Answers
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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Related Questions
A rope is vibrating so as to form the standing wave pattern shown at the right. 1.How many nodes are present in the rope?2.What harmonic is shown in the pattern?3.A guitar string has a fundamental frequency of 120 Hz. What is the frequency of the third harmonic of the string?
Answers
We will have the following:
1. There are 5 nodes.
2. The harmonic shown is the 4th harmonic.
3. We will detemrine the 3rd harmonic as follows:
[tex]\lambda_3=\frac{3}{2}(120Hz)\Rightarrow\lambda_3=180Hz[/tex]As shown in Fig. B9, a block of mass m2=2.1 kg sits on an inclined plane with angle 35 degrees .The coefficients of static and kinetic friction between the block and the plane are unknown.The block is attached to a rope, which is hung over a frictionless and massless pulley and attached to a hanging mass m1.(a) The block my is on the verge of sliding, when the hanging mass is increased to m1=1.6kg.01. find the coefficient of static friction.As shown in Fig. Bob, an identical block (with mass m2) is placed on top of the block on the inclined plane. The hanging mass m1 remains unchanged. The two blocks on the inclined plane are sliding down the incline with the same acceleration a=0.31 m/s^2Find02.the coefficient of kinetic friction.03.what is the minimum value of the coefficient of static friction between the two identical blocks (m2) so that they move together?
Answers
Question 1.
The free body diagrams of the situation are shown below:
The forces applied on m1 are in only the y direction then we only have one equation of motion to get it we use Newton's Second law. Then we have:
[tex]T-W_1=m_1a[/tex]The forces applied on m2 are in the x and y direction, this means that we have two equations of motion. We don't expect this block to move on the y-direction (which we defined); this means that the acceleration in this direction has to be zero. Furthermore, since the blocks m1 and m2 are attach thorugh the rope their acceleration has to be the same; this means that the acceleration of block m2 in the x direction has to be a. Applying this and Newton's second law we have for block 2:
[tex]\begin{gathered} (W_2)_x+f_f-T=m_2a \\ N-(W_2)_y=0 \end{gathered}[/tex]where (W2)x and (W2)y denote the component of the weight in the x and y direction, respectively. Now, since block m2 is on the verge of sliding this means that the system is in equilibrium, that is, the acceleration of the system is equal to zero. Then we have that the equations above take the form:
[tex]\begin{gathered} T-W_1=0 \\ (W_2)_x+f_f-T=0 \\ N-(W_2)_y=0 \end{gathered}[/tex]To determine the coefficient of static friction we firs need to determine the force of fricction. To do this we first solve the first equation for T:
[tex]T=W_1[/tex]Now we plug this value in the second equation and solve for the force of friction:
[tex]\begin{gathered} (W_2)_x+f_f-W_1=0 \\ f_f=W_1-(W_2)_x \end{gathered}[/tex]Now we need to remember that the force of friction can be obtain by:
[tex]f_f=\mu_{}N[/tex]where mu is the coefficient of friction (this rule applies for static and kinetic friction). Then we have:
[tex]\begin{gathered} \mu N=W_1-(W_2)_x_{} \\ \mu=\frac{W_1-(W_2)_x}{N} \end{gathered}[/tex]To find the normal force we use the third equation of motion:
[tex]N=(W_2)_y[/tex]Hence we have:
[tex]\mu=\frac{W_1-(W_2)_x}{(W_2)_y}[/tex]Now we need to remember that the components of the weight on an inclined plane are given by:
[tex]\begin{gathered} W_x=W\sin \theta \\ W_y=W\cos \theta \end{gathered}[/tex]where theta is the angle of the plane.
Plugging this on the expression for the coefficient of friction:
[tex]\mu=\frac{W_1-W_2\sin \theta}{W_2\cos \theta}[/tex]Finally we plug the values given to find the coefficient:
[tex]\begin{gathered} \mu=\frac{(1.6)(9.8)-(2.1)(9.8)\sin 35}{(2.1)(9.8)\cos 35} \\ \mu=0.23 \end{gathered}[/tex]Therefore the coefficient of static friction is 0.23
Question 2
For this question we are going to look at the two block in the inclined plane as one block with mass of 4.2 kg and we are going to name the two blocks as m2.
The free body diagram in this case is:
Applying Newton's second law in each mass lead to the system of equations:
[tex]\begin{gathered} T-W_1=m_1a \\ (W_2)_x-f_f-T=m_2a \\ N-(W_2)_y=0 \end{gathered}[/tex]From the first equation of motion we have:
[tex]T=W_1+m_1a[/tex]Plugging this in the second equation:
[tex](W_2)_x-f_f-W_1-m_1a=m_2a[/tex]but we know that:
[tex]f_f=\mu_{}N[/tex]and:
[tex]N=(W_2)_y[/tex]Then we have:
[tex](W_2)_x-\mu(W_2)_y-W_1-m_1a=m_2a[/tex]Solving for the coefficient and using the expression for the wight on an inclined plane we have:
[tex]\begin{gathered} (W_2)_x-\mu(W_2)_y-W_1-m_1a=m_2a \\ \mu=\frac{W_2\sin \theta-W_1-m_1a-m_2a}{W_2\cos \theta} \end{gathered}[/tex]Plugging the values given we have:
[tex]\begin{gathered} \mu=\frac{(4.2)(9.8)\sin 35-(1.6)(9.8)-(1.6)(0.31)-(4.2)(0.31)}{(4.2)(9.8)\cos 35} \\ \mu=0.18 \end{gathered}[/tex]Therefore the coefficient of kinetic friction is 0.18.
Question 3.
To find the coefficient of static friction between the two blocks on the inclined plane we need that the upper block to be stationary with respect to the lower block, that means that the friction has to be equal to the weight in the x-direction, that is:
[tex]\begin{gathered} f_f=W_2\sin 35 \\ \mu W_2\cos 35=W_2\sin 35 \\ \mu=\frac{\sin 35}{\cos 35} \\ \mu=0.7 \end{gathered}[/tex]Therefore the coefficient between the blocks has to be at least 0.7
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!!
Answers
Answer:
A. the speed of the object
Explanation:
The color wouldn't make any difference to the potential energy and knowing the mass the way the object is shaped or the height of it would make no difference
A 25.0 kg bag of dirt falls 15.0 m at a construction site. Assuming that all of the heat produced is retained by the dirt, how much will its temperature increase? (cdirt = 0.20 cal/g•°C)
Answers
Given:
• Mass of bag, m =25.0 kg
,• Height, h = 15.0 m
,• c = 0.20 cal/g•°C
Let's find by how much the temperature will increase.
Apply the Law of Conservation of Energy:
[tex]mc\Delta T=mgh[/tex]Where:
• m is the mass
,• c is the specific heat capacity
,• g is acceleration due to gravity
,• h is the height.
,• ΔT is the temperature change.
Thus, we have:
[tex]\begin{gathered} mc\Delta T=mgh \\ \\ Eliminate\text{ m on both sides:} \\ c\Delta T=gh \end{gathered}[/tex]Now, plug in the values and solve for ΔT:
[tex]\begin{gathered} \Delta T=\frac{gh}{c} \\ \\ \Delta T=\frac{9.8*15.0}{0.20\times10^3\times4.2} \\ \\ \Delta T=\frac{147}{840} \\ \\ \Delta T=0.175^o\text{ C} \end{gathered}[/tex]Therefore, the temperature change is 0.175° C.
• ANSWER:
0.175° C
A helicopter flies at a constant altitude towing an airborne 65 kg crate as shown in the diagram. The helicopter and the crate only move in the horizontal direction and have an acceleration of 3.0 m/s21) find the vertical component of the tension in the cable (in Newtons). Ignore the effects of air resistance.2) find the magnitude of the tension in the cable (in Newtons). Ignore the effects of air resistance.3) find the angle(with respect to the horizontal) of the tension in the cable (in degrees). Ignore the effects of air resistance.
Answers
Given data:
* The weight of the crate is 65 kg.
* The acceleration of crate and helicopter is,
[tex]a=3ms^{-2}[/tex]Solution:
(1). The forces acting on the crate is represented as,
The y-component of tension is balancing the weight of the crate.
Thus, the y-component (vertical) of tension is,
[tex]\begin{gathered} T_y=W \\ T_y=mg \end{gathered}[/tex]Where m is the mass of crate and g is the acceleration due to gravity,
Substituting the known values,
[tex]\begin{gathered} T_y=65\times9.8 \\ T_y=637\text{ N} \end{gathered}[/tex]Thus, the vertical component of the tesnion is 637 N.
(2). The x-component of tension in the cable is,
[tex]\begin{gathered} T_x=ma \\ T_x=65\times3 \\ T_x=195\text{ N} \end{gathered}[/tex]Thus, the tension in the cable is,
[tex]\begin{gathered} T=\sqrt[]{T^2_x+T^2_y} \\ T=\sqrt[]{195^2^{}+637^2} \\ T=666.2\text{ N} \end{gathered}[/tex]Hence, the tesnion in the cable is 666.2 N.
(3). The angle of tension with the horizontal is,
[tex]\begin{gathered} \tan (\theta)=\frac{T_y}{T_x} \\ \tan (\theta)=\frac{637}{195} \\ \tan (\theta)=3.3 \\ \theta=73.14^{\circ} \end{gathered}[/tex]Thus, the angle made by the tension with the horizontal is 73.14 degree.
State briefly rules of drawing vector on coordinate systems
Answers
In order to draw a vector in the coordinate system, we can follow these steps:
1. Draw the initial point of the vector.
2. Draw the end point of the vector.
3. Create an arrow starting at the initial point and ending at the end point.
For example, let's use a vector that starts at (0, 0) and ends at (3, 4):
Compare the power of one motorcylce that travels twice as fast as a second indetical motorcycle.A.Same amount of powerB.Twice the powerC.4 times the powerD.Half the power
Answers
Given:
The power of one motorcycle travels twice as fast as a second motorcycle.
To compare the power of motorcycles.
Explanation:
Let the speed of one motorcycle be v.
The speed of the second motorcycle will be 2v.
Power is calculated by the formula
[tex]P=\text{ Force}\times velocity[/tex]The power of the first motorcycle will be
[tex]P_1=Fv_1[/tex]The power of the second motorcycle will be
[tex]\begin{gathered} P_2=Fv_2 \\ =F\times2v_1 \\ =2Fv_1 \\ =2P_1 \end{gathered}[/tex]Thus, the power of the second motorcycle is twice the power of the first motorcycle.
A box of mass m = 2 kg is kicked on a rough horizontal plane with an initial velocity v_0 . If the net work done on the crate during its entire motion , until it comes to rest , is -36 J , then the initial velocity v_0 of the box is equal to :
Answers
Given:
The mass of the box is m = 2 kg
The work done is W = -36 J
The final velocity of the object is
[tex]v_f=\text{ 0 m/s}[/tex]To find the initial velocity of the box.
Explanation:
The initial velocity of the box can be calculated as
[tex]\begin{gathered} Work\text{ done = change in kinetic energy} \\ W=\frac{1}{2}m(v_f^2-v_o^2) \\ -36=\frac{1}{2}\times2(0^2-v_o^2) \\ -v_{_0}^2=-36 \\ v_o=6\text{ m/s} \end{gathered}[/tex]Hence, the initial velocity of the box is 6 m/s.
Select the correct answerA car moves with an average speed of 45 miles/hour. How long does the car take to travel 90 miles?O A2 minutesВ.2 hoursOC.45 minutesΟ Ο ΟD45 hoursE90 minutesResetNext
Answers
Given data:
The average speed of the car is
[tex]S=45\text{ miles/hour}[/tex]The distance traveled by the car is
[tex]D=90\text{ miles}[/tex]The average speed can be expressed as,
[tex]\begin{gathered} S=\frac{D}{T} \\ T=\frac{D}{S} \end{gathered}[/tex]Here, T is the time taken by the car.
Substituting the values in the above equation, we get:
[tex]\begin{gathered} T=\frac{90\text{ miles}}{45\text{ miles/hour}} \\ =2\text{ hours} \end{gathered}[/tex]Thus, the time taken by the car is 2 hours, and option (B) is correct.
A block having a mass of m = 19.5 kg is suspended via two cables as shown in the figure. The angles shown in the figure are as follows: a = 15° and B = 35°. We will label the tension in Cable 1 as T1, and the tension in Cable 2 as T2. Solve for T1 and T2
Answers
We will have the next diagram
Then we can sum the forces in x and sum the forces in y
Forces in x
[tex]\sum ^{}_{}F_x=-T_1\sin (\alpha)+T_2\cos (\beta)=0[/tex][tex]\sum ^{}_{}F_x=-T_1\sin (15)+T_2\cos (35)=0[/tex]Forces in y
[tex]\sum ^{}_{}F_y=T_1\cos (\alpha)+T_2\sin (\beta)=mg[/tex][tex]\sum ^{}_{}F_y=T_1\cos (15)+T_2\sin (35)=19.5(9.8)[/tex]We simplify the equations found and we found the next system of equation
[tex]\begin{gathered} -T_1\sin (15)+T_2\cos (35)=0 \\ T_1\cos (15)+T_2\sin (35)=191.1 \end{gathered}[/tex]then we isolate the T2 of the first equation
[tex]T_2=\frac{T_1\sin(15)}{\cos(35)}[/tex]We substitute the equation above in the second equation
[tex]T_1\cos (15)+(\frac{T_1\sin(15)}{\cos(35)})\sin (35)=191.1[/tex]we simplify
[tex]T_1(\cos (15)+\frac{\sin (15)\sin (35)}{\cos (35)})=191.1[/tex][tex]T_1(1.147)=191.1[/tex]We isolate the T1
[tex]T_1=\frac{191.1}{1.147^{}}=166.6N[/tex]then we can substitute the value we found in T1 in the euation with T2 isolate
[tex]T_2=\frac{(166.6)_{}\sin (15)}{\cos (35)}=52.54N[/tex]
Except for the nodes on a standing wave, what is the frequency f of the points executing simple harmonic motion?
Answers
Take into account that in a standing wave, the frequency f of the points executing simple harmonic motion, is simply a multiple of the fundamental harmonic fo, that is:
f = n·fo
where n is an integer and fo is the first harmonic or fundamental.
fo is given by the length L of a string, in the following way:
fo = v/λ = v/(L/2) = 2v/L
becasue in the fundamental harmonic, the length of th string coincides with one hal of the wavelength of the wave.
An ox exerts a forwards force of 7100 N. If the ox has a weight of 8000 N, what is the minimum coefficient of static friction? (HINT: if there was no static friction the ox would slip and not move forward, what friction is required to allow the ox to move without slipping)
Answers
Given data
*An ox exerts a forwards force is F = 7100 N
*An ox has weight is N = 8000 N
The formula for the minimum coefficient of static friction is given as
[tex]\begin{gathered} F=\mu_sN \\ \mu_s=\frac{F}{N} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} \mu_s=\frac{7100}{8000} \\ =0.887 \end{gathered}[/tex]Hence, the minimum coefficient of static friction is 0.887
The speed of light in an unknown medium is measured to be 2.76 x10% m/s. What is the index of refraction of the medium?
Answers
Answer:
Explanation:
The formula for calculating the index of refraction is expressed as
n = c/v
where
n is the index of refraction
v is the speed of light in the medium
c is the speed of light in vacuum and its value is 3 x 10^8 m/s
From the information given,
v = 2.76 x 10^8 m/s
Thus,
n = 3 x 10^8 m/s/2.76 x 10^8 m/s
n = 1.09
the index of refraction of the medium is 1.09
QUESTION 26If the woman in the previous question doubles the constant horizontal force that she exerts on the box to push it on the same horizontal floor,O with a constant speed that is double the speed "vo" in the previous question.with a constant speed that is greater than the speed "vo" in the previous question, but not necessarily twice as great.for a while with a speed that is constant and greater than the speed "vo" in the previous question, then with a speed that increases thereafO for a while with an increasing speed, then with a constant speed thereafter.
Answers
When the woman exerts a
What is the current produced by a potential difference of 240 Volts through a resistance of .28 ohms
Answers
Given:
The potential difference is V = 240 Volts
The resistance is R = 0.28 Ohms
To find the current produced.
Explanation:
The current produced can be calculated by the formula
[tex]I=\text{ }\frac{V}{R}[/tex]On substituting the values, the current produced will be
[tex]\begin{gathered} I=\frac{240}{0.28} \\ =\text{ 857.14 A} \end{gathered}[/tex]Thus, the current produced is 857.14 A
Which of the following inventions came first?fiber opticsthe radiothe televisionthe telegraph
Answers
Telegraph is the invention that came first.
How long will it take a sample of Polonium- 194 to decay to 1/16 of its original amount the half -life of 0.7 seconds
Answers
The time it takes the Polonium-194 to decay to 1/16 of its original amount is 2.8 seconds.
What is half-life?half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay
To calculate the time it takes the sample of Polonium-196 to decay to 1/16 of its original amount, we use the formula below
Formula:
[tex]2^{n/t}[/tex] = R/R'......... Equation 1Where:
n = Total number of time it takes Polonium-194 to decay to 1/16 of its original amountt = Half-life of Polonium-194R = Original amount of Polonium-194R' = Amount of Polonium-194 after decayFrom the question,
Given:
R = 1R = 1/16t = 0.7Substitute these values into equation 1 and solve for n
[tex]2^{n/0.7}[/tex]= 1/(1/16)[tex]2^{n/0.7}[/tex] = 16[tex]2^{n/0.7}[/tex] = 2⁴Equating the base,
n/0.7 = 4n = 0.7×4n = 2.8 seconds.Hence, the time it takes the Polonium-194 to decay is 2.8 seconds.
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The press box at a basketball park is 38.0ft above the ground. A reporter in the press box looks at an angle of 15 degrees below the horizontal to see second base. What is the horizontal distance from the press box to second base?
Answers
The press box at a basketball park is 38.0 ft above the ground.
A reporter in the press box looks at an angle of 15 degrees below the horizontal to see the second base.
Let us draw the diagram to better understand the problem.
Here x is the horizontal distance from the press box to the second base.
With respect to angle 15°, the opposite side is 38 ft and the adjacent side is x.
Recall from the trigonometric ratios,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 15\degree=\frac{38}{x} \\ x=\frac{38}{\tan 15\degree} \\ x=141.8\; ft \end{gathered}[/tex]Therefore, the horizontal distance from the press box to the second base is 141.8 ft.
this is a 3 part questionplease see picture for part A73) The human brain consumes about 22 W of power under normal conditions, though more power may be required during exams.(a) For what amount of time can one Snickers bar (see the note following Problem 48) power the normally functioning brain(one bar provides 280 calories)? (b) At what rate must you lift a 3.6-kg container of milk (one gallon) if the power output of your arm is to be 22 W? (C) How much time does it take to lift the milk container through a distance of 1.0 m at this rate?
Answers
Given,
The power consumed by a brain, P=22 W
The energy per bar, E=280 calories=280×4184=1171.52 kJ
The mass of a milk container, m=3.6 kg
The power output of the arm, P₀=22 W
The distance through which the container needs to be lifted, d=1.0 m
a)
The power is given by,
[tex]P=\frac{E}{t}[/tex]Where t is the time.
On substituting the known values in the above equation,
[tex]\begin{gathered} 22=\frac{1171.52\times10^3}{t} \\ \Rightarrow t=\frac{1171.52\times10^3}{22} \\ =53250\text{ s} \end{gathered}[/tex]That is,
[tex]\frac{53250}{3600}=14.79\text{ hr}[/tex]Therefore one snicker bar can power the brain for 14.79 hr
b)
The power output can also be calculated using the formula,
[tex]\begin{gathered} P=F\times v \\ =mg\times v \end{gathered}[/tex]Where F is the force applied by the container on the arm, v is the rate at which the container must be lifted, and g is the acceleration due to gravity.
On substituting the known values,
[tex]\begin{gathered} 22=3.6\times9.8\times v \\ v=\frac{22}{3.6\times9.8} \\ =0.62\text{ m/s} \end{gathered}[/tex]Thus the rate at which the milk container must be lifted is 0.62 m/s
c)
The rate at which the container must be lifted is given by,
[tex]v=\frac{d}{t}[/tex]Where t is the time it takes to lift the container at the calculated rate.
On substituting the known values,
[tex]\begin{gathered} 0.62=\frac{1}{t} \\ \Rightarrow t=\frac{1}{0.62} \\ =1.61\text{ s} \end{gathered}[/tex]Thus it takes 1.61 s to lift the container through 1 m at the given rate.
A spring block system undergoes a simple harmonic oscillation with an amplitude A = This oscillations in one minute. The maximum acceleration of this oscillator is:
Answers
The maximum acceleration of the oscillator is 1.48 m/s²
Simple harmonic motion is a particular kind of periodic motion in which the restoring force on the moving item is inversely proportional to the size of the displacement and acts in the direction of the object's equilibrium position.
A periodic variable's amplitude is a gauge of its change over a single period.
The amplitude of a simple harmonic motion, A = 15 cm = 0.15 m
The frequency, f = 30 oscillations per minute = 30/60 = 1/2
The maximum acceleration of the oscillator is given as:
a = A × ω²
Now the formula for angular frequency is:
ω = 2πf
Therefore,
a = A × ( 2πf )²
Substituting the values in the equation,
a = 0.15 × ( 2 × π × 1/2 )²
a = 0.15 × π²
a = 1.48 m/s²
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If a sloth is traveling at 0.067 mps or 0.15 mph how long does it take the sloth to travel an 11.5 meter tree
Answers
Answer:
Explanation:
Given:
V = 0.067 m/s
D = 11.5 m
___________
t - ?
t = D / V
t = 11.5 / 0.067 ≈ 172 s or t ≈ 2.87 min or t ≈ 2 min 52 s
A force F1 of magnitude 4.80 units acts on an object at the origin in a direction = 27.0° above the positive x-axis. (See the figure below.) A second force F2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F1 + F2.magnitude unitsdirection ° counterclockwise from the +x-axis
Answers
We will determine the magnitude of the final component as follows:
[tex]\begin{gathered} m=\sqrt{(5cos(27))^2+(5sin(27)+4.8)^2}\Rightarrow m=8.356527029... \\ \\ \Rightarrow m\approx8.36 \end{gathered}[/tex]So, the magnitude is approximately 8.36.
And the direction will be approximately 57.8° counter-clockwise.
This can be seeing as follows:
Derive the equation S=ut+½at²
Answers
Average velocity = (initial velocity + final velocity )/ 2
AVG v = (u+v)/2
Also,
Distance = avg v x time
s= ([u+v]/2) x t
s= distance travelled by a body in time t
u= initial velocity
a= acceleration
From the equation of motion:
v= u +at
Replacing
s= ( [u+u+at]/2)xt
s= [( 2u+ 2at ( x t ]/2
s= (2ut+at^2)/2
s= ut+1/2at^2
Prove that the area of the parallelogram is equal to | A × B |
Answers
The area of a paralellogram with base a and height h is given by:
[tex]A=h\cdot a[/tex]If two adjacent sides of a parallelogram have lengths a and b and are separated by an angle φ, then the base of the parallelogram is a and the height is given by b*sin(φ). Then, the area of the parallelogram is given by:
[tex]A=a\cdot b\cdot\sin (\phi)[/tex]On the other hand, the cross product of two vectors is defined as:
[tex]\vec{a}\times\vec{b}=a\cdot b\cdot\sin (\phi)\hat{n}[/tex]Where the unitary vector is directed toward the direction perpendicular to a and b according to the right hand rule.
The modulus of the cross product of a and b is:
[tex]|\vec{a}\times\vec{b}|=a\cdot b\cdot\sin (\phi)[/tex]We can see that both the area of the parallelogram and the modulus of the cross product have the same expressions. Therefore:
[tex]A=|\vec{a}\times\vec{b}|[/tex]A plant that is 4.1 cm tall is 10.3 cm from a converging lens. You observe that the image of this plant is upright and 6.2 cm tall. What is the focal length of the lens?
Answers
We know that the magnification is given by:
[tex]M=\frac{h^{\prime}}{h}[/tex]where h is the height of the object and h' is the height of the image, then in this case we have:
[tex]M=\frac{6.2}{4.1}[/tex]On the other hand we also know that the magnification is given by:
[tex]M=-\frac{i}{o}[/tex]where i is the distance of the image to lens and o is the distance of the object to the lens. From this we have:
[tex]\begin{gathered} \frac{6.2}{4.1}=-\frac{i}{10.3} \\ i=-\frac{10.3\cdot6.2}{4.1} \end{gathered}[/tex]Once we have the distance of the image we can use the lens equation to find the focal point:
[tex]\begin{gathered} \frac{1}{10.3}+\frac{1}{-\frac{10.3\cdot6.2}{4.1}}=\frac{1}{f} \\ \frac{1}{10.3}-\frac{4.1}{10.3\cdot6.2}=\frac{1}{f} \\ f=(\frac{1}{10.3}-\frac{4.1}{10.3\cdot6.2})^{-1} \\ f=30.41 \end{gathered}[/tex]Therefore the focal distance of the lens is 30.41 cm and this can be round to 30 cm, hence the answer is D
You need to construct a 400 pF capacitor for a science project. You plan to cut two L x L metal squares and place spacers between them. The thinnest spacers you have are 0.20 mm thick. What is the proper value of L?Express your answer in centimeters.
Answers
Consider that the formula for the capacitance of a square parallel plate capacitor is:
[tex]C=\epsilon_o\frac{A}{d}=\epsilon_o\frac{L^2}{d}[/tex]where A=L^2 is the area of each plate, d is the separation between plates and
ε0 is the dielectric permitivity of vacuum ans is equal to 8.82*10^-12 F/m.
If you solve the previous expression for L and replace the given values for d and C, you obtain:
[tex]\begin{gathered} L=\sqrt[]{\frac{dC}{\epsilon_o}} \\ d=0.20mm=0.20\cdot10^{-3}m=2.0\cdot10^{-4}m \\ C=400pF=400\cdot10^{-12}F=4.00\cdot10^{-10}F \\ L=\sqrt[]{\frac{(2.0\cdot10^{-4}m)(4.00\cdot10^{-10}F)}{8.85\cdot10^{-10}\frac{F}{m}}} \\ L\approx0.0095m=0.95cm \end{gathered}[/tex]Hence, the proper value of L to construct the required capacitor is approximately 0.95cm
What causes water to freeze solid when placed in a freezer? Takes heat away from the waterAdds heat to the waterPuts electricity in the waterDoes not let light shine on the water
Answers
Takes heat away from the water.
Water freezes solid when placed in a freezer.
If heat is added water melts.
Electricity in the water doesn't freeze it.
Light doesn't freeze water.
So, the correct answer is:
Takes heat away from the water
A student is sitting in a chair. The student's mass is 55 kg. Find the normal force exerted on the student by thechair, in N.Round your answer to one decimal place
Answers
We have the next diagram
Where N is the normal and W is the weight
Therefore
N=W
The formula to calculate the W is
[tex]W=mg[/tex]where m is the mass and g is the gravity
In our case,
m=55
g=9.8 m/s^2
[tex]W=55(9.8)=539N[/tex]Therefore the normal force
N=539N
ANSWER
the normal force is 539N
Two skydivers jump from an airplane at an altitude of 5000m. Suppose one is 57 kg and the other is 68 kg. Using the data given in the example in class to find the amount of time each takes to get to the ground.Area = 0.18 m² air density = 1.21 kg/m³ drag coefficient C = .070
Answers
Given:
Two skydivers jump from an airplane at an altitude of: d = 5000 m
The mass of the first skydiver is: m1 = 57 kg
The mass of the second skydiver is: m2 = 68 kg
Area = 0.18 m²
Air density = 1.21 kg/m³
Drag Coefficient: C = 0.070
To find:
The amount of time each skydiver takes to get to the ground.
Explanation:
The magnitude of drag force which acts opposite in the opposite direction is equal to the weight of the skydiver. Thus, the magnitude of the drag force can be calculated as:
[tex]\begin{gathered} F_1=m_1g=57\text{ kg}\times9.8\text{ m/s}^2=558.6\text{ kg.m/s}^2 \\ \\ F_2=m_2g=68\text{ kg}\times9.8\text{ m/s}^2=666.4\text{ kg.m/s}^2 \end{gathered}[/tex]Here, F1 is the magnitude of the drag force on the first skydiver and F2 is the drag force on the second skydiver.
The expression for drag force relating to the velocity is given as:
[tex]F=\frac{1}{2}C\rho Av^2[/tex]For the first skydiver the drag force is given as:
[tex]\begin{gathered} F_1=\frac{1}{2}C\rho Av_1^2 \\ \\ \text{ Substituting the values in the above equation, we get:} \\ \\ 558.6\text{ kg.m/s}^2=\frac{1}{2}\times0.070\times1.21\text{ kg/m}^3\times0.18\text{ m}^2\times v_1^2 \\ \\ 558.6\text{ kg.m/s}^2=7.623\times10^{-3}\text{ kg/m}\times v_1^2 \\ \\ v_1^2=\frac{558.6\text{ kg.m/s}^2}{7.623\times10^{-3}\text{ kg/m}} \\ \\ v_1^2=73278.24\text{ m}^2\text{/s}^2 \\ \\ v_1=\sqrt{73278.24\text{ m}^2\text{/s}^2} \\ \\ v_1=270.70\text{ m/s} \end{gathered}[/tex]The velocity v1 of the first skydiver is 270.70 m/s.
The time t1 taken by the first skydiver to get to the ground can be calculated as:
[tex]\begin{gathered} v_1=\frac{d}{t_1} \\ \\ t_1=\frac{d}{v_1} \\ \\ \text{ Substituting the values in the above equation, we get:} \\ \\ t_1=\frac{5000\text{ m}}{270.70\text{ m/s}} \\ \\ t_1=18.47\text{ s} \end{gathered}[/tex]The first skydiver takes 18.47 seconds to get to the ground.
For the second skydiver, the drag force is given as:
[tex]\begin{gathered} F_2=\frac{1}{2}C\rho Av_2^2 \\ \\ \text{ Substituting the values in the above equation, we get:} \\ \\ 666.4\text{ kg.m/s}^2=\frac{1}{2}\times0.070\times1.21\text{ kg/m}^3\times0.18\text{ m}^2\times v_2^2 \\ \\ 666.4\text{ kg.m/s}^2=7.623\times10^{-3}\text{ kg/m}\times v_2^2 \\ \\ v_2^2_{{}}=\frac{666.4\text{ kg.m/s}^2}{7.623\times10^{-3}\text{ kg/m}} \\ \\ v_2^2=87419.65\text{ m}^2\text{/s}^2 \\ \\ v_2=\sqrt{87419.65\text{ m}^2\text{/s}^2} \\ \\ v_2=295.67\text{ m/s} \end{gathered}[/tex]The velocity v2 of the second skydiver is 259.67 m/s.
The time t2 taken by the second skydiver to get to the ground can be calculated as:
[tex]\begin{gathered} v_2=\frac{d}{t_2} \\ \\ t_2=\frac{d}{v_2} \\ \\ \text{ Substituting the values in the above equation, we get:} \\ \\ t_2=\frac{5000\text{ m}}{295.67\text{ m/s}} \\ \\ t_2=16.91\text{ s} \end{gathered}[/tex]The second skydiver takes 16.91 seconds to get to the ground.
Final answer:
The first skydiver takes 18.47 seconds to get to the ground.
The second skydiver takes 16.91 seconds to get to the ground.
An il film (n = 1.42) floating on water is84.8 nm thick. What is the wavelengthIN NANOMETERS of the brightest(m = 1) reflected color?(Hint: If you leave the wavelength in nm,the answer will be in nm. No conversionnecessary.)(Unit = nm)
Answers
Given:
n = 1.42
Thickness, t = 84.8 nm
m = 1
Let's find the wavelength in Nanometers of the brightest reflected color.
Apply the formula:
[tex]t=(m-\frac{1}{2})(\frac{\lambda}{2n})[/tex]Where:
• t = 84.8 nm
,• m = 1
,• n = 1.42
Plug in the values in the formula and solve for the wavelength λ:
[tex]\begin{gathered} 84.8=(1-\frac{1}{2})(\frac{\lambda}{2*1.42}) \\ \\ 84.8=(\frac{1}{2})(\frac{\lambda}{2.84}) \\ \\ 84.8=\frac{\lambda}{2*2.84} \\ \\ 84.8=\frac{\lambda}{5.68} \\ \\ \lambda=84.8*5.68 \\ \\ \lambda=481.67\text{ nm} \end{gathered}[/tex]Therefore, the wavelength is 481.67 nm.
• ANSWER:
481.67 nm