What kind of pressure are expressed in inches of water column?

Four identical masses of 2.5 kg each are located at the corners of a square with 1.0-m sides. What is the net force on any one o

Ghella [55]

Answer:

F=8.0*10^{-10}N

Explanation:

See the attached file for the masses distributions

The force between two masses at distance r is expressed as

$F=\frac{Gm_{1}m_{2} }{r^{2} }\\ G=Gravitional constant \\$

since the masses are of the same value, the above formula can be reduce to

$F=\frac{Gm^{2}}{r^{2} }\\$

using vector notation,Let use consider the force on the lower left corner of the mass due to the upper left side of the mass is

$F_{12} =\frac{Gm^{2}}{r^{2} }j\\$

The force on the lower left corner of the mass due to the lower right side of the mass is

$F_{14} =\frac{Gm^{2}}{r^{2} }i\\$

The force on the lower left corner of the mass due to the upper right side of the mass is

$F_{13} =\frac{Gm^{2}}{d^{2} }cos\alpha i +\frac{Gm^{2}}{d^{2} }sin\alpha j\\$

The net force can be express as

$F=\frac{Gm^{2}}{r^{2} }j +\frac{Gm^{2}}{r^{2} }i +\frac{Gm^{2}}{d^{2} }cos\alpha i +\frac{Gm^{2}}{d^{2} }sin\alpha j\\\\F=Gm^{2}[\frac{1}{r^{2}}+ \frac{1}{d^{2}cos\alpha }]i + Gm^{2}[\frac{1}{r^{2}}+ \frac{1}{d^{2}sin\alpha }]j\\\alpha=45^{0}, G=6.67*10^{-11}Nmkg^{-2}$

if we insert values we arrive at

$F=6.67*10^{-11}*2.5^{2}[\frac{1}{1^{2}}+ \frac{1}{\sqrt{2}^{2}cos45 }]i + 6.67*10^{-11}*2.5^{2}[\frac{1}{1^{2}}+ \frac{1}{\sqrt{2}^{2}sin45}]j\\F=5.643*10^{-10}i+5.643*10^{-10}j$

if we solve for the magnitude, we arrive at

$F=5.643*10^{-10}i+5.643*10^{-10}j \\F=\sqrt{(5.643*10^{-10})^{2} +(5.643*10^{-10})}^{2} \\F=8.0*10^{-10}$

Hence the net force on one of the masses is

$F=8.0*10^{-10}N$

8 0

3 years ago

Advances in genetic engineering show that it is possible to:_____________. 1. enhance learning and memory ability in nonhuman or

san4es73 [151]

Answer:

1. enhance learning and memory ability in nonhuman organisms.

Explanation:

Genetic engineering can be defined as the process by which scientists modify the genome of an organism using new molecular tools. The resulting organism after the modification is known as Genetically Modified Organisms (GMO).

To create this genetically modified organisms requires recombinant DNA.

Advances in genetic engineering show that it is possible to enhance learning and memory ability in nonhuman organisms through biotechnology.

3 0

4 years ago

Two coherent sources of radio waves, A and B, are 5.00 metersapart. Each source emits waves with wavelength 6.00 meters.Consider

alexgriva [62]

Answer

given,

distance between A and B is equal to 5 m

let x be the distance of loud speaker from the source A

For constructive interference, path difference = mλ

x - (5 - x ) = 0 , for m = 0

2 x - 5 = 0

2 x = 5

x = 2.5 cm

For destructive interference

$|x - (5 - x )| = (2 m + 1)\dfrac{\lambda}{2}$

m = 0

$|2x - 5| = \dfrac{\lambda}{2}$

$|2x - 5| = \dfrac{6}{2}$

$\pm(2x - 5) = 3$

x = 4 , 1 cm

3 0

3 years ago

The ratio of red to blue marbles in a bag 3:2. If there are 18 red marbles. How many blue marbles are in the bag

Setler79 [48]

There are 12 blue marbles, because this can basically be modeled as 3/2 = 18/x, which can be solved by mutiplying 3 and 2 by 6

4 0

4 years ago

Tap on the photo. For each diagram, explain why the light behaves in the way that it does.

dem82 [27]

Answer:

Diagram 1, 3 and 4 can be explained with the phenomenon of refraction.

Refraction occurs when a ray of light crosses the interface between two mediums with different optical density: when this occurs, the ray of light is bent and its speed changes, according to Snell's law

$n_1 sin \theta_1 = n_2 sin \theta_2$

where $n_1,n_2$ are the refractive index of the 1st and 2nd medium

$\theta_1, \theta_2$ are the angle that the incident ray and the refracted ray makes with the normal to the interface

In diagram, 1, the ray of light arrives perpendicularly to the interface, so it is refracted through the medium but it doesn't change its direction (only its speed).

In diagram 3, the ray of light is refracted twice: at the 1st interface and at the 2nd interface. In the 1st case, it goes from a medium with lower refractive index to a medium with higher refractive index ( $n_1$ ), this means that $\theta_2$ , so the ray bends towards the normal. Vice-versa, in the 2nd case the ray goes from a medium with higher refractive index to a medium with lower refractive index ( $n_1>n_2$ ), so it bends away from the normal ( $\theta_2>\theta_1$ ).

In diagram 4, the ray of light is also refracted twice. The ray of light here acts exactly the same as in diagram 3, h

However, this time the 2nd interface is the opposite direction with respect to diagram 3, so in this case the ray of light at the 2nd interface bends in the opposite direction (still away from the normal).

Diagram 2 instead is an example of reflection, that occurs when a ray of light bounces off the interface between the two mediums, withouth entering the 2nd medium.

According to the law of reflection:

- The incoming ray, the reflected ray and the normal to the boundary are all in the same plane

- The angle of incidence is equal to the angle of reflection (both are measured relative to the normal to the boundary)

Therefore in this diagram, the ray of light hits the boundary at approx. 45 degrees from the normal, and then it is reflected back approximately at 45 degrees on the other side with respect to the normal.

3 0

4 years ago