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Three forces act on a moving object. One force has a magnitude of 83.7 N and is directed due north. Another has a magnitude of 5

LekaFEV [45]

Answer:

$|\vec{F}_3| = 102.92 \ N$

$\theta = 57 \° 24 ' 48''$

Explanation:

For an object to move with constant velocity, the acceleration of the object must be zero:

$\vec{a} = \vec{0}$ .

As the net force equals acceleration multiplied by mass , this must mean:

$\vec{F}_{net} = m \vec{a} = m * \vec{0} = \vec{0}$ .

So, the sum of the three forces must be zero:

$\vec{F}_1 + \vec{F}_2 + \vec{F}_3 = \vec{0}$ ,

this implies:

$\vec{F}_3 = - \vec{F}_1 - \vec{F}_2$ .

To obtain this sum, its easier to work in Cartesian representation.

First we need to define an Frame of reference. Lets put the x axis unit vector $\hat{i}$ pointing east, with the y axis unit vector $\hat{j}$ pointing south, so the positive angle is south of east. For this, we got for the first force:

$\vec{F}_1 = 83.7 \ N \ (-\hat{j})$ ,

as is pointing north, and for the second force:

$\vec{F}_2 = 59.9 \ N \ (-\hat{i})$ ,

as is pointing west.

Now, our third force will be:

$\vec{F}_3 = - 83.7 \ N \ (-\hat{j}) - 59.9 \ N \ (-\hat{i})$

$\vec{F}_3 = 83.7 \ N \ \hat{j} + 59.9 \ N \ \hat{i}$

$\vec{F}_3 = (59.9 \ N , 83.7 \ N )$

But, we need the magnitude and the direction.

To find the magnitude, we can use the Pythagorean theorem.

$|\vec{R}| = \sqrt{R_x^2 + R_y^2}$

$|\vec{F}_3| = \sqrt{(59.9 \ N)^2 + (83.7 \ N)^2}$

$|\vec{F}_3| = 102.92 \ N$

this is the magnitude.

To find the direction, we can use:

$\theta = arctan(\frac{F_{3_y}}{F_{3_x}})$

$\theta = arctan(\frac{83.7 \ N }{ 59.9 \ N })$

$\theta = 57 \° 24 ' 48''$

and this is the angle south of east.

7 0

3 years ago

You exit the Vet's Office.

kifflom [539]

(1) When you exit the office, your position is 60.8 m and the total distance traveled is 60.8 m.

(2) When you walk to the bank, your position is 60.8 m, displacement is 0 and the total distance traveled is 121.6 m.

(3) When you walk to flower shop, your position is 26.9 m, displacement is 0 and the total distance traveled is 148.5 m.

(4) When you walk to the Vet's Office, your position is 60.8 m, displacement is 60.8 m and the total distance traveled is 182.4 m.

<h3>You exit the Vet's Office</h3>

When you exit the Vet's Office, your position is 60.8 m (assuming your starting position is the bank).

The total distance have you travelled = 26.9 m + 33.9 m = 60.8 m

your new position is 60.8 m

your displacement = 60.8 m - 60.8 m = 0 (assuming your starting position is the bank)

total distance have you travelled = 60.8 m + 60.8 m = 121.6 m

<h3>You walk to the Flower Shop</h3>

your new position is 26.9 m

your total displacement = 0 + 26.9 m = 26.9 m

total distance have you travelled = 26.9 m + 121.6 m = 148.5 m

<h3>You walk to the Vet's Office</h3>

your new position is 26.9 m + 33.9 m = 60.8 m

your total displacement = 26.9 m + 33.9 m = 60.8 m

total distance have you travelled = 148.5 m + 33.9 m = 182.4 m

Learn more about displacement here: brainly.com/question/2109763

#SPJ1

5 0

2 years ago

What object best represents a true scale model of the shape of earth?

BabaBlast [244]

Any object that is spherical in shape would best represent a true scale model of the shape of the Earth. Examples are ping pong balls, billiard balls, marble and other smooth spherical objects. The shape of the Earth is called the oblate spheroid. The "oblate" would refer to an oblong shape and "spheroid" would refer to an almost spherical shape. The earth has on almost spherical shape and has a slightly oblong appearance. The diameter from the South pole to the north pole was measured to have a value of 12714 km while the diameter of the equator is approximately 12756 km. As you can see, the values are not equal. This makes the earth not a perfect sphere.

6 0

4 years ago

Two identical soccer balls are rolled toward each other. What will be true after they collide head-on? (2 points)

Vlada [557]

well it depends on how much force was added but if they both have the same amount of force and they were rolled at the same time either they will bounce backwards or roll backwards not thats your question will they roll backwards are bounce backwards?

8 0

4 years ago

Explain why it takes much more effort to

natali 33 [55]

Answer:

Mass Kinetic Energy and Jules

Explanation:

The train in question is big and heavy and a car is decently heavy but say a train moving at 55 mph can plow through a car and a car driving at 55mph driving at a train will be stopped dead in its tracks. This is because newtons laws of motion specifically an object in motion will stay in motion unless its opposed. The train also has a payload behind it meaning it hurts with force while a car doesn't have to much mass behind it. The train takes loner to stop for as it's acceleration as well as it's deceleration are very slow because its huge and takes a lot of force to stop it while a car is very centralized and compact when it comes to weight and its brakes are usually effective at stopping at 55 mph in about 2 to 6 seconds while a train might stay moving for a good 35 seconds. The force behind the train is immense for as even if the wheels don't spin at all the train will still move since the force behind it is great and a cars tires have a lot of grip and not a lot mass which plays into the force the car has so it can stop simply.

6 0

3 years ago