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$\bullet$ A woman takes her dog Rover for a walk on a leash. To get the little pooch moving forward, she pulls on the leash with a force of 20.0 $\mathrm{N}$ at an angle of $37^{\circ}$ above the horizontal. (a) How much force is tending to pull Rover forward? (b) How much force is tending to lift Rover off the ground?

Forward is 16 Newtons while Lifting is 12 Newtons,

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Marcus G.

October 18, 2020

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

McMaster University

Lectures

04:16

In mathematics, a proof is…

04:48

In mathematics, algebra is…

03:31

A stubbom dog is being wal…

13:43

Two dogs pull horizontally…

02:26

A woman at an airport is t…

03:05

0:00

What force is required to …

05:19

A person is walking three…

07:32

A person is walking two d…

05:12

03:01

01:14

A girl exerts a $36-\mathr…

02:46

Force $A$ car is on a driv…

A horse pulls a cart with …

02:25

To keep her dog from runni…

02:36

How much work must Denise …

04:44

A team of eight dogs pulls…

03:32

01:24

A 70 kg firefighter slides…

04:01

A 15-kg sled is pulled ac…

01:42

A toy cart is pulled a dis…

this's Chapter one problem. 42. So in this problem, we're given a vector man suit in direction. That would be the force that the woman is pulling on the leash with. And then we're asked how much force is tending to pull her over forward and how much force is tending to lift Rover off the ground. So what these questions are asking mathematically is basically what is thie, horizontal component of the source. And what are the vertical component of the force? Because the horizontal component tends to pull over forward and the vertical component tends to lift her over off the ground. So let's start by drawing the force. It's 20 Newton's at an angle of 37 degrees above the horizontal. So put that in blue. Here. Here's our force vector length of 20 Newtons, and then this angle is 37 degrees. So basically looking for the X and Y components of this vector, and you can get that for any given vector by our X. The X component is the magnitude of the vector, which in this case is 20 Newton's times the co sign of the angle measured counterclockwise from the X axis and luckily that is the angle that were given directly in this problem. Why? What's already substituting in one of the values? Well, in this case is co sign of 37 degrees. And so, for the first part, we want that force tending to pullover forward. That's the ex component. So we're going to substitute in 20 Newton's as our magnitude, and you get that The ex component is 16 0.0 Newtons for the white component. We do the same thing, except that it's going to be a sign instead of a co sign. So our why is 20 Newtons ten's a sign of 37 degrees and just looking at that vector, we see that it's more horizontal and vertical, so we expect that our vertical component switch resolving for here is going to be smaller than a horizontal component. So plug in the numbers and we find out that indeed it is smaller. It's only 12.0, mutants. So that's it. Part a 16 Newton's of force tending to pull her over forward and part B 12 Newton's of force that attending to put lift Rover off the ground

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