Answers
Given,
The ant crawls 72 inches every 6 minutes.
And the table of the time and distance covered by the ant.
From the table, the values of distance are,
d₁=6 inches
d₂=12 inches
d₃=18 inches
And the values of corresponding time are,
t₁=0.5 min
t₂=1 min
t₃=1.5 min
The speed of an object is given by the ratio of the distance covered by the object to the time it takes the object to cover the distance.
Thus the speed of the ant is given by,
[tex]v=\frac{d_1}{t_1}=\frac{d_2}{t_2}=\frac{d_3}{t_3}[/tex]On substituting the known values,
[tex]\begin{gathered} v=\frac{6}{0.5}=\frac{12}{1}=\frac{18}{1.5} \\ =12\text{ imches/min} \end{gathered}[/tex]Thus the speed of the ant is 12 inches/min
Related Questions
An object is placed in front of a concave mirror between the center of curvature of the mirror and its focal point as shown in the diagram below three light rays are traced along with their corresponding reflected rays which statement below best describes the image formed
Answers
Given:
An object is placed in front of a concave mirror between the center of curvature of the mirror and its focal point.
To find:
The type of the image
Explanation:
The image is real if the rays after reflection from the mirror actually meet.
Here, the object is placed in front of a concave mirror between the center of curvature of the mirror and its focal point.
The rays after reflection actually meet. So, the image is real.
Hence, the image is real.
Fernando, who has a mass of 43.0 kg, slides down
the banister at his grandparents' house. If the
banister makes an angle of 35.0° with the horizontal,
what is the normal force between Fernando and the
banister?
Answers
From the calculations, the normal force on the body is 345 N.
What is the normal force?Let us recall the theory of Newton that states that action and reaction are equal and opposite. We know that the force that is exerted on an object is equal to the reaction of that surface of the object on the source of the force.
We know that the normal force can be given by the formula;
N = mgcosθ
m = mass of the object
g = acceleration due to gravity
θ = angle involved
We would now have
N = 43.0 kg * 9.8 m/s^2 * cos 35
N = 345 N
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A spaceship of mass m has its engines switched off and is moving in a circular orbit at
height R above the surface of a planet of mass M and radius R.
a) Derive an expression for total mechanical energy E of the orbiting spaceship, in terms of G, m,
M and R.
b) Derive an expression for the minimum speed V the spaceship would need to escape from this
orbit into deep space, in terms of system parameters. (The engines can’t fire for the whole trip;
they can only give the spaceship one boost so it obtains this velocity. Ignore all other celestial
objects.)
Answers
The total mechanical energy of a spaceship will be E = - GMm/2(R+h)
which is moving in circular orbit at height R above the surface of a planet of mass M and radius R . Here, m is the mass of spaceship and G is gravitational force.
Mechanical energy, also known as kinetic energy or potential energy, is the energy that an object possesses when it is in motion or the energy that an object stores due to its location. Renewable energy is also fueled by mechanical energy. In order to efficiently produce electricity or convert energy, many sources of renewable energy depend on mechanical energy.The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation.Therefore, when the engine of spaceship of mass (m) is switch offed and moving in circular orbit of a planet at height R above the surface of a planet of mass M and radius R then the mechanical energy is given by
E = - GMm/2(R+h)
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A solid cylinder (mass 0.274 kg, radius 2.00 cm) rolls without slipping at a speed of 5.00 cm/s. What is its total kinetic energy?
Answers
Given data
*The given mass of the solid cylinder is m = 0.274 kg
*The given radius of the cylinder is r = 2.00 cm = 0.02 m
*The given speed is v = 5.00 cm/s = 0.05 m/s
The formula for the total kinetic energy is given as
[tex]\begin{gathered} U_T=U_k+U_R \\ U_T=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2 \\ =\frac{1}{2}mv^2+\frac{1}{2}(\frac{1}{2}mr^2)(\frac{v}{r})^2 \end{gathered}[/tex]*Here U_K is the translation kinetic energy
*Here U_R is the rotational kinetic energy
*Here 'I' is the moment of inertia of the solid cylinder
Substitute the known values in the above expression as
[tex]\begin{gathered} U_T=\frac{1}{2}(0.274)(0.05)^2+\frac{1}{2}(\frac{1}{2}\times0.274\times(0.02)^2)(\frac{0.05}{0.02})^2 \\ =0.000342+0.000171 \\ =5.13\times10^{-4}\text{ J} \\ =5.13\times10^{-1}\text{ mJ} \end{gathered}[/tex]Hence, the total kinetic energy is U_T = 5.13 × 10^-1 mJ
7.0 mm diameter copper wire carries a current of 7.0 μA. What is the current density?
Answers
The current density of a 7.0 mm diameter copper wire that carries a current of 7.0 μA is 18.19 × 10⁻³ A/m².
The quantity of electric modern-day journeying in step with the unit move-phase region is known as current density and is expressed in amperes per rectangular meter. The more present-day a conductor, the higher could be the modern-day density. current density is the quantity of electrical modern flowing in step with the unit move-sectional region of a material.
subsequently, the SI unit of current density needs to be Ampere/meter2. Ohm's law relates the current flowing via a conductor to the voltage V and resistance R; this is, V = IR. An alternative assertion of Ohm's law is I = V/R.
current I = 0.7 μA
r = 3.5mm
J = I/A = I/πr³
J = 0.7 × 10⁻⁶ / 3.14 × (3.5 × 10⁻³)²
J = 18.19 × 10⁻³ A/m²
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What is the acceleration of a car,
moving along a straight line, that
increases its velocity from 0 to 15
m/s in 10 s?
Answers
The acceleration of a car, moving along a straight line, that increases its velocity from 0 to 15 is A=1.5m/s.
Acceleration = Velocity Change / Time Interval
So,
A=15/10
A=1.5m/s .
A slowing car slows down. It also accelerates because the speed changes. Imagine a car driving down the street. As speed increases, the car has positive acceleration. When a car turns a corner at a constant speed it changes direction and thus accelerates. The faster the rotation the greater the acceleration.
Therefore, any change in velocity in magnitude and direction causes acceleration. The main causes of poor acceleration are air and fuel issues and sensor issues. However mechanical problems can also cause poor performance. The car is moving forward and accelerating in the positive direction so the acceleration is in the same direction as the car is moving. An object can also have positive acceleration if it slows down while moving in a negative direction.
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A 1.2kg ball rolls forward with an acceleration of 1.11 m/s. What is the net force on the ball
Answers
Answer:
1.332 N
Explanation:
Net Force = Mass x Acceleration
1.2 x 1.11 = 1.332 N
I'm so sorry if I'm wrong.
Exit Slip!
Explain how Earth's tilted
axis and its revolution
around the Sun produces
seasons.
Answers
Earth's tilted axis and revolution around the sun causes the seasons.
Different parts of Earth receive the Sun's direct rays, throughout the year. So, it's summer in the Northern Hemisphere when the North Pole tilts toward the Sun. It's winter in the Northern Hemisphere when south Pole tilts toward the Sun.
As we know that the Earth rotates with a constant speed, so that every hour the direct beam will traverse across a single standard meridian. Rotation of Earth 15 degrees is equivalent to unit of one hour . When Earth rotates in such a way that the beam of the sun shifts +1∘ of longitude from East to West and time taken is 4 minutes.
The tilt of the Earth's axis is important because it governs the strength of warming of the sun's energy. The tilt of the surface of the Earth also causes light to be spread across a larger area of land which is termed as called the cosine projection effect.
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A Porsche 914 accelerates uniformly from 0 to 60 miles perhour in 5 seconds. Assuming a frictionless air track and a glider mass of 550grams, find the mass M2 that one must hang from the glider in order to obtain an accelerationequal to that of the Porsche.
Answers
The mass M₂ that one must hang from the glider in order to obtain an acceleration equal to that of the Porsche is 0.664 kilograms.
The initial velocity U of the porche is 0miles/hours or 0m/s.
The final velocity V of the porche is 60miles/hours or 26.84 m/s.
Total time period is 5 seconds,
Using equation of motion,
V+U = at
Putting all the values,
26.84= a(5)
a = 5.364 m/s².
Now, the mass of the glider is 0.550 Kg.
Let us assume that the glider and the mass are connected by a string. The tension in the string is T.
The mass M2 is hanged from one end the glider is on the horizontal surface.
When the system is released,
Total force on glider,
(0.550)a = T
Total force on the mass M2,
M2(a) = M2g - T.
Putting the value of T,
M2a = M2g - (0.550)a
(0.550)a = M2(g-a)
M2 = (0.550)×5.364/(9.8-5.364)
M2 = 0.664 Kg.
The required mass to be hung is 0.664 Kg.
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POSSIBLE POINTS: 2The graph below shows the relationship between the force acting on an object and the acceleration of the object. What is the acceleration of the objectwhen a 3 - newton force acts on it?____________What is the object's mass? ____________
Answers
From the graph we notice that when the force is 3 N the acceleration is 0.6 meters per second per second.
Now, to find the mass we use Newton's second law:
[tex]F=ma[/tex]for the point we found earlier we have:
[tex]\begin{gathered} 3=0.6m \\ m=\frac{3}{0.6} \\ m=5 \end{gathered}[/tex]Therefore the mass of the object is 5 kg
Calculate the area of the plates of a 1 pF parallel plate capacitor in a vacuum if the separation of the plates is 0.1 mm. [ε0=8.85×10-12C2N-1m-2 ]
Answers
Answer:
For parallel plate capacitor ,the capacitance C=dAϵ0
Area, A=ϵ0Cd=8.85×10−121×10−3=1.13×108m2
Pls Check This Answer Is correct or not
actually i am not sure
In the diagram, 91 = -6.39*10^-9 C andq2 = +3.22*10^-9 C. What is the electricfield at point P? Include a + or - sign tomindicate the direction.q2q1P0.424 m-** 0.636 m(Remember, E points away from + charges,and toward - charges.)(Unit = N/C)Enter
Answers
The magnitud of an electric field is given as:
[tex]E=\frac{1}{4\pi\epsilon_0}\frac{\lvert q\rvert}{r^2}[/tex]For the charge 1 the magnitude is:
[tex]\begin{gathered} E_1=\frac{1}{4\pi\epsilon_0}\frac{\lvert-6.39\times10^{-9}\rvert}{(0.424)^2} \\ E_1=319.543 \end{gathered}[/tex]Now, since charge 1 is negative this means that this field points towards the charge, in this case to the left, then the electric field for charge one is:
[tex]\vec{E_1}=-319.543[/tex]For the charge 2 the magnitude is:
[tex]\begin{gathered} E_2=\frac{1}{4\pi\epsilon_0}\frac{\lvert3.22\times10^{-9}\rvert}{(0.636)^2} \\ E_2=71.565 \end{gathered}[/tex]Now, since charge 2 is positive this means that this field points away from the charge, in this case to the left, then the electric field for charge two is:
[tex]\vec{E_2}=-71.565[/tex]Now, the total field on point P is the sum of both electric fields, then the total electri field on this point is:
[tex]E=-391.108[/tex]Jack drops off 10m high red bridge into swimming waters below. Assuming acceleration to be 9.91 m/s^2
A. What Jack speed as he hits the water?
Answers
Jack speed as he hits the water is 14.13m/s
What is speed?
The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time, making it a scalar quantity. The instantaneous speed is the upper limit of the average speed as the duration of the time interval approaches zero. The average speed of an item in a period of time is equal to the distance travelled by the object divided by the duration of the period. Velocity and speed are not the same thing.
The only force on Jack is gravity, which points straight down, and has an acceleration of 9.91m/s². Whether he's falling off a bridge or simply standing still on the surface of the earth, the acceleration due to gravity is the same.
If you're looking for the speed of Jack as he hits the water, you just need to solve for v in the equation[tex]$v^2 = v_0^2 + 2ad$[/tex].
Here,
v is Jack's speed as he hits the water,
[tex]$v_0$[/tex] is Jack's initial speed (which is zero since he's not moving when he jumps),
a is Jack's acceleration (which is 9.91m/s²), and
d is Jack's displacement (which is the height of the bridge, which you said is 10m).
This gives you an answer of [tex]$v = \sqrt{2ad} = \sqrt{2(9.91)(10)} = 14.13 \ \mathrm{m/s}$[/tex]
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This is physics 11th grade and a homework question I don’t understand how to do this or what the question is asking me
Answers
a) Frequency is the number of complete oscillations per second. Looking at the graph, there are 9 complete oscillations in 5 seconds. Thus,
Frequency = 9/5 = 1.8 oscillations per second
Frequency = 1.8 Hz
Period = 1/frequency = 1/1.8
Period = 0.056 s
b) When we differenctiate displacement with respect to time, the result is velocity.
Recall, period = 1/f = 5/9 cycles
1/4 cycle behind = 1/4 x 5/9 = 5/36
It is delayed with 5/36 sec with respect to displacement.
5/36 sec = 0.139 sec
Acceleration = first derivative of velocity = second derivative of displacement = 1/4 cycle behind velocity = 1/2 cycle behind displacement =
5/36 = 0.139 sec delayed with respect to velocity
= 5/18 = 0.2777 secs delayed with respect to displacement
Thus, the number of seconds out of phase with the displacements is 0.278 seconds
c) The formula for calculating the period of an ideal pendulum anywhere is
T = 2π√length/local gravity). We would calculate the local gravity.
From the information given,
length = 0.2
T = P = 5/9
Thus,
5/9 = 2π√0.2/local gravity)
(5/9)/2π = √0.2/local gravity
Square both sides. It becomes
[(5/9)/2π]^2 = 0.2/local gravity
local gravity = 0.2/[(5/9)/2π]^2
local gravity = 25.56 m/s^2
Thus,
acceleration due to gravity = 25.56 m/s^2
Recall, earth's gravity = 9.8 m/s^2
number of g forces = 25.56/9.8
number of g forces = 2.61
A 180 N force acts at 190 degrees and a 140 N force acts at 260 degrees. Determine the magnitude and direction (include angle) of the resultant. Scale is 1cm =10N
NEED HELPPP ASAPPPPPP
Answers
The magnitude of the force is found to be 274.19N.
Force (F1)acting on θ1(190°) is 180N
Force (F2)acting on θ2(260°) is 140N
Therefore the angle between F1 and F2 is
θ2-θ1 = 180°-140° =40°
Now we calculate magnitude of force,
Magnitude of force ,F= F1+F2
F. F = [tex]\sqrt{ ( F1+F2). (F1+F2) }[/tex]
|F|² = [tex]\sqrt{F1 ²+F2 ²+F1 F2 COS θ}[/tex]
F= [tex]\sqrt{ 180²+140²+2×180×140× cos40°}[/tex]
F= [tex]\sqrt{32400+19600+23184}[/tex]
F= [tex]\sqrt{75184}[/tex]
F= 274.19N.
Thus, the magnitude of the force is found to be 274.19N.
The magnitude of the force is the entire quantity of forces acting on an object. When all forces are pulling in the same direction, the force becomes stronger. The strength of a force decreases as it is applied to an object from various angles.
Force has a magnitude and a direction, thus a vector quantity. The outcomes of two equal-sized forces acting in opposite directions one in the east and the other in the west are not the same.
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How long must a 400 W electrical engine work in order to produce 300 kJ of work?
Answers
In order to calculate the time needed, let's use the formula below:
[tex]P=\frac{E}{t}[/tex]Where P is the power in Watts, E is the energy/work in Joules and t is the time in seconds.
First, let's convert the energy from kJ to J (1 kJ = 1000 J):
[tex]300\text{ kJ}=300000\text{ J}[/tex]So, for P = 400, we have:
[tex]\begin{gathered} 400=\frac{300000}{t} \\ t=\frac{300000}{400} \\ t=750\text{ s} \end{gathered}[/tex]Therefore the time needed is 750 seconds.
How far will a car travel going at a speed of 18 m/s in 42 minutes?
O 756 meters.
O2,520 meters.
O 45,360 meters.
O 140 meters.
Answers
Answer:
d = rt
Explanation:
distance = ?
rate = 18 m/s
time = 42 x 60 = 2520 s
distance = 18 x 2520 = 45360 m
Hi Can you help out with this physics question? We may learn a new thing
Answers
Features that must be present for a stable well-designed racing car.
For, a racing car the speed is high and also to finish the race, the car should be easy to turn around.
Lower the centre of gravity more will be its stability.
A low centre of gravity is a must for a stable well-designed racing car.
If an object mass is 2 kg. And an applied force is acting on it at 15 N And the force of friction is 5 N and what is the objects acceleration
Answers
Given,
The mass of the object, m=2 kg
The applied force, F=15 N
The frictional force, f=5 N
The frictional force is a force that opposes the motion of an object. Hence it will be always be directed opposite to the direction of motion of the object.
The net force acting on the object is given by,
[tex]F_n=F-f[/tex]From Newton's second law of motion, the net force is given by,
[tex]F_n=ma[/tex]Where a is the acceleration of the object.
Therefore,
[tex]\begin{gathered} ma=F-f \\ \Rightarrow a=\frac{F-f}{m} \end{gathered}[/tex]On substituting the known values,
[tex]\begin{gathered} a=\frac{15-5}{2} \\ =5\text{ m/s}^2 \end{gathered}[/tex]Therefore the acceleration of the object is 5 m/s²
what is the formula to use when measuring specific heat capacity by method of mixtures?
Answers
Answer: Cs = [m1c1(T - T1) + mcCc(T - Ts)]/Ms(Ts - T)
Explanation:
The concept of heat exchange which is expressed as
heat lost by a hot body = heat gained by a cold body
The specific heat of a solid substance as determined by the method of mixture using the heat exchange concept would be
Heat lost by substance = heat gained by liquid + heat gained by calorimeter
Thus,
MsCs(Ts - T) = m1c1(T - T1) + mcCc(T - Tc)
Dividing both sides by Ms(Ts - T)
The formula for calculating the specific heat capacity by method of mixtures is
Cs = [m1c1(T - T1) + mcCc(T - Ts)]/Ms(Ts - T)
Where
m1 = mass of liquid
c1 = specific heat of liquid
ms = mass of substance
Cs =specific heat of substance
mc = mass of calorimeter
Cc = specific heat of material used in making the calorimeter
T = Final temperature of the mixture
T1 = initial temperature of the liquid
Ts = initial temperature of the substance
FPressure is a function of force and area on which the force is exerted: P =AWhat is the effect of an increase in temperature of a sealed container of gaswith no change in volume?hA. The change in temperature decreases the force of the collisions ofthe container and gas particles, so the pressure decreases.B. The change in temperature increases the force of the collisions ofthe container and gas particles, so the pressure increases.C. The change in temperature decreases the area over whichcollisions of the container and gas particles occur, so the pressureincreases.D. The change in temperature increases the area over whichcollisions of the container and gas particles occur, so the pressuredecreases.
Answers
B: The change in temperature increases the force of the collisions of
the container and gas particles, so the pressure increases.
P = F/A
Force is directly proportional to Force, so , if force increases also Pressure.
The purpose of the auricle is to equalize air pressure on both sides of the eardrums.TrueFalse
Answers
The auricle, also known as pinna is the visible portion of outer ear.
The purpose of auricle is to collect sound waves and send them through ear canal.
The eustachian tube connecting middle ear and back of nose, equalizes air pressure on both sides of the eardrum.
Thus, the statement is false.
A object has a mass of 4 kg and is accelerating at 3 m/s2.The net force acting on the object is [] N.
Answers
In order to calculate the net force acting on the object, we can use the second law of Newton:
[tex]\sum ^{}_{}F=m\cdot a[/tex]So, for a mass of 4 kg and an acceleration of 3 m/s², we have:
[tex]\begin{gathered} F=4\cdot3 \\ F=12\text{ N} \end{gathered}[/tex]Therefore the net force is 12 Newtons.
Calculate the net force.
Answers
The net force acting on the box is 15 N. The force acting on a box is unbalanced because the force on one side is 7 N while the force on other side is 8 N.
What is force?Force is defined as a push or pull exerted on an object as a result of the interaction of the object with another object.
It can also be defined as a factor that can alter how an object moves.
Net force is defined as the force that is the result of all forces concurrently acting on an object.
It can also be defined as all of the forces acting on an object are added together into a vector.
Net force = F1 + F2 + F3
= 7N + 4N + 4N
= 15 N
Thus, the net force acting on the box is 15 N. The force acting on a box is unbalanced because the force on one side is 7 N while the force on other side is 8 N.
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Review the statements below. Select the one that best describes the difference between astronomy and cosmology.
A) Astronomy is a much broader study of the universe as a whole, while cosmology is a more focused study on specific objects or celestial bodies contained within the universe.
B) Astronomy is the study of objects in the universe—how they are formed, their composition, and how they change over time. Cosmology is the study of the entire universe—what objects are contained in the universe, and what is happening to the universe over time, including how it may or may not end.
C) Astronomy is a branch of science that focuses on the beginning, middle, and end of the universe. Cosmology is the study of how objects move, interact, and change.
D) Astronomy is the study of space in general through the use of telescopes and other tools, while cosmology is the study of specific objects in space.
Answers
The statement that correctly differentiates between astronomy and cosmology is as follows: Astronomy is a much broader study of the universe as a whole, while cosmology is a more focused study on specific objects or celestial bodies contained within the universe (option A).
What is astronomy?Astronomy is the study of the physical universe beyond the Earth's atmosphere, including the process of mapping locations and properties of the matter and radiation in the universe.
On the other hand, cosmology is the study of the physical universe, its structure, dynamics, origin and evolution, and fate.
Astronomy studies objects and phenomena beyond Earth, whereas cosmology is a branch of astronomy that studies the origin of the universe and how it has evolved.
Therefore, it can be said that astronomy studies the universe from a much broader sense while cosmology is much more specific study.
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Inside the nucleus, two protons are held together by a force which overcomes the repulsion. This force is called
Answers
Inside the nucleus, two protons are held together by a strong nuclear force which overcomes the repulsion. This is sometimes referred to as strong interaction.
What is strong nuclear force?The strong nuclear force or the strong interaction is strong enough to overcome the repulsive force between the two positively charged protons and thereby allowing protons and neutrons to stick together even in a small space. Protons are held together by the strong attractive nuclear force that binds together protons and neutrons.
The strong force is one of the four fundamental forces of nature that include gravity, electromagnetism, and the weak nuclear force. The strong force holds protons and neutrons within the nucleus of the atom and thus creating densest environments in nature.
The strong force dies off very fast with distance more than gravity or the electromagnetic force. It's difficult to detect the strong force outside of a nucleus.
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A steel railroad track has a length of 24 mwhen the temperature is 8°C.What is the increase in the length of therail on a hot day when the temperature is36 °C? The linear expansion coefficient ofsteel is 11 x 10-6(°C)-1.Answer in units of m.Answer in units of mSecond part:- Suppose the end of rail are rigidly clamped eight Celsius degrees to prevent expansion calculate the thermal stress in the rail if it’s temperature is raised to 36 Celsius degrees Young’s module for Steel is 20×10 to the power of 10 and N/m to the power of two answer in units of N/m to the power of two.
Answers
Given:
• Length = 24 m
,• Temperature, T1 = 8°C
,• Expansion coefficient = 11 x 10⁻⁶(°C)⁻¹
Let's solve for the following:
• (a). The increase in length of the rail when the temperature is 36 °C
To find the increase in length, apply the formula:
[tex]L=L_o*\alpha *(T_2-T_1)[/tex]Where:
Lo = 24 m
α = 11 x 10⁻⁶(°C)⁻¹
T2 = 36 °C
T1 = 8°C
Thus, we have:
[tex]\begin{gathered} dL=24*11\times10^{-6}*(36-8) \\ \\ dL=24*11\times10^{-6}*(28) \\ \\ dL=0.0074\text{ m} \end{gathered}[/tex]The increase in length is 0.0074 m.
• (b). Let's calculate the thermal stress.
To find the thermal stress, we have the formula:
[tex]\text{ thermal stress = }Y\frac{dL}{L}[/tex]Where:
Y is the young modulus = 20 x 10¹⁰ N/m
dL is the change in length = 0.0074 m
L is the length = 24 m
Input values in the formula and solve:
[tex]\begin{gathered} \text{ thermal stress = 20}\times10^{10}*\frac{0.0074}{24} \\ \\ \text{ thermal stress = 6.17}\times10^7\text{ N/m}^2 \end{gathered}[/tex]The thermal stress is 6.17 x 10⁷ N/m².
ANSWER:
• (a). 0.0074 m.
• (b). 6.17 x 10⁷ N/m²
An average froghopper insect has a mass of 12.7 mg and jumps to a maximum height of 278 mm when its takeoff angle is 57.0∘ above the horizontal. Find the takeoff speed of the froghopper.
Answers
Takeoff speed of the froghopper is 2.786 m/s
By analyzing the vertical motion of the froghopper,
The initial vertical velocity of the froghopper as it jumps from the ground is given by
[tex]U_{y}[/tex] = U₀Sinθ
here, θ = 57°
Therefore Sin57° = 0.838
[tex]U_{y}[/tex]= 0.838U₀
Vertical motion is the motion that occurs when the object is thrown all the way up, i.e. , the initial velocity or force acts only in the vertical axis, therefore this motion has only vertical motion.
Maximum height reached by the froghopper is h = 278 mm
h = 0.278 m
As we know that vertical velocity at the point of maximum height will be zero,
[tex]V_{y} = 0[/tex]
Since the vertical motion is an accelerated motion with constant (de)acceleration, so by using Equation of motion,
[tex]V^{2} _{y} - U^{2} _{y} = 2gh[/tex]
[tex]U_y = \sqrt{V^{2} _{y} - 2gh }[/tex]
[tex]U_y = \sqrt{0 - 2(-9.81) (0.278) }[/tex]
[tex]U_{y}[/tex] = 2.335 m/s
[tex]U_{y}[/tex] = 0.838U₀
U₀ = [tex]\frac{U_y}{0.838}[/tex]
U₀ = [tex]\frac{2.335}{0.838}[/tex]
U₀ = 2.786 m/s
The takeoff speed of the froghopper is 2.786 m/s.
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What is the electric field between the plates of a capacitor that has a charge of 10.75 microC and voltage difference between the plates of 97.87 Volts if the plates are separated by 2.11 mm?
Answers
The eletric field on a capacitor is given by the following formula:
[tex]E=\frac{Q}{A\epsilon_0}=\frac{V}{d}[/tex]Where Q is the difference of charge between plates, A is the area, and e0 is a constant. It can also be written as the second formula, where V is the voltage, and d is the distance between plates.
When we use the second formula, with the values from the exercise, we get:
[tex]E=\frac{97.87}{2.11*10^{-3}}=46383.886[\frac{V}{m}][/tex]Thus, our final answer is E=46383.886 V/m
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Concept : Thermodynamics
Answers
A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?
Solution :
The cylinder is completely insulated from its surroundings. As a result, no heat is exchanged between the system (cylinder) and its surroundings. Thus, the process is adiabatic.
Initial pressure inside the cylinder =P1
Final pressure inside the cylinder =P2
Initial volume inside the cylinder =V1
Final volume inside the cylinder =V2
Ratio of specific heats, γ=CVCP=1.4
For an adiabatic process, we have:
P1V1γ=P2V2γ
The final volume is compressed to half of its initial volume.
∴V2=V1/2
P1V1γ=P2(V1/2)γ
P2/P1=V1γ/(V1/2)γ
=21.4=2.639
Hence, the pressure increases by a factor of 2.639.
Answer:
The cylinder is fully isolated from the rest of the environment.
There is no heat exchange between the system (cylinder) and its surroundings as a result of the design. As a result, the process is called adiabatic.
P1 represents the initial pressure inside the cylinder.
P2 is the final pressure within the cylinder.
V1 is the volume of the cylinder at its beginning.
The final volume of the cylinder is equal to V2.
The specific heat ratio, = Cp / Cv = 1.4,
We have the following for an adiabatic process:
P1V1γ = P2V2γ
After compression, the final volume is reduced to half of its original size.
Hence,
V2 = V1 / 2
P1V1γ = P2(V1 / 2)γ
P2 / P1 = V1γ / (V1 / 2)γ
= 21.4
We get,
= 2.639
Therefore, the pressure increases by a factor of 2.639
Explanation:
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