Of the four states of matter, which has particles that are the most tightly packed together?

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

A Ray of light in air is incident on an air to glass boundary at an angle of 30. degrees with the normal. If the index of refrac

elena55 [62]

Answer:

A

Explanation:

Snell's law states:

n₁ sin θ₁ = n₂ sin θ₂

where n is the index of refraction and θ is the angle of incidence (relative to the normal).

The index of refraction of air is approximately 1. So:

1 sin 30° = 1.52 sin θ

θ ≈ 19°

5 0

3 years ago

A metal block has a density of 5000 kg per cubic meter and a mass of 15,000 kg. What is its volume?

Naily [24]

Taking into account the definition of density, the volume of the metal block is 3 m³.

<h3>What is density</h3>

Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.

In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance.

Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

$density=\frac{mass}{volume}$

From this expression it can be deduced that density is inversely proportional to volume: the smaller the volume occupied by a given mass, the higher the density.

<h3>Volume of the metal block</h3>

In this case, you know that:

Density= 5000 $\frac{kg}{m^{3} }$
Mass= 15000 kg
Volume= ?

Replacing in the definition of density:

$5000 \frac{kg}{m^{3} } =\frac{15000 kg}{volume}$

Solving:

volume×5000 $\frac{kg}{m^{3} }$ = 15000 kg

volume= $\frac{15000 kg}{5000 \frac{kg}{m^{3} }}$

<u><em>volume= 3 m³</em></u>

In summary, the volume of the metal block is 3 m³.

Learn more about density:

brainly.com/question/952755

brainly.com/question/1462554

#SPJ12

4 0

2 years ago

Jake drags a sled of mass 25 kg across the snow. The sled is attached to a rope that pulls with a force of 50 N at an angle of 3

madam [21]

Answer:

218.5 N

Explanation:

In order for the sled to be in equilibrium along the vertical direction, the forces acting along this direction must be balanced. So the equilibrium equation is:

$N+F sin \theta - mg =0$