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mmh Two forces, $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2},$ act on the $7.00-\mathrm{kg}$ block shown in the drawing. The magnitudes of the forces are $F_{1}=59.0 \mathrm{N}$ and $F_{2}=33.0 \mathrm{N}$ . What is the horizontal acceleration (magnitude and direction) of the block?

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1.83 $\mathrm{m} / \mathrm{s}^{2}$ to the left

Physics 101 Mechanics

Chapter 4

Forces and Newton’s Laws of Motion

Newton's Laws of Motion

Applying Newton's Laws

University of Washington

Simon Fraser University

Hope College

University of Winnipeg

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.

03:20

Two forces, $\overrightarr…

07:06

Two forces, $\vec{F}_{1}$ …

01:44

Two forces, F1 and F2, act…

03:00

Review Interactive Solutio…

01:41

before starting this probl…

04:57

Three blocks are in contac…

01:56

In the following figure, t…

06:56

Two blocks are sliding to …

02:56

Two blocks connected by a …

04:34

02:52

Two blocks are in contact …

11:09

A 2.00-kg block is placed …

01:36

Two blocks are connected b…

to solve this question and have to use a nuclear second law. And for that you choose the following reference frame vertical access that I will call why and a horizontal axis that I'll call X begin by noticing that the force F one isn't pointing to the axe direction or to the Y direction, but to both directions. So we have to decompose F one in its components. There is one horizontal component. We've F one component X and the vertical component, which is F one component white. Then we can see the following. This angle is an angle off 70 degrees, then these angle is an angle off 90 degrees. Reform. The only possibility for the intern angle these one is that these is 20 degrees. Moreover, this is also 90 degrees and then we again have an angle off 70 degrees appear. Using this angles, we can calculate both components off F one. It was as follows by using the sign off 20 degrees, which is given by in this context the opposite side of triangle. So our foreign component X, divided by F one. We are calculating as one component x because then F one component exit physicals to f times this sign off 20 degrees, then, using the co sign off 20 degrees, we can calculate F one component. Why? Because the coastline involves the address inside off the triangle, which is F one way, then the to sign off 20 is given by F one component. Why divided by f Shoot F one component white music was to f times the co sign off 20 degrees. There is a detail here, actually. Um, minor mistake. That is the following. I'm working with F one, but I have been writing f So let me correct this by adding subscript one. So now we knew Booth F one on its components, and now we're able to apply Newton's second law. Applying it to the X axis tells us that the Net force next direction is it caused the mass off the box times. It's horizontal acceleration, which is acceleration in the X direction, the next forcing next Directions. Composed by F two and F one component Web X. But F one component acts is pointing to the right so f one x minus. F two Is it close to M times a component X But we know that F one X is given by F one times the sign off 20 degrees. Then there's his minus. After on these easy goes to AM times a X. Therefore, the acceleration next direction is given by F one times the sign off 20 degrees minus F troop divided by the mass off the box, plugging in the values that were given by the problem. We got 59 times the sign off 20 minus 33 and this is divided by seven, resulting in the horizontal acceleration off approximately minus 1.83 meters per second squared Notice the minus sign. It tells us that the acceleration is pointing to the negative direction off our exactness or you know the words. It's 1.83 meters per second squared to the left, so it's meeting to the left.

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