Answer:
m = 4.9 10⁸ kg
Explanation:
The expression for the density is
ρ = m / V
m = ρ V
the volume of the atmosphere is the volume of the sphere of the outer layer of the atmosphere minus the volume of the plant
V = V_atmosphere - V_planet
V = 4/3 π R_atmosphere³ - 4/3 π R_venus³
V = 4/3 π (R_atmosphere³ - R_venus³
)
the radius of the planet is R_venus = 6.06 10⁶ m.
The radius of the outermost layer of the atmosphere
R_atmosphere = 50 10³ + R_ venus = 50 10³ + 6.06 10⁶
R_atmosphere = 6.11 10⁶ m
let's find the volume
V = 4/3 pi [(6,11 10⁶)³ - (6,06 10⁶)³]
V = 23,265 10⁶ m³
let's calculate the mass
m = 21 23,265 10⁶
m = 4.89 10⁸ kg
with two significant figurars is
m = 4.9 10⁸ kg
Two spherical shells have a common center. The inner shell has radius R1 = 5.00cm and charge q1=+5.00×10^−6C ; the outer shell has radius R2 = 15.0cm and charge q2=−6.00×10^−6C . Both charges are spread uniformly over the shell surface. Take V=0 at a large distance from the shells.
Part A) What is the electric potential due to the two shells at the distance r =2.50 c from their common center.
part B) What is the electric potential due to the two shells at the distance r= 10.0 cm from their common center.
Answer:
Explanation:
Part A:
Using the formula for electric potential due to a charged spherical shell:
V1 = kq1/R1 and V2 = kq2/R2
where k is the Coulomb constant.
For r < R1, the electric potential due to both shells is:
V = V1 + V2 = kq1/R1 + kq2/R2
For R1 < r < R2, the electric potential due to the outer shell is:
V = V2 = kq2/R2
For r > R2, the electric potential due to both shells is:
V = V1 + V2 = kq1/r + kq2/R2
Substituting the given values, we get:
V = (9.0x10^9 Nm^2/C^2)(5.00x10^-6 C)/0.025 m + (9.0x10^9 Nm^2/C^2)(-6.00x10^-6 C)/0.15 m
V = -4.32x10^5 V
Therefore, the electric potential due to the two shells at a distance of 2.50 cm from their common center is -4.32x10^5 V.
Part B:
For r < R1, the electric potential due to both shells is:
V = V1 + V2 = kq1/R1 + kq2/R2
For R1 < r < R2, the electric potential due to both shells is:
V = V1 + V2 = kq1/r + kq2/R2
For r > R2, the electric potential due to both shells is:
V = V1 + V2 = kq1/r + kq2/r
Substituting the given values, we get:
V = (9.0x10^9 Nm^2/C^2)(5.00x10^-6 C)/0.1 m + (9.0x10^9 Nm^2/C^2)(-6.00x10^-6 C)/0.1 m
V = 4.80x10^5 V
Therefore, the electric potential due to the two shells at a distance of 10.0 cm from their common center is 4.80x10^5 V.
27 1 point
A student has tested several types of wood for density. The best way of presenting this information graphically would be to use which item?
Scatterplot
Pie Chart
Line Graph
Bar Graph
Previous
Search
The best way of presenting the information on density graphically would be to use a D, bar graph.
What is a bar graph?A bar graph is a type of chart that uses rectangular bars to represent data. The bars are typically arranged in columns, with the independent variable (in this case, the type of wood) on the x-axis and the dependent variable (in this case, the density) on the y-axis.
A bar graph is the best choice for this data because it allows for easy comparison of density of different types of wood. We can see at a glance which type of wood is the densest and which type of wood is the least dense.
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does the mass of a parachute affect terminal velocity?
Answer:
The greater weight increases the terminal velocity by acting as an extra force against gravity and air resistance.
You are playing in a volley ball game Your team has 12 and the other team has 18.
How many points does your team needs to win?
How many points does the other team needs to win?
Answer:
you need 7 points and the other team just needs to stop you from scoring
Explanation:
What was the big bang?
The big bang is how astronomers explain the way the universe began. It is the idea that the universe began as just a single point, then expanded and stretched to grow as large as it is right now—and it is still stretching!
What's This Big Bang All About?
In 1927, an astronomer named Georges Lemaître had a big idea. He said that a very long time ago, the universe started as just a single point. He said the universe stretched and expanded to get as big as it is now, and that it could keep on stretching.
What an Idea!
The universe is a very big place, and it’s been around for a very long time. Thinking about how it all started is hard to imagine.
Some More Information
Just two years later, an astronomer named Edwin Hubble noticed that other galaxies were moving away from us. And that’s not all. The farthest galaxies were moving faster than the ones close to us.
This meant that the universe was still expanding, just like Lemaître thought. If things were moving apart, it meant that long ago, everything had been close together.
Everything we can see in our universe today—stars, planets, comets, asteroids—they weren't there at the beginning. Where did they come from?
A Tiny, Hot Beginning
When the universe began, it was just hot, tiny particles mixed with light and energy. It was nothing like what we see now. As everything expanded and took up more space, it cooled down.
The tiny particles grouped together. They formed atoms. Then those atoms grouped together. Over lots of time, atoms came together to form stars and galaxies.
The first stars created bigger atoms and groups of atoms. That led to more stars being born. At the same time, galaxies were crashing and grouping together. As new stars were being born and dying, then things like asteroids, comets, planets, and black holes formed!
Earthquakes occur along large cracks (faults) at or near the boundary between two tectonic plates. Why do some faults generate earthquakes while others move peacefully?
Prove the formular for calculating attraction
The formula for calculating attraction is F=GMmr².
Gravitational attractionGravitational attraction is the force of attraction that occurs on all bodies
which have a mass as a result of the force of gravitational force.
The Force is directly proportional to the product of their masses and
inversely proportional to the square of the distance between them.
Gravitational attraction = F=GMmr².
where F is the Force, G is gravitational constant, M and m are masses and r²
is square of the distance between the masses.
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Particles q1 =+9.33 uC, q2 =+4.22 uC, and q3=-8.42 uC are in a line. Particles q1 and q2 are separated by 0.180 m and particles q2 and q3 are separated by 0.230 m. What is the net force on particle q2?
The net force on q₂ will be 1.07 x 10⁻² N, pointing to the left.
To find the net force on particle q₂, we need to calculate the force due to q₁ and q₃ individually and then add them up vectorially. We can use Coulomb's law to calculate the force between two point charges:
F = k × (q₁ × q₂) / r²
where F is the magnitude of the force, k is Coulomb's constant (k = 8.99 x 10⁹ Nm²/C²), q1 and q2 are the charges of the two particles, and r is the distance between them.
The force due to q₁ on q₂ can be calculated as:
F₁ = k × (q₁ × q₂) / r₁²
where r1 is the distance between q₁ and q₂ (r₁ = 0.180 m).
Similarly, the force due to q₃ on q₂ can be calculated as:
F₂ = k × (q₃ × q₂) / r₃²
where r₃ is the distance between q₂ and q₃ (r₃= 0.230 m).
The direction of each force can be determined by the direction of the electric field due to each charge. Since q₁ and q₃ have opposite signs, their electric fields point in opposite directions. Therefore, the force due to q₁ points to the left and the force due to q₃ points to the right.
To find the net force, we need to add up the forces vectorially. Since the forces due to q₁ and q₃ are in opposite directions, we can subtract the magnitude of the force due to q₃ from the magnitude of the force due to q₁ to get the net force on q₂:
Fnet = F₁ - F₃
Substituting the values we get:
Fnet = k × (q₁ × q₂) / r₁² - k × (q₃ × q₂) / r₃²
Plugging in the values we get:
Fnet = (8.99 x 10⁹ Nm²/C²) × [(9.33 x 10⁻⁶ C) × (4.22 x 10⁻⁶ C) / (0.180 m)² - (-8.42 x 10⁻⁶ C) × (4.22 x 10⁻⁶ C) / (0.230 m)²]
Fnet = 1.07 x 10⁻² N
Therefore, the net force on q₂ is 1.07 x 10⁻² N, pointing to the left.
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03: Hook's law suggests that F is directly proportional to -x, how much true you have found this statement in your experiment? Explain any differences.
Hooke's Law can be given as follows sometimes:
The restoring force of a spring is equal to the spring constant multiplied by the displacement from its normal position:
F = -kx
Where, F = Restoring force of a spring (Newtons, N)
k = Spring constant (N/m)
x = Displacement of the spring (m)
The negative sign relates to the direction of the applied force and by convention, the minus or negative sign is present in F = -kx. The restoring force F is directly proportional to the displacement (x), according to Hooke's law. When the spring is compressed, the displacement (x) is negative. It is zero when the spring is at its original length and positive when the spring is extended.
Practically, Hooke's Law is applicable only within a limited frame of reference, and through experimenting, this statement proves to be true. Because materials cannot be compressed beyond a certain size or expanded beyond a certain size without some permanent deformation or change of their original state.
The law only applies under some conditions such as a limited amount of force or deformation. Factually, many materials will noticeably deviate from Hooke's law even before those elastic limits are reached.
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A 0.5 kg drone traveling 15 m/s crashes into a tree. What is the momentum of the drone before and after the
crash?
A) 7.5 kg • m/s before and 0 kg · m/s after
B) 30 kg - m/s before and 0 kg • m/s after
C) 0 kg • m/s before and after due to the crash
D) 7.5 kg · m/s before and after
1. The momentum of the drone before the crash is 7.5 kg•m/s
2. The momentum of drone after the crash is 0 kg•m/s
The correct answer to the question is Option A. 7.5 kg•m/s before and 0 kg•m/s after
Momentum is simply defined as the product of mass and velocity i.e
Momentum = mass × velocity
With the above formula, we can obtain the answers to the questions given above.
1. Determination of the momentum before the crash
Mass = 0.5 Kg
Initial Velocity = 15 m/s
Momentum =?Momentum = mass × velocity
Momentum = 0.5 × 15
Momentum = 7.5 Kg•m/sThus, the momentum of the drone before the crash is 7.5 Kg•m/s
2. Determination of the momentum after the crash
Mass = 0.5 Kg
Final Velocity = 0 m/s
Momentum =?Momentum = mass × velocity
Momentum = 0.5 × 0
Momentum = 0 Kg•m/s
Thus, the momentum of the drone after the crash is 0 Kg•m/s
The correct answer to the question is Option A. 7.5 kg•m/s before and 0 kg•m/s after
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Answer:
1. 7.5 kg ⋅ m/s before and 0 kg ⋅ m/s after
2. 7.2 kg ⋅ m/s
3. 40,000 kg⋅m/s
4. It must have decreased.
5. She will move in the same direction at the same speed forever.
6. two balls colliding in deep space
7. magnetism
8. Determine the momentums of the two particles before the collision and add them together. Determine the momentums of the two particles after the collision and add them together. Verify that both sums are the same.
9. 2.0 m/s
10. 1.1 m/s
11. 81 kJ
12. Increase the input force and decrease the output displacement.
13. 4 m
What is the threshold velocity vthreshold(water) (i.e., the minimum velocity) for creating Cherenkov light from a charged particle as it travels through water (which has an index of refraction of n
Answer:
2.3*10^8m/s
Explanation:
Using
V = c/n
Where c= speed of light
n = refractive index of water
By substituting
We have
V= 3*10^8m/s/1.33
= 2.3*10^8m/s
Look at the diagram below. From the frame of reference of the person riding
scooter B, what is the velocity of scooter A?
Scooter A
8 km/hr east
12 km/hr west
Scooter B
OA. 20 km/hr west
B. 20 km/hr east
OC. 4 km/hr east
D. 4 km/hr west
The equation below can be used to find the specific heat capacity of a substance. What is the specific heat capacity if it takes 1000 J of energy to heat 25 g of this substance by 100°C? Give your answer in J/kg°C.
Answer:
400J/kg°C
Explanation:
The specific heat capacity will be 400 J/kg °C. Specific heat capacity is the relationship between the amount of energy delivered to a substance and the increase in temperature that results.
What is specific heat capacity ?The amount of heat required to increase a substance's temperature by one degree Celsius is known as specific heat capacity.
Similarly
Mathematically, specific heat capacity is given by;
\(\rm C = \frac{E}{m \times \theta }\)
The given data in the problem is;
The specific heat of the substance is,C in J/kg °C.
The energy is,E =1000 JIs
The mass is,m= 25 g
\(\rm \theta\) Is the temperature difference = 100 °C.
On substituting the given data;
\(\rm C = \frac{E }{m \times \theta } \\\\ C = \frac{1000}{25\times 10^{-3} \times 100 } \\\\ C = 400 \ J/kg^0C.\)
Hence, the specific heat capacity will be 400 J/kg °C.
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How to solve conservation of momentum
Answer:
Step 1: List the mass and velocity of the object. Step 2: Convert any values into SI units (kg, m, s). Step 3: Multiply the mass and velocity of the object together to get the momentum of the object.
an ideal gas at 20centigree In a press 1.5×10pa and compress,a.isothamally,b.adaibatically until it volume in 1/3 in each case reversible.calculate in each case the final pressure and temperature of d gas (the ratio all specific capacity=Cp/Cv=1.4
a) The final pressure and temperature for the isothermal compression are \(4.5*10^5 Pa\) and 293 K, respectively, while b) the final pressure and temperature for the adiabatic compression are\(5.58*10^5 Pa\) and 515 K, respectively.
a. Isothermal compression:
For an isothermal process, the temperature remains constant. Therefore, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.
Since the process is isothermal, we can write:
\(P_1V_1 = P_2V_2\)
where P1 and V1 are the initial pressure and volume, and\(P_2\)and\(V_2\)are the final pressure and volume.
We are given that the volume is compressed to 1/3 of its original volume, so\(V_2 = (1/3)V_1\). Substituting this into the equation above gives:
\(P_2 = (V_1/V_2)P_1 = 3P_1\) = \(4.5*10^5 Pa\)
To find the final temperature, we can use the ideal gas law again:
PV = nRT
Rearranging, we get:
T = PV/(nR)
Substituting the values we know, we get:
T = (\(1.5*10^5\)Pa)(V1)/(nR)
Since the process is isothermal, the temperature remains constant, so the final temperature is the same as the initial temperature:
T2 = T1 = 293 K
b. Adiabatic compression:
For an adiabatic process, there is no heat transfer between the gas and its surroundings. Therefore, we can use the adiabatic equation:
PV^γ = constant
where γ = Cp/Cv is the ratio of specific heats.
Since the process is adiabatic and reversible, we can write:
\(P_1V_1\)^γ = \(P_2V_2\)^γ
We are given that the volume is compressed to 1/3 of its original volume, so V2 = (1/3)V1. Substituting this into the equation above gives:
\(P_2 = P_1(V_1/V_2)\)^γ = \(P_1\)\((3)^{(1.4)\) = \(5.58*10^5 Pa\)
To find the final temperature, we can use the adiabatic equation again:
\(T_2 = T_1(P_2/P_1)\)^((γ-1)/γ) = T1(5.58/1.5)^(0.4) = 515 K
Therefore, the final pressure and temperature for the isothermal compression are \(4.5*10^5 Pa\)and 293 K, respectively, while the final pressure and temperature for the adiabatic compression are \(5.58*10^5\) Pa and 515 K, respectively.
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Which is a chemical property of iron? A. It forms iron oxide (rust) when exposed to moisture and air. B. It is a gray–black metal that is hard to the touch. C. It has a melting point of 2795°F (1536°C). D. It is a good conductor of heat.
Answer:
a
Explanation:
it corrodes after repeated exposure to excess moisture and dry air the rust itself can be turned back into iron after melting it and removing the waste
28. A basketball player runs down the court, following the path indicated by the vectors A, B, and C in Figure 3-43. The magnitudes of these three vectors are A=10.0 m, B=20.0 m, and C=7.0 m. Find the magnitude and direction of the net displacement of the player using the graphical method and the component method of vector addition. Compare your results.
Given:
Magnitude of vector A = 10.0 m
Magnitude of vector B = 20.0 m
Magnitude of vector C = 7.0 m
Let's find the magnitude and direction of the net displacement using the component method of vector addition.
The vector of magnitude r which makes an angle θ with the positive x-axis in vector form is:
\(R=r(\cos \theta i+\sin \theta j)\)Vector A:
From the figure, vector A makes an angle of -90° with the x-axis, thus, we have:
\(\begin{gathered} A=10.0(\cos (-90)i+\sin (-90)j) \\ \\ A=10.0(0i+(-1)j) \\ \\ A=-10.0j \end{gathered}\)Vector B:
Vector B makes an angle of 45° with a magnitude of 20.0 m. Thus, we have:
\(\begin{gathered} B=20.0(\cos 45i+\sin 45i) \\ \\ B=20.0(0.5\sqrt[]{2}i+0.5\sqrt[]{2}j) \\ \\ B=10.0\sqrt[]{2i}+10\sqrt[]{2}j \end{gathered}\)Vector C:
Vector C makes an angle of -30° with a magnitude of 7.0 m. Thus, we have:
\(\begin{gathered} C=7.0(\cos (-30)i+\sin (-30)j) \\ \\ C=3.5\sqrt[]{3}i+3.5j \end{gathered}\)To find the net displacement, apply the formula:
Net displacement = A + B + C
Hence, we have the net diplacement below:
\(\begin{gathered} A+B+C \\ \\ (-10.0j)+(10.0\sqrt[]{2}i+10.0\sqrt[]{2}j)+(3.5\sqrt[]{3}i+3.5j) \\ \\ =10.0\sqrt[]{2}i+3.5\sqrt[]{3}i-10.0j+10.0\sqrt[]{2}j+3.5j \\ \\ =20.202i+0.642j \end{gathered}\)To find the magnitude of the net displacement, we have:
\(\begin{gathered} \text{ magnitude=}\sqrt[]{20.202^2+0.642^2} \\ \\ \text{ magnitude=}\sqrt[]{408.12+0.412} \\ \\ \text{magnitude = }\sqrt[]{408.53} \\ \\ \text{magnitude = }20.212 \end{gathered}\)To find the direction, we have:
\(\begin{gathered} \tan ^{-1}(\frac{y}{x}) \\ \\ =\tan ^1(\frac{0.642}{20.202}) \\ \\ =1.8\degree \end{gathered}\)Therefore, the magnitude of the net displacement is 20.21 m while the direction is at 1.8 degrees.
ANSWER:
Magnitude = 20.21 m
Direction = 1.8°
Question 4 of 25
A person drops two objects from the same height. One object weighs 15 N,
and the other weighs 10 N. How does the mass of the objects relate to the
force of gravity on them?
A. The 15 N object has twice the mass of the 10 N object.
B. The 15 N object has more mass than the 10 N object.
C. The 10 N object has more mass than the 15 N object.
D. The 10 N object has the same mass as the 15 N object.
A diver jumps from a 3.0 m board with an initial upward velocity of 5.5 m/s. What is the time the diver was in the air?
The answer is that the time the diver was in the air is 1.13 seconds.
To determine the time the diver was in the air, we can use the kinematic equation:
Δy = viΔt + 1/2at²,
where Δy is the displacement, vi is the initial velocity, a is the acceleration due to gravity (g), and t is the time.The initial velocity, vi, is given as 5.5 m/s, and since the diver jumps upwards, the displacement, Δy, is equal to the height of the board, which is 3.0 m. The acceleration due to gravity, a, is -9.8 m/s² (negative because it acts downwards).Substituting the known values into the equation:3.0
m = (5.5 m/s)t + 1/2(-9.8 m/s²)t²
Simplifying, we get:
4.9t² + 5.5t - 3.0 = 0
We can solve for t using the quadratic formula:
t = (-5.5 ± √(5.5² - 4(4.9)(-3.0))) / (2(4.9))= (-5.5 ± 1.59) / 9.8= -0.47 s or 1.13 s
Since time cannot be negative, the time the diver was in the air is 1.13 seconds.
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Which statement best describes how light behaves with liquids, gases, and solids?
A. Light is unable to travel through liquids but travels easily through solids and some gases.
B. Light is unable to travel through gases but does travel through liquids and solids.
C. Light travels easily through liquids and gases, as well as through some solids like
glass.
D. Light travels easily through solids but is unable to travel through liquids and gases.
(20 points!)
Answer:
C number is write i think
The first P-wave of an earthquake travels 5600 kilometers from the epicenter and arrives at a seismic station at 10:05 a.m. At what time did this earthquake occur?
Ahhhhhh I have a Regent's test in 2 hours and I don't know how to solve this type of question! Any help would be appreciated.
Anyone know what the steps to do this are? I dont even need an answer, just how to get to it. Thank you!
The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.
The p-waves travel with a constant velocity of 7 km/s
The time can be calculated by using the formula
t = d / v
where
T1 = 10:05 a.m
d is the distance they take to travel from the epicenter
v is the speed of the p-waves
On average, the speed of p-waves is
v = 7 km/s
d = 5600 km (given)
Substituting the values in the formula;
t = d / v
t = 5600 ÷ 7
t = 800 seconds
Converting into minutes,
t = 800 ÷ 60
t = 13.3
≈ 13 mins
T1 - 13 mins = T2
10:05 - 13 mins = 9.52 am
It means the earthquake occurred prior 13 minutes, that is at 9.52 am.
Therefore, the earthquake occurred at 9.52 am.
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A2.00 kg block is pulled across a
flat, frictionless floor with a 4.17 N
force directed 40.0° above
horizontal. What is the normal force
acting on the block?
(Hint: It is NOT = mg)
normal force (ND)
Answer:
Explanation:
R + 4.17sin(40) = mg
R = mg - 4.17sin(40)
= 2(9.8) - 4.17sin(40)
= 16.91957567
= 16.92 N
A 2.00 kg block is pulled across a flat, friction less floor with a 4.17 N force directed 40.0° above horizontal. The normal force acting on the block 16.92 N.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Given in the question,
R + 4.17 sin(40) = mg
R = mg - 4.17 sin(40)
= 2(9.8) - 4.17 sin(40)
= 16.91957567
= 16.92 N
A 2.00 kg block is pulled across a flat, friction less floor with a 4.17 N force directed 40.0° above horizontal. The normal force acting on the block 16.92 N.
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In the context of energy transfers with hot and cold reservoirs, the sign convention is that _______________.
Answer:
Qc>0; Qh>0
Explanation:
In the context of energy transfers with hot and cold reservoirs, the sign convention is QC > 0; QH < 0.
What is energy transfer?The conversion of one form of energy into another, or the movement of energy from one place to another is known as energy transfer.
Given that there are two energy reservoirs. Heat and work sign convention is:
If the heat is adding to the system then it is considered positive and if heat is going out from the system then it is considered negative. If the work is done on the system then it is taken as negative and if the work is done by the system then it is taken as positive.As, heat is going out that from the hot reservoir ,it is taken as negative- QH < 0.
As heat is coming inside the cold reservoir that is why it is taken as positive - QC > 0.
Therefore, QC > 0 and QH < 0 is the correct answer.
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A shop sign weighing 215 N hangs from the end of auniform 175-N beam as shown in (Figure 1).Find the tension in the supporting wire (at 35.0 degrees)
In order to find the tension in the wire, let's first decompose it in its vertical and horizontal components:
\(\begin{gathered} T_x=T\cdot\cos (35\degree) \\ T_y=T\cdot\sin (35\degree) \end{gathered}\)Now, since the system is stable, the sum of vertical forces is equal to zero, so we have:
\(\begin{gathered} T_y-175-215=0 \\ T_y-390=0 \\ T_y=390 \\ T\cdot\sin (35\degree)=390 \\ T\cdot0.57358=390 \\ T=\frac{390}{0.57358} \\ T=679.94\text{ N} \end{gathered}\)So the tension in the wire is equal to 679.94 N.
Explain the mode of operation of x-ray
Answer:
If x-rays get in touch with our body tissues, they create a picture of a metal film. The high energizing rays are unable to penetrate soft tissue, such as skin and organs and travel through the laser. The places where the x-rays pass soft tissues are Black areas of an X-ray.
Answer:
Explanation:
Mode of Operation: In the X-ray tube a Low voltage high p.d is applied between the hot cathode and the anode. Electrons are emitted from the cathode and are accelerated to an extremely high speed. ... They are produced by increasing the p.d. between the cathode and anode.
Ca(s) + PbCl2(aq) → CaCl2(uq) + Pb(s)
Answer: It is a balance equation
Explanation:
The diagram below shows snapshots of an oscillator at different times . What is the frequency of the oscillation ?
In the diagram tha shows snapshots of an oscillator at different times, the frequency of the oscillation is 0.555 Hz.
How to calculate the periodThe period of the oscillation is the time taken for the for the object to return to its original position. (ie. Displacement = 0). From the above snapshot,
Period of oscillation = 1.80s.
From here, finding the frequency is simple as, Frequency = 1/Period. Hence,
Frequency = 1/1.80
= 0.555 Hz (3 sf).
The frequency of the oscillation is indeed 0.555 Hz. The frequency represents the number of oscillations or cycles per second. In this case, the object completes approximately 0.555 oscillations per second.
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Two charges q1 and q2 exert a force of 20 N on each other. If the charge of q1 is doubled, what will the new force be? 1) 40N 2) 80N 3) 20 N 4) 10 N
Given :
Two charges q1 and q2 exert a force of 20 N on each other.
To Find :
If the charge of q1 is doubled, what will the new force be?
1) 40 N 2) 80 N 3) 20 N 4) 10 N
Solution :
We know, electrostatic force between two charges is given by :
\(F = \dfrac{kq_1q_2}{r^2}\)
Here, F = 20 N.
\(20 = \dfrac{kq_1q_2}{r^2}\)
Now, if \(q_1\) is doubled :
\(F'= \dfrac{k(2q_1)q_2}{r^2}\\\\F'= 2\dfrac{kq_1q_2}{r^2}\\\\F'= 2\times F\\\\ F'= 2\times 20 \ N\\\\F'= 40 \ N\)
Therefore, if the charge of q1 is doubled, new force will be 40 N.
Water flows at a speed of 13 m/s through a pipe that has a diameter of 1.2 m. What is the
diameter of the smaller end of the pipe that the water comes out with a speed of 30 m/s?
The diameter of the smaller end of the pipe is approximately 0.78 meters.
To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.
The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity
Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2
Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2
Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30
Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30
0.36 * 13 = (diameter2/2)^2 * 30
4.68 = (diameter2/2)^2 * 30
Dividing both sides by 30:
0.156 = (diameter2/2)^2
Taking the square root of both sides:
0.39 = diameter2/2
Multiplying both sides by 2:
0.78 = diameter2
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Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform acceleration towards (-)direction, Uniform deceleration towards (+) direction and Uniform deceleration towards (-) direction in displacement time graph.Can you draw the shapes for each type ?
Explanation:
Yes, there are differences in the shapes of position-time graphs for uniform acceleration and uniform deceleration in different directions. Let's consider each case separately:\(\hrulefill\)
(1) - Uniform acceleration towards the positive direction:
In this case, the object is moving in the positive direction with a constant acceleration. The displacement-time graph will typically be a curve that starts from an initial position and shows a steady increase in displacement over time. The shape of the graph will depend on the specific acceleration value.
(2) - Uniform acceleration towards the negative direction:
In this case, the object is moving in the negative direction with a constant acceleration. The displacement-time graph will also be a curve, but it will show a steady decrease in displacement over time.
(3) - Uniform deceleration towards the positive direction:
In this case, the object is initially moving in the positive direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a positive slope and gradually levels off.
(4) - Uniform deceleration towards the negative direction:
In this case, the object is initially moving in the negative direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a negative slope and gradually levels off.