The equivalence principle is a fundamental law of physics that states that inertial forces and gravitational forces are similar in nature and are often indistinguishable from each other.
The application of the equivalence principle to in combination with the general theory of relativity allowed the refinement of the equations of the theory helping give birth to the theory of general relativity.
For example, in special relativity objects are considered to be moving with a constant velocity. When the principle of equivalence is introduced this allows considering inertial frames or accelerated frames of reference and the gravitational forces in a system thus completing the special theory of relativity.
When the acceleration in the general theory of relativity is considered to be zero then it reduces to the special theory of relativity.
An aluminum sphere is 8.55 cm in diameter. What will be it's % change in volume if it is heated from 30 C to 155 C?
We know that
• The sphere diameter is 8.55 cm.
,• The temperature change is from 30 C to 155 C.
First, we have to find the radius of the sphere. The radius is the half diameter.
[tex]\begin{gathered} r=\frac{d}{2}=\frac{8.55\operatorname{cm}}{2} \\ r=4.275\operatorname{cm} \end{gathered}[/tex]Now we have to find the volume of the sphere using the following formula.
[tex]V=\frac{4}{3}\pi(r)^3[/tex]Where r = 4.275 cm.
[tex]\begin{gathered} V=\frac{4}{3}\pi(4.275\operatorname{cm})^3 \\ V\approx327.26(cm)^3 \end{gathered}[/tex]Then, we use the following formula
[tex]V_2-V_1=BV_0(T_2-T_1)[/tex]Where the initial volume is 327.26 cubic cm, B is a constant about thermal expansion for aluminum, and we have to find the final volume to then calculate the percentage change.
[tex]\begin{gathered} \Delta V=75\times10^{-6}\cdot327.26(155-30) \\ \Delta V=75\times10^{-6}\cdot327.26(125) \\ \Delta V\approx3.07(cm)^3 \end{gathered}[/tex]This means that the volume change is 3.07 cubic centimeters.
At last, we have to divide the volume change by the initial volume, and then we have to multiply it by 100% to express it as a percentage.
[tex]\frac{\Delta V}{V_1}\times100=\frac{3.07}{327.26}\times100\approx0.938[/tex]Therefore, the percentage change is 0.938%.Two skaters with the same mass face each other standing still. Both skaters push off each other and they love in opposite directions. What’s the momentum before pushing off? Total momentum after pushing off? Momentum of each in comparison to each other after pushing off
We will have the following:
Total momentum before pushing each other off: 0.
Total momentum after pushing each other off: 0.
Momentum of each other after pushing off in comparison to each other:
*Person 1: A positive value.
*Person 2: A negative value of equal magnitude to the momentum of person 1.
11. If 100. g of gold-198 decays to 12.5 g in 25.3 days, what is the half-life of gold-198?
Given data
*The amount of gold-198 is N = 100 g
*The gold-198 decays is n = 12.5 g
*The given time is T = 25.3 days
The expression for the radioactivity decay is given as
[tex]N=n(\frac{1}{2})^{\frac{T}{t}}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} 100=12.5(\frac{1}{2})^{\frac{25.3}{t}} \\ t=8.43\text{ days} \end{gathered}[/tex]You have measured a carts mass and observed that it changed position. What other information do you need to determine the carts momentum during that time? A. The carts electric charge. B. The net force on the cart. C. The displacement of the cart. D. The carts gravitational potential energy
Given that we know the mass and displacement of an object for a given amount of time, to determine the momentum we can use the fact that the change in momentum is equal to the impulse. This can be written as:
[tex]Ft=m\Delta v[/tex]Where:
[tex]\begin{gathered} F=\text{ net force} \\ t=\text{ time} \\ m=\text{ mass} \\ \Delta v=\text{ change in velocity} \end{gathered}[/tex]Therefore, we need to know the net force in order to determine the momentum in that time.
I just need part c please The first one I know it’s 32
We are given that in a falling object the distance "d" is directly proportional to the square of the time and the proportionality constant is 16. This means that the function of distance is given by:
[tex]d(t)=16t^2[/tex]The average rate of change is given by the following formula:
[tex]r=\frac{d(t_f)-d(t_0)}{t_f-t_0}[/tex]Where:
[tex]t_f,t_0=\text{ final and initial time}[/tex]Now, we substitute the values of "d(t)":
[tex]r=\frac{16t_f^2-16t_0^2}{t_f-t_0}[/tex]We can factor the numerator and we get:
[tex]r=16\frac{(t_f-t_0)(t_f+t_0)}{t_f-t_0}[/tex]Simplifying we get:
[tex]r=16(t_f+t_0)[/tex]For the first 2 seconds we have:
[tex]\begin{gathered} t_0=0 \\ t_f=2s \end{gathered}[/tex]Substituting the values we get:
[tex]\begin{gathered} r=16(2s+0s) \\ r=32 \end{gathered}[/tex]Therefore, the average rate of change is 32
For the next 2 seconds we have:
[tex]\begin{gathered} t_0=2s \\ t_f=4s \end{gathered}[/tex]Now, we substitute the values:
[tex]\begin{gathered} r=16(4s+2s) \\ r=96 \end{gathered}[/tex]Therefore, the rate of change in the next two seconds is 96.
For the next 2 seconds we have:
[tex]\begin{gathered} t_0=4s \\ t_f=6s \end{gathered}[/tex]Substituting the values we get:
[tex]\begin{gathered} r=16(6s+4s) \\ r=160 \end{gathered}[/tex]Therefore, the rate of change is 160
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!!
Two samples of water are prepared, one with red food coloring and one with blue. When carefully combined, the red-colored water is able to float on top of the bluecolored water. Which statement best explains this result?
A. The blue-colored water is hotter and more dense.
B. The red-colored water is cooler and more dense .
C. The blue-colored water is cooler and less dense.
D. The red- colored water is hotter and less dense.
Answer:
B. The red-colored water is cooler and more dense .
i’m a really confused on what to do the teacher didn’t really explain it well so i’m clueless on what to do..
ANSWER:
0, no direction
balanced
STEP-BY-STEP EXPLANATION:
We must add all the forces, the horizontal and vertical.
We must take into account the direction of the force, to the right and up are positive while to the left and down are negative.
Therefore:
[tex]\begin{gathered} F_{Rvertical}=F_n+F_g=20+(-20)=20-20=0 \\ F_{\text{Rhorizontal}}=F_{\text{app}}+F_{\text{fric}}=20+(-20)=20-20=0 \end{gathered}[/tex]Being the vertical and horizontal forces 0, the net force is 0 as it has no magnitude and no direction.
It is balanced, since the net force is 0
A _____ stores electrical energy, whereas _____ is the ratio of a stored charge on each plate to the electric potential difference between the plates.capacitor, electrical potentialcapacitor, capacitanceinsulator, energyinsulator, capacitance
A capacitor stores electrical energy, whereas capacitance is the ratio of a stored charge on each plate to the electric potential difference between the plates. Therefore, second option is correct.
Whenever the charge stored in the capacitor increases it increase the capacitance of capacitor but when the potential difference increases it decrease the capacitance of a capacitor.
A 1,982-kg car starts from rest at the top of a driveway 6.74 m long that is sloped at an angle of 30 degrees with the horizontal. If an average friction force of 2,721 N impedes the motion of the car, find the speed (in m/s) of the car at the bottom of the driveway.Use the approximation that g ≈ 10 m/s2.
In this situation, we cannot apply the law of conservation of energy, as there is friction. For us to solve, let us start by writing the balance equations. We'll have:
[tex]\sum F_x=P*sin(30)-Fat=ma[/tex][tex]\sum F_y=N-P*cos(30)=0[/tex]In order to find out the acceleration, we can use the first equation:
[tex]a=\frac{P*sin(30)-Fat}{m}=\frac{1982*10*sin(30)-2721}{1982}=3.627\frac{m}{s^2}[/tex]The car will then suffer this acceleration on the sloped plane. With this, we can calculate its speed by the end using the equations for a uniformly accelerated movement:
[tex]S(t)=S_0+v_0t+\frac{at^2}{2}\Rightarrow6.74=\frac{3.627*t^2}{2}\Rightarrow t=1.928s[/tex]This is the time the car will take to reach the bottom. By replacing this on the equation for the velocity we get:
[tex]v(t)=v_0+at=0+3.627*1.928=7\frac{m}{s}[/tex]Then, our final answer is 7 m/s
A serving size of Lays Potato Chips is 15 chips. There are 160 calories in one serving and 10 grams of fat. If you eat two servings how many calories and grams of fat are there? Question 5 options: 320 calories, 20 gram of fat 160 calories, 10 grams of fat 340 calories, 15 grams of fat 325 calories, 25 grams of fat
If you eat two servings of Lays Potato Chips, you would have consumed 320 calories and 20 gram of fat.
One serving of Lays Potato Chips = 15 chips
Calories in one serving of Lays Potato Chips = 160 cal
Fat in one serving of Lays Potato Chips = 10 g
Calories in two serving of Lays Potato Chips = 160 * 2 = 320 cal
Fat in two serving of Lays Potato Chips = 10 * 2 = 20 g
Two serving of Lays Potato Chips will have twice the fat and calories of one serving of Lays Potato Chips. So multiply the values of calories and fats by 2 to get the required value.
Therefore, if you eat two servings Lays Potato Chips, you would have consumed 320 calories and 20 gram of fat.
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If you eat two servings of Lays Potato Chips, there are 320 calories and 20 gram of fat so option 1 is correct.
Given:
A serving size of Lays Potato Chips is 15 chips.
There are 160 calories in one serving and 10 grams of fat.
Calories in two serving of Lays Potato Chips = calories in one serving *2
= 160 * 2
= 320 calories.
Fat in two serving of Lays Potato Chips = fat in one serving * 2
= 10 * 2
= 20 grams
Therefore, if you eat two servings Lays Potato Chips, there are 320 calories and 20 gram of fat so option 1 is correct.
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Tory experiments with pulleys in physics class. She applies 60 newtons of force to a single pulley to lift a bowling ball. By adding another pulley, she'd get a mechanical advantage of 2. Whats the minimum input force she'll need to lift the ball if she adds another pulley?
Given,
The force applied by Tory, F=60 N
Mechanical advantage after adding the second pulley, MA=2
As Tory applies 60 N of force when there is only one pulley, the weight of the ball is 60 N.
Thus the output force is 60 N.
The mechanical advantage is given by,
[tex]MA=\frac{\text{output force}}{input\text{ force}}[/tex]On substituting the known values,
[tex]\begin{gathered} 2=\frac{60}{\text{input force}} \\ \Rightarrow input\text{ force}=\frac{60}{2} \\ =30\text{ N} \end{gathered}[/tex]Thus the minimum input force tory need to apply is 30 N
A motion detector detected that a toy car covered 2 m at a constant speed of 0.25 m/s. Sketchthe graph to represent the motion of an obiect.
Explanation
the function for the distance is given by
[tex]\text{distance}=\text{ sp}eed\cdot time\text{ }[/tex]then, let
speed= 0.25 m/s
time= t
distance= 2m
hence, replace
[tex]\begin{gathered} \text{distance}=\text{ sp}eed\cdot time\text{ } \\ \text{distance}=0.25\frac{m}{s}\cdot t \\ d(t)=0.25t\Rightarrow equation\text{ of the line} \end{gathered}[/tex]Step 2
now, to graph the line we need 2 points
a) when t= 0
[tex]\begin{gathered} d(t)=0.25t\Rightarrow equation\text{ of the line} \\ d(0)=0.25\cdot0 \\ d(0)=0 \\ so \\ \text{coordinate 1(0,0)} \end{gathered}[/tex]P1(0,0)
b) when the car has covered 2m
let d=2
replace and solve for x
[tex]\begin{gathered} d(t)=0.25t\Rightarrow equation\text{ of the line} \\ 2=0.25t \\ \text{divide both sides by 0.25} \\ \frac{2}{0.25}=\frac{0.25t}{0.25} \\ 8=t \\ \text{hence, after 8 seconds, the distance is 2 m, so the coordinate is} \\ (8,2) \end{gathered}[/tex]P2(8,2)
finally, draw a line that passes through the point P1(0,0) and P2(8,2)
I hope this helps you
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute, rpm) and the cube of its diameter. If a shaft of a certain material 2 inches in diameter can transmit 36 hp at 75 rpm, what diameter must the shaft have in order to transmit 134 hp at 35 rph
the shaft must have 4 inches of diameter
Explanation
Step 1
given that The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute, rpm) and the cube of its diameter.
[tex]Power\propto diamter^3v[/tex]so
a) If a shaft of a certain material 2 inches in diameter can transmit 36 hp at 75 rpm
[tex]\begin{gathered} 36\text{ hp=\lparen2 in\rparen}^3*75\text{ rpm*k} \\ 36=600\text{ k} \\ k=\frac{36}{600}=0.06 \end{gathered}[/tex]b)what diameter must the shaft have in order to transmit 134 hp at 35 rph
[tex]\begin{gathered} Power\propto diamter^3v \\ Power=d^3*v*k \\ replace \\ 134=d^3*35*0.06 \\ 134=d^3*2.1 \\ divide\text{ both sides by 2.1} \\ \frac{134}{2.1}=\frac{d^3*2.1}{2.1} \\ 63.80=d^3 \\ cubic\text{ root in both sides} \\ \sqrt[3]{63.80}=\sqrt[3]{d^3} \\ 3.996=d \\ rounded \\ d=4\text{ inches} \end{gathered}[/tex]therefore
the shaft must have 4 inches of diameter
I hope this helps you
A spring stores 68 J of potential energy when it is stretched by 6 cm. What is the spring constant?
The formula for calculating the elastic potential energy is expressed as
Elastic potential energy = 1/2kx^2
where
k represents the spring constant
x represents the compression or distance by which the spring was stretched.
From the information given,
Elastic potential energy = 68
x = 6 cm
we would convert 6 cm to m. Recall,
100cm = 1 m
6 cm = 6/100 = 0.06 m
By substituting these values into the formula, we have
68 = 1/2 x k x 0.06^2
68 = 0.0018k
k = 68/0.0018
k = 37777.78 N/m
The spring constant is 37777.78 N/m
1. what is the range of the infrared part of the electromagnetic spectrum A.microwaves to red light B.radio waves to microwavesC. X-rays to gamma raysD. ultraviolet to x-rays
The range of the infrared wave is from the red to the microwave.
the rannge of wavelength of the infrared is ,
[tex]2-14\mu m[/tex]Hence, A is the correct option.
Find the x-component of thisvector:47.3m39.40
We know that
• The angle of direction is 39.4.
,• The magnitude of the vector is 47.3 m.
To find the horizontal component, use the following formula.
[tex]v_x=v\cdot\cos \theta[/tex]Use the given information to find the horizontal component.
[tex]v_x=47.3m\cdot\cos 39.4\approx36.6m[/tex]Therefore, the x-component is 36.6(m).Describe the cause of waves as a fluid motion
Wind is the most frequent cause waves. The friction between the wind and the surface of the water produces wind-driven waves, also known as surface waves. A wave crest is produced when wind continuously disturbs the water's surface in an ocean or lake.
Waves that include longitudinal and transverse motions include water waves, for instance. The particles move in clockwise rings through the waver as a wave passes over it. The circles' radius gets smaller the deeper into the ocean you go.The disturbance propagates through the medium as a result of the medium's particles oscillating repeatedly and periodically about their equilibrium position. Without any real transfer of the medium's particles, energy and momentum are moved from one place to another.To know more about waves
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The neutrons within the nucleus of an atom have what charge?Question 15 options:negativesame as an electronsame as a protonno charge
The nuclues of an atom contains the proton and the nuetron. The proton is positively charged while the nuetron has no charge.
I need to know how to do these and the formula too.
Answer:
a = 4m kgm/s & b. v = 4 m/s
Explanation:
a:
A is approaching in the opposite direction of B
So let's take the velocity of A as negative.
Here we'd need to solve this using conservation of momentum.
m1u1 + m2u2 = m1v1 + m2v2
So initial momentum = (m X (-4)) + (m X 8) = -4m + 8m = 4m
b:
After collision sphere A stops, so v = 0 for sphere A
Using the conservation of momentum formula, we get
(m X (-4)) + (m X 8) = (0 X m) + (m X v) [let the final velocity of B be v]
⇒ 4m = vm
⇒ v = 4 m/s
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Here is the answer of a tutor
Take a look.
[tex]\sqrt[2]{24+5}[/tex]A vector has the components Ax=22 m and Ay=13 m. What is the magnitude of thisvector? What angle does this vector make with the positive x axis?
Answer:
Magnitude = 25.55 m
Angle = 30.58 degrees
Explanation:
If the vector has the components Ax = 22 and Ay = 13, we can represent the vector as:
Therefore, the magnitude of this vector is the magnitude of the red vector. It means that we can calculate its length using the Pythagorean theorem where 22 and 13 are the legs, so:
[tex]\sqrt[]{Ax^2+Ay^2}=\sqrt[]{22^2+13^2}=\sqrt[]{484+169}=\sqrt[]{653}=25.55\text{ m}[/tex]Then, we can find the angle using the trigonometric function tangent, so:
[tex]\begin{gathered} \tan \theta=\frac{Ay}{Ax} \\ \tan \theta=\frac{13}{22} \\ \tan \theta=0.5909 \\ \theta=\tan ^{-1}(0.5909) \\ \theta=30.58 \end{gathered}[/tex]So, the answers are:
Magnitude = 25.55 m
Angle = 30.58 degrees
A strobe-light series of pictures is taken of a red ball and a blue ball. The red ball was allowed to drop straight down, and the blue ball was given an initial horizontal velocity. Lines are drawn connecting each red ball image with the corresponding blue ball image. Describe the lines connecting the images.1) The lines slope down from the red ball to the corresponding blue ball.2) The lines slope up from the red ball to the corresponding blue ball.3) The lines are vertical.4) The lines are horizontal.
The lines are horizontal.
Horizontal velocity doesn't have any effect on the acceleration or speed of falling. In every picture, the red and the blue are both at the same HEIGHT, even though the blue one is pulling away horizontally.
What percentage of the speed of light in vacuum is the speed of light in a diamond? Incorrect: Your answer is incorrect. answer in:_____%
Explanation
Step 1
find the speed of ligth in the diamond:
to do that we can use the formula
[tex]refractive\text{ index\lparen}\mu)=\frac{c(\text{ speed of light in vaccum\rparen}}{s(\text{ speed of light in the material\rparen}}[/tex]we know that :
[tex]\begin{gathered} refractive\text{ index of diamond\lparen}\mu)=2.42 \\ speed\text{ of llight in the vaccum=c=300000 }\frac{km}{s} \end{gathered}[/tex]so, replace and solve for speed of light in the diamond
[tex]\begin{gathered} refractive\text{ index\lparen}\mu)=\frac{c(\text{ speed of light in vaccum\rparen}}{s(\text{ speed of light in the material\rparen}} \\ 2.42=\frac{3*10^5\frac{km}{s}}{s} \\ s=\frac{3\times10^5\frac{km}{s}}{2.42} \\ s=123966.9\text{ }\frac{km}{s} \\ \end{gathered}[/tex]finally, to find the percentage apply this formula
[tex]\begin{gathered} \text{ \% }=\frac{speed\text{ of light in diamond}}{spped\text{ of ligth invaccum}}*100\text{ \%} \\ replace \\ \text{ \%=}\frac{123966.9\frac{km}{s}}{3*10^5\frac{km}{s}}*100\text{ \%} \\ \text{ \%=0.413*100\%} \\ \text{ \%=41.3 \%} \\ rounded\text{ 41\%} \end{gathered}[/tex]so, the answer is
41 %
I hope this helps you
The figure below is made of 1-inch cubes. Two cubes have been removed from each row of the middle layer of a prism.What is the volume of the figure above? A. 34 in3 B. 38 in3 C. 40 in3 D. 36 in3
The volume of the prism is given by:
[tex]\begin{gathered} V=w\cdot l\cdot h \\ so\colon \\ V=4\cdot2\cdot5 \\ V=40in^3 \end{gathered}[/tex]Since two cubes have been removed from each row, the new volume is:
[tex]V_T=40in^3-4in^3=36in^3[/tex]Answer:
36 in³
The metric unit of charge, the Coulomb, is ________.A) the charge of just one electron or protonB) the smallest unit of charge used in scienceC) is an amount of energy equivalent to equal numbers of electrons and protonsD) equivalent to a large number (6.25 x 1018) of unitary charges
The meteric unit of charge, the Coulomb, is equivalent to a large number of (6.25 x 10^18) of unitary charges.
Hence, the correct option is (D)
Abby, who has a mass of 45.0 kg, is riding at 40.0 m/s in her red sports car whenshe must suddenly slam on the brakes to avoid hitting a deer crossing the road. Shestrikes the air bag, that brings her body to a stop in 0.500 s. What average forcedoes the seat belt exert on her?
We are given the following information
Mass = m = 45.0 kg
Initial speed = vi = 40.0 m/s
Time = t = 0.500 s
We are asked to find the average force that the seat belt exerted on her.
Recall from Newton's second law of motion,
[tex]F=m\cdot a[/tex]Where a is the acceleration of the car and is given by
[tex]v_f=v_i+a\cdot t[/tex]Where vf is the final velocity of the car that must be 0 since the car was stopped.
[tex]\begin{gathered} 0=40.0+a\cdot0.500 \\ a=\frac{-40.0}{0.500} \\ a=-80\; \; \frac{m}{s^2} \end{gathered}[/tex]The negative sign indicates deacceleration since the card was stopped.
So, the force is
[tex]\begin{gathered} F=m\cdot a \\ F=45\cdot80 \\ F=3600\; N \end{gathered}[/tex]Therefore, the seat belt exerted a force of 3600 N on her.
A pumpkin pie in a 10.50 in diameter plate is placed upon a rotating tray. Then, the tray is rotated such that the rim of the pie plate moves through a distance of 258 in. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees.
The angular distance traveled in degree, radian and revolution are : 49°, 0.273 radian and 0.14 revolution respectively
What is angular velocity?The angular distance traveled around a circular path is the number of radians the path subtends.It can also be defined as the angle made by a body while moving in a circular path.
From the definition, angular distance (theta) = distance moved/radius.
radius = diameter/2
radius= 10.50/2= 5.25inches
angular distance= 258/5.25= 49.14°
in revolution , = 49.14/360=0.14 revolution
in radian ,= 49.14/180= 0.273radian
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A closed-pipe resonator is closed at both ends. Is this true or false?
A closed cylinder air column must have a closed end and an open end.
Then, the answer is:
[tex]\text{False}[/tex]What happens to Centripedal force on the planet around a star if the radius of an orbit is doubled ? assume that velocity remains the same A) the Centripedal force will be half of its original value B) the Centripedal force will be double its original value C) the Centripedal force will be 1/4 of its original value D) the Centripedal force will not change
We will have the following:
We know that:
[tex]F_c=\frac{mv^2}{r}[/tex]If we double the radius, then:
[tex]F_c=\frac{mv^2}{(2r)}\Rightarrow F_c=\frac{1}{2}\frac{mv^2}{r}[/tex]So, the centripetal force will be half of its original value. [Option A]
What is the voltage of a circuit that has a resistance of 100 and an internal current of 2 amps 200 volts0 0.02 voltsO 50 volts
Given,
The resistance of the circuit, R=100 Ω
The current in the circuit, I = 2 A
From Ohm's law, we have,
[tex]V=IR[/tex]Where V is the voltage.
On substituting the known values,
[tex]V=2\times100=200\text{ V}[/tex]Thus the voltage of the internal circuit is 200 V.
That is the correct answer is the 1st option.