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The drawing shows a $25.0-\mathrm{kg}$ crate that is initially at rest. Note that the view is one looking down on the top of the crate. Two forces, $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2},$ are applied to the crate, and it begins to move. The coefficient of kinetic friction between the crate and the floor is $\mu_{\mathrm{k}}=0.350 .$ Determine the magnitude and direction (relative to the $x$ axis) of the acceleration of the crate.

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1.61 $\mathrm{m} / \mathrm{s}^{2}$ $34.6^{\circ}$ abov

03:50

Dading Chen

Physics 101 Mechanics

Chapter 4

Forces and Newton’s Laws of Motion

Newton's Laws of Motion

Applying Newton's Laws

Chew C.

October 12, 2020

A person pushes on a 72.6 kg refrigerator with a horizontal force of -267 N

Catherine A.

October 27, 2020

Dading C., thanks this was super helpful.

This will help alot with my midterm

Cornell University

Simon Fraser University

University of Sheffield

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.

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

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The drawing shows a $25.0-…

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The drawing shows 25.0-kg …

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A. $1000-\mathrm{N}$ crate…

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A $25.0$ -kg crate rests o…

So the drawing, which looks something like this, You have F two Is 54. Newton's pointing to the right. F one is 80 Newtons pointed up into the left, this is the y axis and that is the X axis. Yeah, Okay, so we need to determine the magnitude in the direction of the acceleration of the great, So notice that if you're pulling to the right and up into the right, the direction of motion is going to be to the left. So our acceleration needs to be positive to find this net force. It's the square root of F one x plus F two, X squared plus F one Y squared. There's no F T Y term, because FT was only in the X direction. So 88 F one X is 88 co sign of 55 degrees from the figure. So, plugging this in and we get a force of 126 nine newtons. So, looking at the son of all of the forces, you have friction pulling you in the opposite direction. So the sum of all of the forces is mass times acceleration From Newton's 2nd law. So this is the forest minus the friction, which is um UK times the normal force here. The normal force is equal to the weight. So um U k mg. We know the U K. We know and jesus constant. We just found F. So actually the masses cancelled, so we don't need to worry about the masses. And we get that the acceleration Is equal to 1.65 meters per second squared and the angle is equal to the inverse tangent of the Y component of the forces, which is F one way over the X component, which is F one X plus F two. So we get an angle of 34.6°

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