access. You have normal force exerted by the ramp on the piano directly, upwards. And of course, then you have the man pushing. In this case, the man is pushing up, um, pushing the panic of In this case, the man is pushing perilous t inclined. So So you have force the force of the man pushing f sports. And so all you need to do here is resolved forces, and we'll do it in the extraction because F is entirely in your ex direction. So that would be zero in the ex direction, because the net force zero for a constant velocity. So this means that the force of gravity, which w is mg but that's not all we need mg in though in the extraction. So this would be MG sign 11 degrees. And that's because that's simply because, um, this is 11 degrees. This's there. W Okay, so you need seeing you. You basically want your force component in this extraction rate and the the geometry will work out. If you take any sign paid in this case and not co sign so mg sign 11 minus half because after is acting in the other direction in Syria and so f must be mg sign 11. So the mg is so masses 1 80 kilograms. She is, of course, 9.8 meters per second squared. Multiply that by sign 11 and you get force of 3 37 Nunes Okay, Part B, you're pushing. So it's weren't confusingly, but this would be the same as part of a And because you're again pushing off pushing, uh, parallel, uh, terraplane and finally for part. See, he was a good thing. And here you have the man pushing horizontal. So that means Is that so? It's straw everybody. Diagram of that situation have gravity acting downwards normal forest acting perpendicular to the direction. But then you have a horizontal for us. This is not exactly huh aligned with the X axis horizontal force f It's acting, um, to the right. Okay. And so this f is also inclined at 11 degrees. And that's because ramp itself is inclined at 11. Jeez, hand. And so again, we resolve forces net forcing the extraction, will you? Zero. So this means that f coast 11 this time Because because your extraction really is the along here on your wind direction is long the normal force. Right? So, uh, so you have an angle of coastline between your f m? Yeah, you're hubs, your X axis here, and so coast time 11 is equal again to n g sine 11 as in part A. And so that gives us that f will be equal to N G 10 11 because, remember, signed data over co signed data is just tending right, and so and again is 1 80 She is 9.8. So this gives us Finally is 3 43

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