Given:
Energy = 8.1 x 10⁻¹⁵ eV.
Let's find the frequency of the pendulum.
To find the frequency, apply the formula for the energy of a light quantum:
[tex]E=hf[/tex]Where:
E is the energy
h is Planck's constant = 6.63 x 10⁻³⁴ m² kg/s
f is the frequency.
Where:
1 eV = 1.6 x 10⁻¹⁹ J.
Rewrite the formula for f and solve:
[tex]f=\frac{E}{h}[/tex]Thus, we have:
[tex]f=\frac{8.1\times10^{-15}*(1.6\times10^{-19})}{6.63\times10^{-34}}[/tex]Solving further:
[tex]\begin{gathered} f=\frac{8.1\times10^{-15}*(1.6\times10^{-19})}{6.63\times10^{^{-34}}} \\ \\ \\ f=1.95\text{ Hz.} \end{gathered}[/tex]Therefore, the frequency of the pendulum is 1.95 Hz.
ANSWER:
1.95 Hz
Why are metals the best conductors of electricity? Why are metals the best magnetisers ? What is the key characteristic of metals that allows us to answer these two apparently different questions?
Question: What is the key characteristic of metals that allows us to answer these two apparently different questions?
Answer:
Explanation:
The atoms of a metal contains at least one free electron. Conduction of electricity is due to the these free electrons.
Magnetism is also affected by the availability of free electrons.
Thus, metals are good conductors of electricity and also the best magnetisers because of the availability of free electrons in metals
What is the extension force (in lbf) of a 14 inch diameter cylinder with a 10 inch rod and pressure of 700psi?
The given problem can be exemplified in the following diagram:
To determine the extension force we will use the definition of pressure:
[tex]P=\frac{F}{A}[/tex]Where "F" is the force, and "A" is the area. To determine the area we will use the following equation:
[tex]A=\frac{\pi D^2}{4}[/tex]Where "D" is the diameter. The force acts over the area of the 10 inches diameter alone, therefore we don't need to have into account the area of the rod. Replacing the value of the diameter we get:
[tex]A=\frac{\pi(14in)^2}{4}[/tex]Solving the operation:
[tex]A=153.94in^2[/tex]Replacing in the formula for the pressure we get:
[tex]P=\frac{F}{153.94in^2}[/tex]Since we are required to determine the force, we will multiply both sides by the area:
[tex]153.94in^2P=F[/tex]Replacing the given value of the pressure we get:
[tex](153.94in^2)(700\frac{lbf_{}}{in^2})=F[/tex]Solving the operations we get:
[tex]107756.62lb_f[/tex]Therefore, the extension force is 107756.62 lbf.
A uniform rod of mass m=1.0 kg and length L=2 meters is free to rotate about its center as shown in the figure. A constant torque is applied by a constant force of magnitude F=5.0 N to one end of the rod, as shown. To be clear, the force is always perpendicular to the rod, which rotates about the axis indicated by the red line.a) If the rod is initially at rest, how long does it take to reach an angular velocity omega=30 radians/s. b) Assuming the torque stops when the angular velocity is 30 radians/s, what is the total rotational energy of the rod? c) The rod suddenly turns into a uniform sphere of radius R=1m and mass M=1.0 kg rotating about its center. Assuming angular momentum is conserved, what is the angular velocity of the sphere omegasphere?
a)
If the length is 2 meters and the rod rotates about its center, so 2 meters is the diameter, and the radius of rotation is 1 meter.
Then, if the force is 5 N, let's calculate the torque:
[tex]\begin{gathered} \tau=F\cdot r \\ \tau=5\cdot1=5\text{ Nm} \end{gathered}[/tex]Then, calculating the rotational inertia and the angular acceleration, we have:
[tex]\begin{gathered} I=\frac{1}{2}mr^2 \\ I=\frac{1}{2}\cdot1\cdot1^2=0.5 \\ \\ \alpha=\frac{\tau}{I}=\frac{5}{0.5}=10 \end{gathered}[/tex]The angular acceleration is 10 rad/s², so to reach an angular velocity of 30 rad/s, it takes 3 seconds.
b)
The rotational energy can be calculated with the formula below:
[tex]\begin{gathered} E_k=\frac{1}{2}I\cdot\omega^2 \\ E_k=\frac{1}{2}\cdot0.5\cdot30^2 \\ E_k=225\text{ J} \end{gathered}[/tex]c)
The angular momentum is given by:
[tex]\begin{gathered} L=I\cdot\omega \\ L=0.5\cdot30 \\ L=15 \end{gathered}[/tex]Then, since the rod turns into a sphere, the new rotational inertia is:
[tex]\begin{gathered} I=\frac{2}{5}mr^2 \\ I=\frac{2}{5}\cdot1\cdot1^2 \\ I=\frac{2}{5}=0.4 \end{gathered}[/tex]So the new angular velocity is:
[tex]\begin{gathered} L=I\cdot\omega \\ 15=0.4\cdot\omega \\ \omega=\frac{15}{0.4}=37.5\text{ rad/s} \end{gathered}[/tex]Finding the coefficient of friction,I need how I would find the friction coefficient
the coefficient is 0.267
ExplanationFree-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object
Step 1
so, to graph the forces we use the Cartessian plane
let the x-axis paralle to the inclided plane
therefore,the weigth is a force acting directly to the center of the earth , ( bottomof page), so we have to find the x and y components of the weitgh
hence
the Free body diagram would be
Step 2
how to find the friction coefficient
the force of friction (ff) is given by
[tex]\begin{gathered} ff=\mu *N \\ where\text{ }\mu\text{ is the coefficient } \\ Nis\text{ the normal force} \end{gathered}[/tex]so, to find the coefficient we need the Normal force
if we do the sum of forces in y -axis equal zero
[tex]\begin{gathered} N-wcos(15)=0 \\ N=wcos(15) \end{gathered}[/tex]now, x -axis
[tex]\begin{gathered} ff-wsin(15)=0 \\ ff=wsin(15) \end{gathered}[/tex]finally, replace and solve for the coefficient
[tex]\begin{gathered} ff=\mu N \\ w*sin(15)=\mu *wcos(15) \\ divide\text{ both sides by w cos\lparen15\rparen} \\ \frac{wsin(15)}{wcos(15)}=\frac{\mu *w*cos(15)}{wcos(15)} \\ \frac{sin(15)}{cos(15)}=\mu \\ tan(15)=\mu \\ 0.267=\mu \end{gathered}[/tex]therefore, the coefficient is 0.267
I hope this helps you
I want to know how to answer this and I'm having difficulties telling what type of force is acting on an object.
A phonograph record has an initial angular speed of 33 rev/min . The record slows to 11 rev/min in 2.0 seconds. What is the records angular acceleration in rad/s2 during this time interval ?
In order to calculate the angular acceleration, we can use the following formula:
[tex]a=\frac{v_f-v_i}{t}[/tex]Where vf is the final angular speed, vi is the initial angular speed and t is the interval of time.
Since the speed is in rev/min, we need to convert to rad/s.
Knowing that 1 rev = 2π rad and 1 min = 60 s, we have:
[tex]\begin{gathered} 33\text{ rev/min}=33\cdot\frac{2\pi\text{ rad}}{60\text{ s}}=3.456\text{ rad/s} \\ 11\text{ rev/min}=11\cdot\frac{2\pi\text{ rad}}{60\text{ s}}=1.152\text{ rad/s} \end{gathered}[/tex]Now, using vf = 1.152, vi = 3.456 and t = 2, we have:
[tex]a=\frac{1.152-3.456}{2}=\frac{-2.304}{2}=-1.152\text{ rad/s2}[/tex]So the angular acceleration is -1.152 rad/s².
A pulse travels along a string that is fixed to a wall, as shown. The pulse reaches the wall and is reflected. Which of the following diagrams illustrates the orientation of the reflected pulse?
Using the concept of Simple Harmonic motion, we got that phase of the string wave changes by 180° and velocity gets reversed.
Simple Harmonic Motion or SHM is defined as motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards a mean position. The acceleration of particle executing simple harmonic motion is given by a(t) = -ω2 x(t). Here, ω is the angular velocity of particle.
A pulse of string wave when travels along a stretched string and reaches the fixed end of the string, then it will be reflected back to the same medium and the reflected ray suffers a phase change of π with the incident wave but the wave's velocity after reflection reverses its direction.
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Concave lenses havefocal lengths and always formimages.A. negative; virtualOB. positive; virtualC. positive; realD. negative; realSUBMIT
We will have that concave lenses have negative focal lengths and always form a virtual image.
[Option A]
While Dexter is on a camping trip with his boy scout troop, the scout leaderhands each boy a compass and map. The directions on Dexter's map read asfollows: "Walk 500.0 m north, 200.0 m east, 300.0 m south, and 400.0 m west."If he follows the map, what is Dexter's displacement? Solve graphically.
To solve this problem graphically we need perform the following steps:
Draw the axis and labeled them correctly.
We choose an appropriate scale to represent one meter, for example we can choose 1 cm to represent 50 meters; in that way 500 m will be represented by an arrow with length 10 cm.
We draw an arrow pointing north of 10 cm.
We draw an arrow pointing east of 4 cm from the head of the previous arrow.
We draw an arrow pointing south of 6 cm from the head of the previous arrow.
We draw an arrow pointing west of 8 cm from the head of the previous arrow.
We draw an arrow from the origin to the head of the last arrow.
We measure the horizontal projection of the last arrow and the vertical projection, this will give us the displacement in the x and y direction, respectively.
This is shown in the diagram below:
Therefore, the displacement of Dexter from the origin is -200 m on x and 200 m on y, this can be also said as Dexter is 200 m west and 200 m north from where he began.
A miniature quadcopter is located at xi = 1.50 m and yi = 4.70 m at t = 0 and moves with an average velocity having components vav, x = 2.70 m/s and vav, y = −2.50 m/s. What are the x-coordinate and y-coordinate (in m) of the quadcopter's position at t = 3.10 s?
Answer:
xf = 9.87 m and yf = -3.05 m
Explanation:
The x and y coordinated can be calculated using the following equation
xf = xi + Vav,x(t)
yf = yi + Vav,y(t)
Where xi, yi are the initial positions, Vav,x and Vav,y are the averages velocities and t is the time.
Replacing the given values, we get that the equations are
xf = 1.50 + 2.70t
yf = 4.70 - 2.50t
Now, we can calculate the position at t = 3.10s, replacing t by 3.10, so
xf = 1.50 + 2.70(3.10)
xf = 1.50 + 8.37
xf = 9.87 m
yf = 4.70 - 2.50(3.10)
yf = 4.70 - 7.75
yf = -3.05 m
Therefore, the x-coordinate and y-coordinate are xf = 9.87 m and yf = -3.05 m
which property justifies the statement below? x(y-3)=xy-3xis it associative, transitive, distributive, or communitive
Given the equation:
x(y - 3) = xy - 3x
Let's identify the property which justifies the statement.
Here, the property which was applied is the distributive property.
The law of distributive property states that multiplying the sum of two or more addends by a given value will amount to the same result as multiplying the addends individually by the number and adding the products.
In this equation, we can see x is distributed into the values in the parentheses.
Therefore, the property that justifies this statement is the distributive property.
ANSWER:
Distributive property
You are told that the value of a car of the given model, based on its age, is less than $6000. Give a range of values that could represent the car.
The following equation represents the value (y) of a car based on its age (x).
[tex]y=-800x+12000[/tex]We are told that the value of a car of the given model, based on its age, is less than $6000.
So, we can write
[tex]6000<-800x+12000[/tex]Let us solve the above inequality for x.
[tex]\begin{gathered} 6000<-800x+12000 \\ 6000-12000<-800x \\ -6000<-800x \\ \frac{-6000}{-800}<\frac{-800x}{-800} \\ 7.5>x \\ x<7.5 \end{gathered}[/tex]This means that the age of the car is less than 7.5 years.
Therefore, the possible range of values that could represent the age of the car is 0 to 7.5 years.
[tex]0I have an algerbra 2 question.
In order to find out if the exponential function represents a growth or a decay, let's look at the number that is base to the exponent x.
If the number is greater than 1, so the function represents a growth, and if the number is less than 1, the function represents a decay.
Since the number is 1.075, the function represents a growth.
To find the % increase, first let's convert the number to percentage, and then subtract 100%:
[tex]\begin{gathered} 1.075=1.075\cdot100\text{\%}=107.5\text{\%} \\ 107.5\text{\%}-100\text{\%}=7.5\text{\%} \end{gathered}[/tex]So the percent increase is 7.5%.
(i) Discuss your understanding about symmetric and non-symmetric projectile motion, give
some examples. (ii) Discuss your understanding about uniform and non-uniform circular
motions; give some examples.
In a symmetric projectile motion, the trajectory is symmetrical. In a non-symmetric projectile motion, the projectile path will not be symmetrical.
An example of symmetrical projectile motion is a ball launched with an initial velocity which lands at the same height from which it was launched. An example of non-symmetrical projectile motion is a ball launched with an initial velocity which lands at a different height from which it was launched.
In an uniform circular motion, an object moves with constant speed. So its angular and tangential acceleration becomes zero. But due to its change in direction, its centripetal acceleration has a non zero value. In a non-uniform circular motion, the object does not move with constant speed.
Therefore, in a symmetric projectile motion, the trajectory is symmetrical. In a non-symmetric projectile motion, the projectile path will not be symmetrical.
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Derive Kinetic Energy and Potential Energy.
Answer:
[tex]\begin{gathered} \Delta K=\frac{1}{2}m(v_f)^2-\frac{1}{2}m(v_i)^2 \\ P=m\cdot g\cdot h \end{gathered}[/tex]Explanation: We need to derive the formula for both Kinetic energy and potential energy, the derivation of these formulas is as follows:
(i) Kinetic energy:
[tex]\begin{gathered} \Delta K=\Delta W=F\cdot\Delta d\cdot\cos (\theta) \\ \theta=0 \\ \therefore\Rightarrow \\ \Delta K=F\cdot\Delta d\Rightarrow(1) \end{gathered}[/tex]By using the Kinematic equations of motions, equation (1) can be changed to the kinetic energy formula as follows:
[tex]\begin{gathered} (1)\Rightarrow\Delta K=F\cdot\Delta d=m\cdot a\cdot\Delta d\Rightarrow(2) \\ (v_f)^2=(v_i)^2+2a\Delta d \\ \therefore\Rightarrow \\ a\Delta d=\frac{(v_f)^2-(v_i)^2}{2} \\ \text{ Substituting above in the }(2)\text{ gives the formula:} \\ \Delta K=m\cdot\frac{(v_f)^2-(v_i)^2}{2} \\ \Delta K=\frac{1}{2}m(v_f)^2-\frac{1}{2}m(v_i)^2 \\ \text{ This is the kinetic energy formula} \end{gathered}[/tex](ii) Potential-energy:
Potential energy is basically the work needed to lift an object to a certain height, mathematically, the derivation would be as follows:
[tex]\begin{gathered} \Delta P=\Delta W=F\cdot\Delta d \\ \Delta d=\Delta h \\ \therefore\Rightarrow \\ \Delta P=m\cdot a\cdot\Delta h \\ a=g \\ \therefore\Rightarrow \\ \Delta P=m\cdot g\cdot\Delta h \\ \text{ Simple version:} \\ P=m\cdot g\cdot h \end{gathered}[/tex]Two long, parallel wires separated by 0.496 m carry equal currents of 11.062 A in the same direction. Find the magnitude of the net magnetic field 0.703 m away from each wire on the side opposite the other wire . Express your answer in microTesla.
In order to solve this exercise, let us first recap about point and cross notation. They are used to indicate vectors which are entering and leaving the screen. They are as follows:
You can think of it as an arrow. When the arrow is going away from us, we see the end of it, which is a cross. However, when it is coming in our direction, we see its tip, which is a point.
Now, starting into the problem, we can draw it as the following:
This happens as each wire with a flowing current generates a magnetic field that spins around it, as you can see in this drawing:
Now, we want to calculate the resulting magnetic field in the following point:
So, we can calculate our resulting magnetic field as:
[tex]B=\frac{\mu_0i}{2\pi}(\frac{1}{r_1}+\frac{1}{r_2})[/tex]Which, replacing the values, gives us:
[tex]B=\frac{\mu_0*11.062}{2\pi}*(\frac{1}{0.703}+\frac{1}{0.703+0.496})=4.99\mu T[/tex]Then, our final answer is B=4.99uT
Determine the volume in cubic inches (in. ^3) of a 2 liter bottle
Given
Volume of the bottle, V=2 l
To find
The volume in cubic inch
Explanation
We know,
[tex]\begin{gathered} 1\text{ l=61.024 cubic inch} \\ \Rightarrow2\text{ l=2}\times61.024\text{ cubic inch} \\ =122.048\text{ cubic inch} \end{gathered}[/tex]Conclusion
The required volume is 122.048 cubic inch
6) If a system has 48 J of work done on it and absorbs 22 J of heat, what is the value of ΔE for this change?
ANSWER
ΔE = 70 J
EXPLANATION
Given:
• The work done on the system, W = 48 J
,• The heat absorbed by the system, Q = 22 J
Find:
• The change of energy of the system, ΔE
We will use the convention where:
• Heat transferred to the system: positive (otherwise negative)
,• Work done on the system: positive (otherwise negative)
By the first law of thermodynamics,
[tex]\Delta E=Q+W[/tex]Replace with the known values and solve,
[tex]\Delta E=22J+48J=70J[/tex]Hence, the change in the system's internal energy is 70 J.
I
Suppose you have an electrical device that needs a steady current of
10 milliamperes. You need to greatly increase the length of the wire
between the battery pack and the appliance. What changes will you
need to make in your circuit to keep a steady current?
main answer- by keeping resistance constant,voltage should be increased
supporting answer-For keeping the current constant we must keep the resistance constant so that the current will stay constant
When the length of the conductor is going to be increased then the voltage should also be increased as there is a resistance increase due to the length increase at the conductor because it goes by the formula r is equal to raw l by a where is the resistivity of the conductor and length of the conductor by divided by area of the conductor
To keep the following current constant reverse increase the voltage supply to the circuit
final answer-by keeping resistance constant,voltage should be increased
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You will need to increase the cross-sectional area of the wire in order to keep the current steady.
What is wire?
A wire is a thin, malleable metal strand. The most common way to make wire is to draw the metal through a hole in a draw plate or die. When expressed in terms of a gauge number, wire gauges are available in a variety of common sizes. Mechanical loads are carried by wires, frequently in the form of wire rope. A "wire" can refer to an electrical cable in the context of electricity and telecommunications signals. This type of cable may have a "solid core" made up of a single wire or multiple strands woven together in stranded or braided forms. While wire is often cylindrical in shape, it can also have alternative cross-sections, such as square, hexagonal, flattened rectangular, or other shapes, for both aesthetic and technical uses, such as high-efficiency voice coils in loudspeakers.
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A stone is thrown straight upward and reaches a maximum height of 32.1 m above itslaunch point. What was the initial speed with which the stone was thrown upwards?Answer:m/s
The initial speed = 25.08 m/s
Explanation:The maximum height, H = 32.1 m
The initial speed, u = ?
The acceleration due to gravity, g = 9.8 m/s²
Write out the maximum height formula and solve for u
[tex]H=\frac{u^2}{2g}[/tex]Substitute H = 32.1 and g = 9.8
[tex]\begin{gathered} 32.1=\frac{u^2}{2(9.8)} \\ \\ u^2=32.1(2)(9.81) \\ \\ u^2=629.16 \\ \\ u=\sqrt{629.16} \\ \\ u=25.08\text{ m/s} \end{gathered}[/tex]The initial speed = 25.08 m/s
A white crowned sparrow flying horizontally with a speed of 1.80m/s folds its wings and begins to drop in free fall. (a) How far does the sparrow fall after traveling a horizontal distance of 0.500m? (b) If the sparrows initial speed is increased, does the distance of fall increase, decrease or stay the same?
First, find the time that it takes for the sparrow to travel 0.500m at a speed of 1.80 m/s. Since speed is the ratio between distance and the time taken to travel that distance, then:
[tex]v=\frac{d}{t}[/tex]Isolate t from the equation:
[tex]\Rightarrow t=\frac{d}{v}[/tex]Replace d=0.500m and v=1.80 m/s to find the time:
[tex]t=\frac{0.500m}{1.80\frac{m}{s}}=0.2777\ldots s[/tex]During that time, the sparrow falls vertically according to the equation:
[tex]h=\frac{1}{2}gt^2[/tex]Where g is the gravitational acceleration on Earth:
[tex]g=9.81\frac{m}{s^2}[/tex]Replace the value of g and t=0.2777...s to find how far does the sparrow fall:
[tex]h=\frac{1}{2}(9.81\frac{m}{s^2})(0.2777\ldots s)^2=0.378472\ldots m[/tex]If the initial speed is increased, it will take less time to travel 0.500m, and then, the falling time will be decreased, and so the distance of fall would decrease. However, the horizontal speed does not affect the distance of fall if the fall time is the same (but the horizontal displacement would increase).
Therefore, the answers are:
a) The sparrow falls a distance of 0.378m
b) The distance of fall would decrease since it would take less time to travel 0.500m.
AM radio signals are broadcast at frequencies between 550 kilohertz (kHz) and 1600 kilohertz. FM radio signals are broadcast at frequencies between 88.0 megahertz (MHz) and 108.0 megahertz. a. What is the wavelength of an AM station with a frequency of 790 kilohertz? Include units in your answer.b. What is the wavelength of an FM station with a frequency of 98.7 megahertz? Include units in your answer.
a)
From the information given,
Lowest frequency = 550 khz = 550 x 10^3 hz
Highest frequency = 1600 khz = 1600 x 10^3 hz
The formula for calculating wavelength is expressed as
wavelength = velocity/frequency
Recall, radio signals travel at the speed of light and speed of light = 3 x 10^8 m/s
Thus, for a frequency of 790 khz which is equal to 790 x 10^3 hz,
the wavelength of the AM station would be
3 x 10^8/790 x 10^3
wavelength of the AM station = 379.75 m
b) From the information given,
Lowest frequency = 88 mhz = 88 x 10^6 hz
Thus, for a frequency of 98.7 mhz = 98.7 x 10^6 hz,
wavelngth of FM station would be
3 x 10^8/98.7 x 10^6
wavelength of the FM station = 3.04 m
4. Thunderstorms are caused by warm and cold air colliding and making a large cloud which is positively charged near the top of the cloud, but negatively charged near the bottom of the cloud. (a) What charge is the surface of the ground? Explain how you know. (b) The thunderclouds are 15,000 meters high off the ground and if there’s a tall tree, 70 meters tall, how much voltage does a single lightning bolt containing 6.25 x 1019 electrons have as it strikes the tree?
let's go,
Generally,
Thunderstorms are caused by warm and cold air colliding and making a large cloud that is positively charged near the top of the cloud but negatively charged near the bottom of the cloud. the charge on the surface of the ground will be positive.
To calculate voltage --- By measuring the length of a lightning strike, multiplying it by the energy per length required.
[tex]\begin{gathered} V=(15000-70)\times(6.25\times10^{19}) \\ \\ V=93,312.5\times10^{19} \\ \\ V=9.33125\times10^{23} \end{gathered}[/tex]If ⃗ , and ⃗ are all in the same direction, can we say, ⃗ . ( . ⃗ ) = (⃗ . ). ⃗ ? Explain
your answer.
Answer:
yes because it doesn't matter the order
why have u added mgsin thetha to calculate total force
Since the man will move together with the box, he will climb the ramp as well, therefore he needs to add an extra force that is equal to the component of his own weight in the ramp direction.
The image below illustrates the forces:
So, the force F is applied on the box, but also an additional force equal to Wx needs to be applied in the man, so he can also climb the ramp:
[tex]\begin{gathered} W=m\cdot g \\ Wx=W\cdot\sin (\theta) \\ Wx=m\cdot g\cdot\sin (\theta) \end{gathered}[/tex]Why use sine and not cosine in the formula? The diagram below explains when to use each one:
Determine the image distance and image height for a 5.00 cm tall object placed 20.0 cm from a double convex lens with a focal length of 15.0 cm.
Given:
the height of the object is
[tex]h_0=5\text{ cm}[/tex]The distance of the object is
[tex]d_0=-20\text{ cm}[/tex]The focal length of the lens is
[tex]f=15\text{ cm}[/tex]Required: the distance of the image and height of the image.
Explanation:
the lens formula is given by
[tex]\frac{1}{f}=\frac{1}{d_i}-\frac{1}{d_0}[/tex]Plugging all the values in the above relation, we get:
[tex]\begin{gathered} \frac{1}{15\text{ cm}}=\frac{1}{d_i}-\frac{1}{-20\text{ cm}} \\ \frac{1}{d_i}=\frac{1}{15\text{ cm}}-\frac{1}{20\text{ cm}} \\ \frac{1}{d_i}=\frac{4-3}{60\text{ cm}} \\ d_i=60\text{ cm} \end{gathered}[/tex]Thus, the distance of the image is 60 cm.
now calculate the height of the image
we know that
[tex]\frac{h_i}{h_0}=\frac{d_i}{d_0}[/tex]substitute all the values in the above relation, we get:
[tex]\begin{gathered} h_i=5\text{ cm}\times\frac{60}{-20} \\ h_i=-15\text{ cm} \end{gathered}[/tex]Thus, the height of the image is 15 cm.
A worker pushes a crate with a horizontal force of 225 N a distance of 8.0 M. How much work did the worker do on the crate?11,200 J1,800 J3,920 J0 J
We area asked to determine the work done by pushing a crate a distance of 8 meters using a force of 225N. To do that we will use the following formula:
[tex]W=Fd[/tex]Where:
[tex]\begin{gathered} W=\text{ work} \\ F=\text{ horizontal force} \\ d=\text{ distance} \end{gathered}[/tex]Now, we plug in the values:
[tex]W=(225N)(8m)[/tex]Now, we solve the operations:
[tex]W=1800J[/tex]Therefore, the amount of work done is 1800 Joules.
A grinding wheel 0.37 m in diameter rotates at 2400 rpm.(A) Calculate its angular velocity in rad/s.(B) What is the linear speed of a point on the edge of the grinding wheel? (C) What is the acceleration of a point on the edge of the grinding wheel?
A) Angular velocity = 251.36 rad/s
B) Linear speed = 46.50 m/s
C) Acceleration = 11687.8 m/s^2
Explanations:A) Angular velocity, w = 2400 rpm
Note that:
1 rpm = (2π)/60
Therefore:
2400 rpm = (2π/60) x 2400 rad/s
2400 rpm = 80π rad/s
2400 rpm = 80 x 3.142
2400 rpm = 251.36 rad/s
The angular velocity, w = 251.36 rad/s
B) The relationship between linear speed(v) and angular velocity(w) is:
v = wr
The diameter, d = 0.37m
Radius, r = d/2
r = 0.37/2
r = 0.185m
Substituting r = 0.185m and w = 251.36 rad/s into v = wr:
v = 251.36 x 0.185
v = 46.50 m/s
C) The acceleration a point on the edge of the grinding wheel is the centripetal acceleration, and is given by the formula:
[tex]\begin{gathered} a\text{ = }\frac{v^2}{r} \\ a\text{ = }\frac{46.50^2}{0.185} \\ a\text{ = }\frac{2162.25}{0.185} \\ a\text{ = }11687.8m/s^2 \end{gathered}[/tex]What is the term for an object that does not allow any light to pas through it? opaque, transparent, or translucent
Answer:
Opaque
Explanation:
Opaque objects are objects that doesn't allow the light to pass through them
Transparent objects are objects that allow almost all light to pass through them
Translucent object are objects that allow some light to pass through them
Then, the answer is opaque.
Answer:
I think opaque im not sure
Explanation:
Point A is on the ground, and points B and C are h = 20 meters above the ground. Point B is directly above point A, and point C is L = 40 meters away from point A as shown.(a) How much work must be done by an external agent to move a 2 kg object from rest at point A to rest at point B?(b) How much work must be done to move the same object from rest at point A to rest at point C?
Given the mass of the object, m = 2 kg
Distance between point A and B, h= 20 m
(a) To find work done in moving the object from A to B
Work done is
[tex]\begin{gathered} W1=Force\times displacement\text{ } \\ =mgh \end{gathered}[/tex]Here, g is the acceleration due to gravity whose value is 9.8 m/s^2.
Substituting the values, we get
[tex]\begin{gathered} W1=2\times9.8\times20 \\ =\text{ 392 J} \end{gathered}[/tex](b) To find work done in moving the object from A to C
Gravitational force is a conservative force and work done depends only on the initial and final position and not on the path.
So, the work done will be
[tex]\begin{gathered} W2=\text{mgh} \\ =2\times9.8\times20 \\ =\text{ 392 J} \end{gathered}[/tex]