To find:
The relation between the pressure and the velocity of the fluid.
Explanation:
The Bernoulli's principle states that the increase in the velocity of the fluid occurs simultaneously with the decrease in the static pressure of the fluid.
That is, the velocity of the fluid is inversely proportioinal to the pressure of the fluid.
Final answer:
Thus the relationship between a fluid's velocity and its pressure is an inverse relationship.
Therefore, the correct answer is option A.
A particular heating element draws 18.014 A of current and heats 176.251 g of water from 20oC to 87.714oC in 7.167 minutes. What is the resistance of the heating element ? Specific heat of water is 4.186 J/g deg C.
Given:
The current drawn by the heating element is: I = 18.014 A.
Mass of the water is: m = 176.251 g.
The temperature difference of water is: T = 87.714 deg C - 20 deg C = 67.714 deg C.
Time for which the change in temperature occurs: t = 7.167 minutes
The specific heat of water is: c = 4.186 J/g degC.
To find:
The resistance of the heating element.
Explanation:
The expression for the heat is given as:
[tex]Q=mcT[/tex]Substitute the values in the above equation, we get:
[tex]\begin{gathered} Q=176.251\text{ g}\times4.186\text{ J/g deg C}\times67.714\text{ deg C} \\ \\ Q=49958.4876\text{ J} \end{gathered}[/tex]Joule's equation for electric heating is given as:
[tex]Q=I^2Rt[/tex]Here, R is the resistance of the heating element.
Rearranging the above equation, we get:
[tex]R=\frac{Q}{I^2t}[/tex]Substituting the values in the above equation, we get:
[tex]\begin{gathered} R=\frac{49958.4876\text{ J}}{18.014^2\text{ A}^2\times7.167\text{ m}} \\ \\ R=\frac{49958.4876\text{ J}}{324.5042\text{ A}^2\times7.167\times60\text{ s}} \\ \\ R=0.3580\text{ }\Omega \end{gathered}[/tex]Final Answer:
The resistance of the heating element is 0.3580 Ω.
Which of the following is not true of all waves?Waves carry energy from one place to another.Waves need a mechanical medium through which to propogate.Waves can be used to carry infomation across distances.For a wave propagating in a given medium, wavelength is inversely proportional to frequency.
Given:
Some statements about the waves
To find:
The statement which is not true of all waves
Explanation:
The waves carry energy from one place to another. The wavelength of a wave is,
[tex]\lambda=\frac{v}{f}[/tex]Here, 'v' is the speed of the wave and 'f' is the frequency of the wave.
So, the wavelength is inc=versely proportional to frequency in a given medium.
The waves line electromagnetic waves do not need any mechanical medium to propagate, they can travel without any media.
Hence, the statement "Waves need a mechanical medium through which to propogate" is not true.
The force of attraction between m1 and m2 is 76 N. What will this force become if m2 is tripled?
The new force is obtained as 228 N since the product of the masses is directly proportional to the force.
What is the new force?From the Newton law of universal gravitation, we can see that the gravitational force that exists between two masses is directly proportional to the product of the masses and inversely proportional to the distance between the masses.
Where the distance between the masses, remain the same, we can see that the new force would be three times the initial force since the the force and the mass are directly proportional.
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a clay ball (0.65kg) is thrown at a wall and sticks. The speed of the ball before hitting the wall was 15 m/s. It took 45 miliseconds for the clay to come to a stop and make contact with the wall. What was the average force the wall exerted on the wall during the collision?
In order to determine the average force the wall exerted on the ball, use the following formula:
[tex]F=\frac{\Delta p}{\Delta t}[/tex]where
Δp: change in momentum
Δt: change in time = 45 ms = 0.045 s
F: force = ?
calculate the change in momentum as follow:
[tex]\Delta p=m\Delta v=(0.65kg)(15\frac{m}{s}-0\frac{m}{s})=9.75\text{ kg}\cdot\text{m/s}[/tex]next, replace Δp and Δt into the formula for F:
[tex]F=\frac{9.75\text{ kgm/s}}{0.045s}=216.67N[/tex]Hence, the average force exterded by the wall on the ball was approximately 216.67N
Calculate the power of a 2057 Ω night light plugged into a 120 V source.
Lets write the data down:
R = 2057 Ω
V = 120 V
The power of the night light is given by:
[tex]P=\frac{V^2}{R}[/tex]Plug in the data in the formula:
[tex]\begin{gathered} P=\frac{120^2}{2057} \\ P=\frac{14,400}{2057} \\ P\approx7.0W \end{gathered}[/tex]The power of the night light is 7.0 W.
What is the net force on a 4.12kg dog that accelerates at 3.02 m/s^2
Answer: Net force = 12.4 N
Explanation:
We would apply the formula which is expressed as
Net force = mass x acceleration
From the information given,
mass = 4.12
acceleration = 3.02
Net force = 4.12 x 3.02
Net force = 12.4 N
On slide 2f and 2g, what is the value of ΣF if the object is in equilibrium?a)0N b)It is impossible to tell
From the given figure, let's determine sum of forces (ΣF) if the object is in equilibrum.
When an object is said to be in equilibrum, the forces are balanced. This means that the object is in a state of equilibrum.
If an object is in a state of equilibrum, the sum of all forces is zero.
Therefore, we have:
ΣFx = 0 N
ΣFy = 0 N
ΣF = √(ΣFx)² + (ΣFy)²= 0 N
Therefore, the value of ΣF if the object is in equilibrum is 0N.
ANSWER:
a) 0N
Question 5 of 10Which phrase is the best definition of matter?A. A substance that cannot be divided into smaller piecesB. The smallest piece of a chemical compound that retains theproperties of the compoundC. Something that occupies a volume of space and also has massD. A substance that can change in both volume and shape
Something that occupies a volume of space and also has mass is the best definition of matter.
everything that occupies space and has mass. Matter, in the form of atoms, which are made up of protons, neutrons, and electrons, makes up all physical objects. Greek philosophers Democritus (470–380 BC) and Leucippus are credited with originating the notion that matter was composed of constituent parts or particles (490 BC).
Atoms form the basis of matter. One proton makes up the most fundamental atom, the protium isotope of hydrogen. Atoms are composed of protons, neutrons, and electrons, however these particles are based on fermions. Despite fitting certain definitions of matter, quarks and leptons aren't commonly regarded as types of matter. It's easiest to just declare that matter is made up of atoms at the majority of levels.
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Imagine an asteroid at rest in space that cracks into two pieces. The first piece moves at 1.4 times the speed of the second piece. Calculate the ratio of the first piece’s mass to the second piece’s mass
Since the total linear momentum of the system was 0 before the asteroid cracking into two pieces, then the magntude of the linear momentum of each piece must be the same after the cracking.
Then:
[tex]m_1v_1=m_2v_2[/tex]If the speed of the first piece is 1.4 times the speed of the second, then:
[tex]\begin{gathered} v_1=1.4v_2 \\ \Rightarrow m_1\times1.4v_2=m_2v_2 \\ \Rightarrow1.4m_1=m_2 \\ \Rightarrow m_1=\frac{m_2}{1.4} \\ \Rightarrow\frac{m_1}{m_2}=\frac{1}{1.4} \end{gathered}[/tex]Then, the ratio of the first piece's mass to the second piece's mass is 1:1.4
in a particle accelerator a proton moves at constant speed 0.750c in a circle of radius 663 m. what is the net force on the proton?
In a particle accelerator a proton moves at constant speed 0.750c in a circle of radius 663 m. The net force on the proton will be .0127 * [tex]10^{-11}[/tex] N
Any object moving in a circle (or along a circular path) experiences a centripetal force. That is, there is some physical force pushing or pulling the object towards the center of the circle.
Force = m ( [tex]v^{2} / R[/tex])
m= mass
v = speed
R = radius
force = 1.67 * [tex]10^{-27}[/tex] * [tex](0.75 * 3 * 10^{8}) ^{2}[/tex] / 663 = 0.0127 * [tex]10^{-11}[/tex] N
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A diver shines a flashlight upward from beneath the water (n=1.33) at an angle of 40.0° to the vertical. At what angle does the light refract through the air above the surface of the water?
Given:
The refractive index of water, n₁=1.33
The angle of incidence, θ₂=40.0°
To find:
The angle of refraction.
Explanation:
The refractive index of the air is n₂=1
From the snell's law,
[tex]n_1\sin\theta_1=n_2\sin\theta_2[/tex]Where θ₂ is the angle of refraction.
On substituting the known values,
[tex]\begin{gathered} 1.33\sin40.0\degree=1\sin\theta_2 \\ \implies\theta_2=sin^{-1}(\frac{1.33\sin40.0\degree}{1}) \\ =58.75\degree \end{gathered}[/tex]Final answer:
The angle of refraction is 58.75°
A 6 kg sign is suspended by two strings making angles with the ceiling as shown in the diagram. Determine the magnitudes of the tensions in each string. Remember that 1kg exerts a force of 9.8 N. please use sine/cosine law for this question
The triangle representing the given scenario is shown below
T1 and dT2 represents the tension in each spring
We would apply the sine rule which is expressed as
a/SinA = b/SinB = c/SinC
where
A, B and C are the angles of the triangle
a, b and c are the sides opposite the respective angles
Thus,
A = 42
a = T1
B = 23
b = T2
C = 115
c = 58.8
T1/sin42 = 58.8/sin115
By cross multiplying, it becomes
T1sin115 = 58.8sin42
T1 = 58.8sin42/sin115
T1 = 43.41
T2/sin23 = 58.8/sin115
By cross multiplying, it becomes
T2sin115 = 58.8sin23
T2 = 58.8sin23/sin 115
T2 = 25.35
The magnitude of the tension in each string are 43.41 N and 25.35 N
In the figure below a given point charge is shown following five different paths through a uniform electric field. In which path is the change in potential energy for the point charge the greatest? (The electric field lines are shown in blue and the paths are show in green.)
ANSWER
Path D
EXPLANATION
We want to identify the path for which the change in potential energy for the point charge is greatest.
The change in potential energy of the point charge is equal to the amount of work that is done by the charge to move from its position along the path taken. This implies that the greatest change in potential energy will occur along the path that requires that the most work is done.
Work done is dependent on force and distance moved by the point charge. Hence, the farther the distance travelled by the point charge, the greater the work done in the motion.
Since path D has the longest distance, then, it is in path D that the change in potential energy for the point charge is the greatest.
Why is the sand on a dry beach not a fluid but when a wave comes in and out the sand does become a fluid and your feet sink when standing on it?
When the sand is mixed with the water, it will form a quicksand. It behaves like a solution, and when the water is removed from the sand, it will act as a solute.
When our feet sink into the sand, our movements will cause you to dig yourself deeper into it.
a ray of light hits a flat mirror with an incident angle of 39.20 degrees. What angle does it reflect at? (do not put in units)
Given
A ray of light hits a flat mirror with an incident angle of 39.20 degrees.
To find
What is the angle of reflection?
Explanation
According to the law of reflection,
The angle of incidence is equal to the angle of reflection.
Here the angle of incidence is 39.20 deg
So the angle of reflection is 39.20 deg
Conclusion
The angle of reflection is 39.20 deg
If it takes 0.8 s for your voice to be heard at a distance of 272 m, what is the temperature of the air?
V = 331 + 0.59 Tc
v= d/t = 272 / 0.8 = 340 m/s
340 = 331 + 0.59 Tc
340 - 331 = 0.59 TC
9 = 0.59 Tc
9/0.59 = Tc
Tc = 15.25°C
66) The fundamental wavelength for standing sound waves in an empty pop bottle is 0.88 m. (a) What is the length of the bottle? (b) What is the frequency of the third harmonic of this bottle?
Explanation
Step 1
Let
[tex]\begin{gathered} \text{fundamental wavelength=0.88 ,} \\ \lambda=2L \\ \text{hence, replace} \\ 0.88m=2\text{ L} \\ \text{divide both sides by 2} \\ \frac{0.88m}{2}=\frac{2\text{ L}}{2} \\ 0.44=L \end{gathered}[/tex]hence, the length of the bottle is 0.44 meters
Step 2
What is the frequency of the third harmonic of this bottle?
For the third harmonic, the length of the string is equivalent to three-halves of a wavelength,so
[tex]\begin{gathered} third\text{ armonci= }\frac{\text{3}}{2}\cdot0.88\text{ m} \\ third\text{ armonci= }1.32\text{ m} \\ \end{gathered}[/tex]so
[tex]\begin{gathered} 1.32=2L \\ \end{gathered}[/tex]replace in the quation and solve for
Let speed of sound = 343 m/s
[tex]\begin{gathered} f=\frac{v}{\lambda} \\ \text{replacing} \\ f=\frac{343}{0.88} \\ f=389.77\text{ Hz} \end{gathered}[/tex]I hope this helps
you
What is the potential difference across a curling iron if there is a current of 2.5 A transferring 9360 J in 32s?
Power is expressed as energy/time
Thus means that
power = energy/time
From the information given,
energy = 9360 J
time = 32 s
Thus,
power = 9360/32 = 292.5 J/s = 292.5 watts
The formula relating potential difference which is the same as voltage, current and power is expressed as
P = IV
where
P = power = 292.5
I = current = 2.5
V = potential difference = ?
Thus, we have
292.5 = 2.5V
V = 292.5/2.5
V = 117 V
The potential difference is 117 V
A pendulum has a mass of 3kg and is lifted to a height of .3m. What is the maximum speed of the pendulum
Given data
*The given mass of the pendulum is m = 3 kg
*The given height is h = 0.3 m
The formula for the maximum speed of the pendulum is given as
[tex]v_{\max }=\sqrt[]{2gh}[/tex]*Here g is the acceleration due to the gravity
Substitute the values in the above expression as
[tex]\begin{gathered} v_{\max }=\sqrt[]{2\times9.8\times0.3} \\ =2.42\text{ m/s} \end{gathered}[/tex]Hence, the maximum speed of the pendulum is 2.42 m/s
An object with a mass of 5kg is moving with a force of 25N. What is the object's acceleration?
According to Newton's second law, F=ma
Where F is the force acting on the object, m is the mass of the object, and a is the acceleration of the body due to the applied force.
It is given in the question,
m=5 kg
F=25 N
On substituting the known values in the above equation,
[tex]25=5\times a[/tex]On rearranging the above equation,
[tex]a=\frac{25}{5}=5m/s^2[/tex]Therefore the object's acceleration is 5 m/s²
True or false. Iron fillings can indicate the presence of a magnetic field
Iron Filings are small shavings of ferromagnetic material.
Ferromagnetic material aligns with a magnetic field.
So, Iron fillings can indicate the presence of a magnetic field
True
During a hockey game, two hockey players (m1 = 82kg and m2 = 76kg) collide head on in a 1 dimensional perfectly instant collision. If the first hockey player is moving to the left at a velocity 4.2 m/s and the second hockey player is moving in the opposite direction at a velocity of 3.4 m/s, how fast are they both moving after they collide, assuming they stick together after they collide? How much kinetic energy is lost as a result of the collision?
Given:
The mass of player 1 is m1 = 82 kg
The initial velocity of player 1 is
[tex]v_{i1}=\text{ 4.2 m/s}[/tex]towards left.
The mass of player is m2 = 76 kg
The initial velocity of player 2 is
[tex]v_{i2}=\text{ -3.4 m/s}[/tex]in opposite direction.
Required:
The final velocity after the collision assuming they stick together.
The loss of kinetic energy after collision.
Explanation:
According to the conservation of momentum, the final velocity will be
[tex]\begin{gathered} m1v_{i1}+m2v_{i2}=(m1+m2)v_f \\ v_f=\frac{m1v_{i1}+m2v_{i2}}{m1+m2} \\ =\text{ }\frac{(82\times4.2)-(76\times3.4)}{82+76} \\ =0.544\text{ m/s} \end{gathered}[/tex]The loss in kinetic energy will be
[tex]\begin{gathered} \Delta KE=KE_{after}-KE_{before} \\ =\frac{1}{2}(m1+m2)(v_f)^2-\frac{1}{2}m1(v_{i1})^2-\frac{1}{2}m2(v_{i2})^2 \\ =\frac{1}{2}(82+76)(0.544)^2-\frac{1}{2}\times82\times(4.2)^2-\frac{1}{2}\times76\times(3.4)^2 \\ =23.38-723.24-439.28 \\ =-1139.14\text{ J} \end{gathered}[/tex]Final Answer:
The final velocity after the collision assuming they stick together is 0.544 m/s.
The loss of kinetic energy after the collision is 1139.14 J.
Force can be given as ?
The force is, momentum/time.
option 1
Two 4.952 cm by 4.952 cm plates that form a parallel-plate capacitor are charged to +/- 0.576 nC. What is the electric field strength inside the capacitor if the spacing between the plates is 2.97 mm?
In order to solve this question, we will need to know the E-field of a capacitor
E = sigma/epsilon naught
To find sigma (charge density), we will need to divide the total charge by the area
sigma = (.576 x 10^-9)/(4.952x10^-2)^2 = 2.34 x 10^-7
E = 2.34 x 10^-7/ (8.85x10^-12) = 26541.04 V/m
(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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What does the lower scale read? Answer in units of N
We will have the following:
First, we are given:
*Mass of the breaker: 1.1kg
*Mass of water: 3.3 kg
*Mass of metallic alloy: 4.2kg
*Density of the alloy: 5300kg/m^3
*Density of water: 1000kg/m^3
Now, we find the volume of water displaced by the alloy:
[tex]V_{\text{w}}=4.2\operatorname{kg}\cdot\frac{m^3}{5300\operatorname{kg}}\Rightarrow V_w=\frac{21}{26500}m^3\Rightarrow V_w\approx7.92\cdot10^{-4}m^3[/tex]Then, from the reading in the hanging scale we will have the force experienced by the alloy due to the upthrust when placed in water, that is:
[tex]R=mg-\rho Vg[/tex]So:
[tex]R=(4.2\operatorname{kg})(9.8m/s^2)-(1000\operatorname{kg}/m^3)(\frac{21}{26500}m^3)(9.8m/s^2)[/tex][tex]\Rightarrow R=33.39396226\ldots N\Rightarrow R\approx33.4N[/tex]The reading on the lower scale is due to the weight of the water in the breaker and upthrust on the scale:
[tex]R=g(m_1+m_2)+\rho Vg[/tex]Finally:
[tex]R=(9.8m/s^2)(1.1\operatorname{kg}+3.3\operatorname{kg})+(1000\operatorname{kg}/m^3)(\frac{21}{26500}m^3)(9.8m/s^2)[/tex][tex]\Rightarrow R=50.886003774\ldots N\Rightarrow R\approx50.9N[/tex]So, the readin on the lower scale is approximately 50.9N.
A spring with a spring constant of 30.0N/m Is compressed 5.00m. What is the force that the spring would apply
Force of the Spring = -(Spring Constant) x (Displacement)
so , Here we need to put the values
F = 30* 5 = 150N
Here, the Force applied is 150N. So, the correct ans is C
Prove that the area of the parallelogram is equal to | A × B |
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]Jontell finds a giant spring that has a 350N/m spring constant. Jontell figures out how to compress is 1.5m. If Jontell and his spring propelled cart's mass is 85kg, how fast is he going after the push fromthe spring? PEspring1/2*k*x?^2
Given data
*The given mass of the propelled cart's is m = 85 kg
*The given spring constant is k = 350 N/m
*The spring compresses at a distance is x = 1.5 m
The formula for the speed is given by the conservation of energy as
[tex]\begin{gathered} U_{p.e}=U_k \\ \frac{1}{2}kx^2=\frac{1}{2}mv^2 \\ v=\sqrt[]{\frac{kx^2}{m}} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v=\sqrt[]{\frac{350\times(1.5)^2}{85}} \\ =3.04\text{ m/s} \end{gathered}[/tex]An atom of carbon-14 isotope has more protons than an atom of carbon-12 isotope. Is this true or false?
Carbon-12 and carbon-14 are isotopes of each other. Isotopes are the elements that contain the same number of protons but a different number of neutrons.
CArbon-12 contains six protons and six neutrons. While carbon-14 contains six protons and eight neutrons.
Thus the given statement is false.
