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(II) The block shown in Fig. 43 has mass $m=7.0 \mathrm{kg}$ andlies on a fixed smooth frictionless plane tilted at an angle$\theta=22.0^{\circ}$ to the horizontal. (a) Determine the acceleration of the block as it slides down the plane. (b) If the block startsfrom rest 12.0 $\mathrm{m}$ up the plane from its base, what will be theblock's speed when it reaches the bottom ofthe incline?

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a.) $$a=3.67 \mathrm{m} / \mathrm{s}^{2}$$b.) 2.452s

Physics 101 Mechanics

Chapter 4

Dynamics: Newton's Laws of Motion

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Moment, Impulse, and Collisions

Rebecca U.

October 14, 2020

Cornell University

Hope College

University of Winnipeg

McMaster University

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.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

03:59

(II) The block shown in Fi…

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03:15

The block shown in Fig. 4-…

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The block shown in the fig…

02:36

'11. The block shown …

02:12

Draw a free-body diagram o…

09:50

04:44

A block slides down a fric…

02:11

08:31

In Fig. $6-62,$ a 5.0 kg b…

06:17

A block is projected up a …

11:13

110 A $5.0 \mathrm{~kg}$ b…

Okay, so let's first draw the incline with free body diagram of the incline. And we have a mass A lying on this incline. Forced normal always always acts perpendicular to the surface of contact. So this would be forced, normal and always, always going straight down would be the weight. Ah, we have an angle here, Fada. And now we can't evaluate. We want to find the, um total X displacement s so we can say that the sum of forces in the X direction would be equal to M g sign of data. This would be the X component of gravity, and this would equal the mass times acceleration. So the acceleration would be equal to G sign of data if the masses here will cancel out. And so this is gonna equal a 9.8 meters per second squared sine of 22 degrees. And so we find that their acceleration is going to be Ah, let's actually keep it 9.8. Yeah, because we don't really need to evaluate. We can actually evaluate at the very end. So when we want to find the change in displacement in the extraction, we confined, We can use rather to de Cana matics, so Velocity Final squared would be a true equal to velocity. Initial squared plus two a Delta X and so here. Delta X would essentially be equal to negative the initial squared divided by two times a so Delta X would be equal to negative negative 4.5 meters per second quantity squared, and then this would be divided by two times acceleration of 9.8 sign of 22 degrees. And so this is giving us negative 2.758 meters. Now, the fact that is negative means that this would be up the plane. So essentially you're giving an initial velocity, and you just simply want to see how far up the planet goes given that the incline restriction lists and ah, in this case, gravity would be the only thing that would be stopping you stopping the block. So this would be your answer for a part A. And then for part B, we want to find the round trip time. So for Part B, we need to say that the final equals V initial plus 80. However, if we're trying to find the round trip time for tea. Ah, we can say that T is gonna equal velocity final minus Flossie Initial divided by a. However, in this case, because we're looking at the round trip time, the final velocity would actually be positive 4.5 meters per second because it's going up the incline stopping and then coming back down. The and the block will have the same mass initially as it will as it. Okay, so the initial velocity, it'll if it has a certain initial velocity, it will stop. Ah, again, 2.758 meters off the plane. However, once it once it reaches back to you, it will have that same inertial velocity. So that's why the final velocity is positive. Four points, five meters per second and then will be negative. A rather minus negative, 4.5 meters per second. This would account for the initial in the initial velocity of the block and then again divided by 9.8 times sign of 22 degrees. And so are our hour round trip time will be 2.452 seconds and this will be our final answer. That is the end of the solution. Thank you for watching

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