Absolute zero, technically known as zero kelvins, equals −273.15 degrees Celsius, or -459.67 Fahrenheit, and marks the spot on the thermometer where a system reaches its lowest possible energy, or thermal motion.
How many significant figures are in 0.0067?
Answer:
2
Explanation:
there are 2 significant figures in there
A rollercoaster moves from the bottom of a hill and approaches the top of the hill. If friction between the wheels and the track is ignored, which statement describes the components of the total energy?
*answer choices pic attached*
{If anyone has the answers to the Energy Flows Quick Check or others please let me know}.
Answer:
The kinetic energy remains same and gravitational potential energy increases.
Explanation:
KINETIC ENERGY:
As, we know that the kinetic energy depends upon the speed of the object. Hence, the kinetic energy is given as:
K.E = (1/2)mv²
where,
m = mass
v = speed
K.E = Kinetic Energy
Since, the friction is ignored, therefore the speed of roller coaster will remain same.
Therefore, its Kinetic Energy will also remain same.
POTENTIAL ENERGY:
The potetial energy od a body depends upon its height, as follows:
P.E = mgh
where,
P.E = potential Energy
m = mass
g = acceleration due to gravity
h = height
As, the roller coaster moves up hill its height increases.
Therefore, its potential energy will also increase.
hence, the correct option is:
The kinetic energy remains same and gravitational potential energy increases.
Please help! Will give a lot of points
Question 6 is the answer I need
Answer:
B
Explanation:
A bicameral system describes a government that has a two-house legislative system, such as the House of Representatives and the Senate that make up the U.S. Congress.
Two charged point-like objects are located on the x-axis. The point-like object with charge q1 = 4.60 µC is located at x1 = 1.25 cm and the point-like object with charge q2 = −2.14 µC is located at x2 = −1.80 cm.
A) Determine the total electric potential (in V) at the origin.
B) Determine the total electric potential (in V) at the point with coordinates (0, 1.50 cm).
Answer:
a) the total electric potential is 2282000 V
b) the total electric potential (in V) at the point with coordinates (0, 1.50 cm) is 1330769.23 V
Explanation:
Given the data in the question and as illustrated in the image below;
a) Determine the total electric potential (in V) at the origin.
We know that; electric potential due to multiple charges is equal to sum of electric potentials due to individual charges
so
Electric potential at p in the diagram 1 below is;
Vp = V1 + V2
Vp = kq1/r1 + kq2/r2
we know that; Coulomb constant, k = 9 × 10⁹ C
q1 = 4.60 uC = 4.60 × 10⁻⁶ C
r1 = 1.25 cm = 0.0125 m
q2 = -2.06 uC = -2.06 × 10⁻⁶ C
location x2 = −1.80 cm; so r2 = 1.80 cm = 0.018 m
so we substitute
Vp = ( 9 × 10⁹ × 4.60 × 10⁻⁶/ 0.0125 ) + ( 9 × 10⁹ × -2.06 × 10⁻⁶ / 0.018 )
Vp = (3312000) + ( -1030000 )
Vp = 3312000 -1030000
Vp = 2282000 V
Therefore, the total electric potential is 2282000 V
b)
the total electric potential (in V) at the point with coordinates (0, 1.50 cm).
As illustrated in the second image;
r1² = 0.015² + 0.0125²
r1 = √[ 0.015² + 0.0125² ]
r1 = √0.00038125
r1 = 0.0195
Also
r2² = 0.015² + 0.018²
r2 = √[ 0.015² + 0.018² ]
r2 = √0.000549
r2 = 0.0234
Now, Electric Potential at P in the second image below will be;
Vp = V1 + V2
Vp = kq1/r1 + kq2/r2
we substitute
Vp = ( 9 × 10⁹ × 4.60 × 10⁻⁶/ 0.0195 ) + ( 9 × 10⁹ × -2.06 × 10⁻⁶ / 0.0234 )
Vp = 2123076.923 + ( -762962.962 )
Vp = 2123076.923 -792307.692
Vp = 1330769.23 V
Therefore, the total electric potential (in V) at the point with coordinates (0, 1.50 cm) is 1330769.23 V
a) The total electric potential is 2282000 V
b) The total electric potential (in V) at the point with coordinates (0, 1.50 cm) is 1330769.23 V
What is electric potential?The electric potential is defined as the amount of work energy needed to move a unit of electric charge from a reference point to a specific point in an electric field.
Given the data in the question and as illustrated in the image below;
a) Determine the total electric potential (in V) at the origin.
We know that; electric potential due to multiple charges is equal to sum of electric potentials due to individual charges
Electric potential at p in diagram 1 below is;
\(V_P=V_1+V_2\)
\(Vp = \dfrac{kq_1}{r_1} + \dfrac{kq_2}{r_2}\)
we know that; the Coulomb constant, k = 9 × 10⁹ C
q1 = 4.60 uC = 4.60 × 10⁻⁶ C
r1 = 1.25 cm = 0.0125 m
q2 = -2.06 uC = -2.06 × 10⁻⁶ C
location x2 = −1.80 cm; so r2 = 1.80 cm = 0.018 m
so we substitute
Vp = ( 9 × 10⁹ × 4.60 × 10⁻⁶/ 0.0125 ) + ( 9 × 10⁹ × -2.06 × 10⁻⁶ / 0.018 )
Vp = (3312000) + ( -1030000 )
Vp = 3312000 -1030000
Vp = 2282000 V
Therefore, the total electric potential is 2282000 V
b)The total electric potential (in V) at the point with coordinates (0, 1.50 cm).
As illustrated in the second image;
\(r_1^2=0.015^2+0.0125^2\)
\(r_1 = \sqrt{[ 0.015^2 + 0.0125^2 ]\)
\(r_1 = \sqrt{0.00038125}\)
\(r_1 = 0.0195\)
Also
\(r_2^2 = 0.015^2 + 0.018^2\)
\(r_2 = \sqrt{0.015^2 + 0.018^2}\)
\(r_2 = \sqrt{0.000549\)
\(r_2 = 0.0234\)
Now, Electric Potential at P in the second image below will be;
Vp = V1 + V2
\(Vp = \dfrac{kq_1}{r_1} + \dfrac{kq_2}{r_2}\)
we substitute
Vp = ( 9 × 10⁹ × 4.60 × 10⁻⁶/ 0.0195 ) + ( 9 × 10⁹ × -2.06 × 10⁻⁶ / 0.0234 )
Vp = 2123076.923 + ( -762962.962 )
Vp = 2123076.923 -792307.692
Vp = 1330769.23 V
Therefore, the total electric potential (in V) at the point with coordinates (0, 1.50 cm) is 1330769.23 V
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What is the definition of Heat Transfer
Answer:
Heat transfer is an engineering discipline that concerns the generation, use, conversion, and exchange of heat (thermal energy) between physical systems.
Explanation:
Answer:
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes.
Explanation:
hope that helps
why did the rocky planets form in the inner section of the solar system
Answer:
Because it was too hot for volatile compounds (like water) to condense in the inner solar system, rocky planetesimals formed from compounds with high melting points, such as iron and rocky silicates
A child of mass 22.0 kg is riding a playground merry-go-round that is rotating at 40.0 rev/min. What centripetal force must she experience to stay on if she is 1.25 m from the center
Answer:
Centripetal Force = 483.3 N
Explanation:
A centripetal force is the force that tends to keep a mocing object along a curved path and it is directed towards the centre of the rotatio, while centrifugal force is an apparent force that tends to force a rotating object away from the center of the rotation.
The formula for centripetal force is given by:
\(F_c = \frac{mv^2}{r} \\where:\\F_C = centripetal\ force\\m = mass\ = 22kg\\\omega =angular\ velocity = 40.0\ rev/min\)
Let us work on the angular velocity (ω), by converting to radians/ seconds
ω = 40 rev/min,
1 rev = 2π rad
∴ 40 rev = 2π × 40 rad = 80π rad
1 min = 60 seconds
\(\therefore\ 40\ rev \slash min = \frac{80\ \times\ \pi\ rad}{60\ seconds} \\40\ rev \slash min = 4.189\ rad \slash sec\)
Next let us find the velocity (v) from the angular velocity. Velocity (v) and angulsr velocity (ω) are related by the equation:
v = ω × r (m/s)
v = 4.189 × 1.25
v = 5.24 m/s
Finally, the centripetal force is calculated thus:
\(F_c = \frac{mv^2}{r} \\\\F_c = \frac{22 \times (5.24)^2 }{1.25} \\\\F_c = \frac{604.07}{1.25}\\ F_c = 483.3N\)
PLEASE BE FAST IM BEING TIMEDDDDD
If the current of a circuit is 2.8A. Find the number of charge in Coulomb in
3 seconds.
Answer:
I=Q/T
2.8=Q/3
8.4C=Q
Explanation:
Which law of thermodynamics does each of the following scenarios violate (if any)?
A machine that pulls all thermal energy out of a refrigerated space
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
A machine that can pull 1000J of heat out of a refrigerated space and into a warmer space without external work
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
A machine that can turn 1000J of heat directly into 1000J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
A machine that can create 1000J of heat from 100J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
A machine that can pull 1000J of heat out of a refrigerated space and put 1500J of heat into a warmer space if it uses 500J of external work
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
Below are the required answers and explanations for each of the scenarios listed.
1. A machine that pulls all thermal energy out of a refrigerated space: This violates the second law of thermodynamics. This is because the second law of thermodynamics states that no heat engine can have an efficiency of 100 percent, and no heat transfer can occur from a colder to a warmer object without external work being done.
2. A machine that can pull 1000J of heat out of a refrigerated space and into a warmer space without external work: This violates the second law of thermodynamics. The second law of thermodynamics states that no heat transfer can occur from a colder to a warmer object without external work being done.
3. A machine that can turn 1000J of heat directly into 1000J of electricity: This does not violate any of the laws of thermodynamics.
4. A machine that can create 1000J of heat from 100J of electricity: This does not violate any of the laws of thermodynamics.
5. A machine that can pull 1000J of heat out of a refrigerated space and put 1500J of heat into a warmer space if it uses 500J of external work: This does not violate any of the laws of thermodynamics.
a) Option 2 is correct answer.
b) Option 2 is correct answer.
c) Option 4 is correct answer.
d) Option 4 is correct answer
e) Option 4 is correct answer.
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Bonnie has 16 coins in her pocket worth $1.50. What are two different combinations of coins she could have in her pocket?
If the distance between two objects is cut in half, what happens to the
gravitational force between them?
A. It decreases to 1/2 its original magnitude.
B. It decreases to 1/4 its original magnitude.
O
C. It increases to 4 times its original magnitude.
D. It increases to 2 times its original magnitude.
Can you please help me I’m confused with the negatives
Given that the mass of the ball, m = 5 kg
The initial velocity of the ball is
\(V_o=6\text{ m/s}\)The final velocity of the ball is
\(V_f=4\text{ m/s}\)We have to find the work done.
The work done can be calculated by the formula,
\(\begin{gathered} W=\text{ change in kinetic energy} \\ =\frac{1}{2}m(V_f)^2-\frac{1}{2}m(V_o)^2 \end{gathered}\)Substituting the values, the work done will be
\(\begin{gathered} W=\frac{1}{2}\times5\times(4)^2-\frac{1}{2}\times5\times(6)^2 \\ =40-90 \\ =-50\text{ J} \end{gathered}\)Thus, the work done will be -50 J
Consider the circuit in Figure 5 with e(t) = 12sin(120pit) V. When S1 and S2 are
open, i leads e by 30°. When SI is closed and S2 is open, i lags e by 30°. When S1 and S2 are closed, i has an amplitude 0.5A. What are R, L, and C?
Based on the information, it should be noted that the resistance R is 0.5 Ω.
How to calculate the resistanceWhen S1 and S2 are open, i leads e by 30°. In this case, the circuit consists of only the inductor (L) and the capacitor (C) in series. Therefore, the impedance of the circuit can be written as:
Z = jωL - 1/(jωC)
Since i leads e by 30°, we can express the phasor relationship as:
I = k * e^(j(ωt + θ))
Z = jωL - 1/(jωC) = j(120π)L - 1/(j(120π)C)
Re(Z) = 0
By equating the real parts, we get:
0 = 0 - 1/(120πC)
Let's assume that there is a resistance (R) in series with the inductor and capacitor. The impedance equation becomes:
Z = R + jωL - 1/(jωC)
Z = R + jωL
Im(Z) = ωL > 0
Substituting the angular frequency and rearranging the inequality, we have:
120πL > 0
L > 0
This condition implies that the inductance L must be greater than zero.
When S1 and S2 are closed, i has an amplitude of 0.5 A. In this case, the impedance is:
Z = R + jωL - 1/(jωC)
Since the amplitude of i is given as 0.5 A, we can express the phasor relationship as:
I = 0.5 * e^(j(ωt + θ))
By substituting this phasor relationship into the impedance equation, we can determine the value of R. The real part of the impedance must be equal to R:
Re(Z) = R
Since the amplitude of i is 0.5 A, the real part of the impedance must be equal to 0.5 A: 0.5 = R
Therefore, the resistance R is 0.5 Ω.
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A car moves from rest with an acceleration of 0.2ms
Find its velocity when it has moved a
distance of 50m
From the problem we notice that the question
does not involver. Therefore, the required equation
is)
Explanation:
Given:
Δx = 50 m
v₀ = 0 m/s
a = 0.2 m/s²
Find: v
The problem does not involve time. Therefore, the required equation is:
v² = v₀² + 2aΔx
Plug in values and solve:
v² = (0 m/s)² + 2 (0.2 m/s²) (50 m)
v = 4.47 m/s
The velocity of the car when it has moved a distance of 50 meters is approximately 4.47 m/s.
To find the velocity of the car when it has moved a distance of 50 meters, we can use the following equation of motion:
v² = u² + 2as
Where:
v = final velocity
u = initial velocity (which is 0 in this case as the car starts from rest)
a = acceleration
s = distance traveled
Plugging in the values into the equation:
v² = 0² + 2(0.2)(50)
v² = 0 + 20
v² = 20
Taking the square root of both sides:
v = √20
v = 4.47 m/s
Therefore, the velocity of the car when it has moved a distance of 50 meters is approximately 4.47 m/s.
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Rhea is driving north in a straight line. After driving for 2.4 kilometers, she turns west, and drives for 3.1 km. At the end of her drive, what is the magnitude of her displacement vector? To find the magnitude of a resultant vector, use the Pythagorean theorem: a² + b² = c² A) 3.9 km B) 5.5 km (this one is incorrect) C) 2.8 km D) 2.3 km
Option A) 3.9 km is the correct answer. the magnitude of Rhea's displacement vector is approximately 3.92 km.
In order to find out the magnitude of Rhea's displacement vector, we have to add up all of the displacement vectors.
Then we can use the Pythagorean theorem to calculate the magnitude of the resultant vector.
Since Rhea is first driving north for 2.4 km and then west for 3.1 km, we can represent her displacement vectors as follows: Δx = 0 km and Δy = 2.4 km for the first vector, and Δx = -3.1 km and Δy = 0 km for the second vector.
We can then add these vectors together by adding their components: Δx = 0 km + (-3.1 km) = -3.1 km and Δy = 2.4 km + 0 km = 2.4 km.
This gives us a resultant vector of -3.1 km east and 2.4 km north.
Using the Pythagorean theorem, we can find the magnitude of this vector: \(\sqrt{(\(-3.1 km)^{2} + (2.4 km)^{2} ) } = \sqrt{(9.61 + 5.76) km^{2} } = \sqrt{15.37 km^{2} } \approx 3.92 km.\)
Therefore, the magnitude of Rhea's displacement vector is approximately 3.92 km.
Therefore, option A) 3.9 km is the correct answer.
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A continental polar air mass forms in
a. the Pacific Ocean.
b. northern Canada.
c.
the Gulf of Mexico.
the desert Southwest.
d.
Please select the best answer from the choices provided
А
B
ОООО
С
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my uq xbbbnxnjjxjxusjhhhwhhhnn he c x. Yes suhsjjdhhehy yes eirui
M I was going ask m
Iqijjm.ndjbh
Answer:
B. Northern Canada
Explanation:
A continental polar air mass can form over the land during the winter months. In the Northern Hemisphere, it originates in northern Canada or Alaska. As it moves southward, it brings dry weather conditions to the United States. Temperature and humidity levels are both low. Hope this helps :)
PLEASE HELP! Thank you!
Chloe and Sarah are driving bumper cars. Chloe, who is traveling west at 3.9 m/s, is behind Sarah, who is traveling west at 1.6 m/s. The total mass of Chloe’s car is 163 kg, and total mass of Sarah’s car is 179 kg. Immediately after Chloe collides with Sarah, Chloe’s velocity reduces to 0.95 m/s west. What is Sarah’s velocity immediately after the collision?
A. 5.2 m/s
B. 4.0 m/s
C. 4.3 m/s
D. 4.6 m/s
Sarah’s velocity immediately after the collision is 4.3 m/s west.
option C is the correct answer.
What is Sarah’s velocity immediately after the collision?Sarah’s velocity immediately after the collision is calculated by applying the principle of conservation of linear momentum as follows;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is the mass of Sarah's carm₂ is the mass of Chloe's caru₁ is the initial velocity of Sarahu₂ is the initial velocity of Chloev₁ is the final velocity of Sarahv₂ is the final velocity of ChloeSarah’s velocity immediately after the collision is calculated as;
179 (1.6) + 163(3.9) = 179v₁ + 163(0.9)
922.1 = 179v₁ + 146.7
179v₁ = 775.4
v₁ = 4.3 m/s
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Complete the Aristotle quote:
"States of character arise from ______________."
A state of character arises from the repetition of similar activities
Aristotle was a renowned scientist and philosopher. He has made significant contributions to society. He is renowned for his quotable sayings as well. Because of the correlation between the states of character and the distinctions between them, the behaviors we display must be of a specific type. States of character: The traits that "allow us to stand well or poorly in relation to the passions." Because: We are not commended and criticized only for having the ability to feel pleasure, grief, etc., virtues are not capacities.
Here in this quote, similar behaviors give birth to similar states of character
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Krish has a sample of matter. It is clear and smells sour. The sample is also thick but it flows when poured.
Answer:
It is a liquid because it flows.
Explanation:
because liquids dont have to be a certain color they are liquid as long as they flow
Answer:
It is liquid because it flows
Explanation:
Given vector A with magnitude 2N and vector B magnitude 4N, what are the minimum and maximum magnitudes of A+B?
-- If A and B are pointing in exactly opposite directions, then their sum A+B is the minimum possible value. A+B = 2 N in the same direction as B.
-- If A and B are pointing in exactly the same direction, then their sum A+B is the maximum possible value. A+B = 6 N in that same direction.
can anyone write for me all the equation of linear motion
All the equations of motion are as follows, Displacement (s) equation, Final velocity (v) equation, Average velocity (v_avg) equation, Displacement (s) equation with average velocity, and Displacement (s) equation.
Equations of MotionIn terms of its motion as a function of time, equations of motion define how a physical system behaves. In more detail, the equations of motion define how a physical system behaves as a collection of mathematical functions expressed in terms of dynamic variables.
s = ut + (1/2)at^2v = u + atv_avg = (u + v) / 2s = v_avg * ts = (u + v) / 2 * tv^2 = u^2 + 2asIn conclusion, equations of motion define how a physical system behaves in terms of how its motion changes over time.
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37 POINTS PLEASE HELP MEE. The distance from A to B consists of an uphill section and a downhill section. A cyclist rides from A to B and then returns to A for a period of 4 hours and 30 minutes. When traveling as well as when returning the uphill speed is 15 km / h and the speed at the downhill is 20 km / h. Do you calculate the length of the distance from A to B?
The distance from A to B is 39.375 Km.
What is the total distance travelled by the cyclist?
The total distance travelled by the cyclist is given by the formula below:
Total distance = average speed * total time takenTotal distance = (15 + 20)/2 * 4.5
Total distance = 78.75 Km
Thus, distance from A to B = 78.75/2 = 39.375 Km
In conclusion, the total distance travelled is determined from the average speed and total time taken.
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On your drive home from school, you travel 1200 m in 80 s, then 400 min 20 s.
What is your average speed in m/s?
Average speed = Total distance/total time taken
\( = \frac{1200 + 400}{80 + 20} \)
\( = \frac{1600}{100} \)
\( = \frac{16}{1} \)
\( = 16 \: ms {}^{ - 1} \)
The velocity time graph of an object mass 50 g is shown in figure study graph and answer
1)calculate force acting on object in time interval 0-3 seconds
2)calculate the force acting on the object in the time interval 6-10 seconds
3)Is there any time interval in which no force acts on object.Justify
1) The force acting on the object during the time interval 0-3 seconds is 1/3 N.
2) The force acting on the object during the time interval 6-10 seconds is -0.5 N.
3) There is no time interval in which no force acts on the object.
(i) Force acting on the object in time interval 0-3 seconds. Force acting on the object is equal to the product of its mass and acceleration, i.e.,F = ma.
In the given velocity-time graph, the acceleration of the object can be determined by determining the slope of the velocity-time graph from 0 to 3 seconds.
Slope = (change in velocity) / (change in time)= (20-0) / (3-0) = 20/3 m/s^2
Acceleration, a = slope= 20/3 m/s^2
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × 20/3= 1/3 N.
Therefore, the force acting on the object during the time interval 0-3 seconds is 1/3 N.
(ii) Force acting on the object in time interval 6-10 seconds. Similar to the first question, the force acting on the object in time interval 6-10 seconds can be determined by determining the acceleration of the object during this time interval.
The slope of the velocity-time graph from 6 seconds to 10 seconds can be determined as follows:
Slope = (change in velocity) / (change in time)= (-20-20) / (10-6) = -40/4= -10 m/s^2 (negative sign indicates that the object is decelerating)
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × (-10)= -0.5 N.
Therefore, the force acting on the object during the time interval 6-10 seconds is -0.5 N.
(iii) Time interval in which no force acts on the object. There is no time interval in which no force acts on the object. This is because, as per Newton's first law of motion, an object will continue to remain in a state of rest or uniform motion along a straight line unless acted upon by an external unbalanced force.In other words, if the object is moving with a constant velocity, there must be a force acting on the object to maintain its motion.
Therefore, there is no time interval in which no force acts on the object.
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Which diagram shows magnets that will attract each other? 2 bar magnets side by side with their long axes vertical, both red S on top and blue N on bottom. 2 bar magnets top to bottom with their long axes vertical, the top one with red S on top and blue N on bottom and the bottom magnet with blue N on top and red S on bottom. 2 bar magnets top to bottom with their long axes vertical, the top one with blue N on top and red S on bottom and the bottom magnet with red S on top and blue N on bottom. 2 bar magnets top to bottom with their long axes vertical, the top one with red S on top and blue N on bottom and the bottom magnet with red S on top and blue N on bottom.
2 bar magnets top to bottom with their long axes vertical, the top one with red S on top and blue N on bottom and the bottom magnet with red S on top and blue N on bottom. this diagram shows magnets that will attract each other. Hence option D is correct.
What is Magnet ?A permanent magnet is an item constructed of magnetised material that generates its own persistent magnetic field. A refrigerator magnet, for example, is commonly used to hold notes on a refrigerator door. Ferromagnetic (or ferrimagnetic) materials are those that can be magnetised and are strongly attracted to a magnet. These include the elements iron, nickel, and cobalt, as well as their alloys, some rare-earth metal alloys, and naturally occurring minerals such as lodestone. Although ferromagnetic (and ferrimagnetic) materials are the only ones that are strongly attracted to a magnet and are widely thought to be magnetic, all other substances respond weakly to a magnetic field via one of many different forms of magnetism.
Hence option D is correct.
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A sample of an unknown material appears to weigh 300N in air and 200N when immersed in alcohol of density 700kg/m^3 . What is the volume and density of the material
Answer:
the volume of the material is 0.0145 m^3 and its density is 20690.3 kg/m^3.
Explanation:
To solve the problem, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Let's first find the weight of the unknown material in air:
W_air = 300 N
Next, let's find the weight of the unknown material in alcohol:
W_alcohol = 200 N
We can find the buoyant force acting on the material by subtracting the weight in alcohol from the weight in air:
F_buoyant = W_air - W_alcohol = 300 N - 200 N = 100 N
According to Archimedes' principle, this buoyant force is equal to the weight of the alcohol displaced by the material:
F_buoyant = ρ_alcohol * V * g
where ρ_alcohol is the density of the alcohol, V is the volume of the material, and g is the acceleration due to gravity.
Substituting the values we know:
100 N = 700 kg/m^3 * V * 9.81 m/s^2
Solving for V:
V = 0.0145 m^3
Finally, we can find the density of the material by dividing its weight in air by its volume:
ρ_material = W_air / V = 300 N / 0.0145 m^3 = 20690.3 kg/m^3
Therefore, the volume of the material is 0.0145 m^3 and its density is 20690.3 kg/m^3.
6. A picture of weight, w is hanging from a steel nail as shown in the figure below. The nail has a diameter of 1.50 mm and an original length, Lo = 5.0 mm. Useful Information: The shear modulus, G for steel is 80 x 10° N.m². (a) (b) (c) 1.50 mm 3 Ax = 1.80 μm W Lo = 5.00 mm M What kind of deformation occurs in this case? How are stress and strain in this deformation related to each other? [3] When the picture is hung from the nail, the head of the nail displaces vertically downwards by an amount Ax = 1.80 µm. Find the mass of the picture. Neglect the weight of the nail. [6] What angle does the nail make with the horizontal after the picture is hung from it? [2]
The mass of the picture is approximately 5.19 kilograms.
How to solve for the problemThe deformation in this case is called shear deformation, a type of deformation that occurs when parallel internal surfaces slide past one another. It is caused by shear stress in the structure. The shear stress (τ) is the force (F) applied divided by the cross-sectional area (A) of the nail. The shear strain (γ) is the displacement (Δx) divided by the original length (L0).
The relationship between shear stress and shear strain is given by the shear modulus (G) in the formula:
τ = G * γ
To find the weight of the picture, we need to calculate the shear stress first:
The cross-sectional area A of the nail is given by the formula for the area of a circle:
A = πr² = π(d/2)² = π(0.0015 m / 2)² = 1.767 x 10^-6 m².
The shear strain γ is given by:
γ = Δx / L0 = (1.80 x 10^-6 m) / (5 x 10^-3 m) = 0.36.
The shear stress τ can now be calculated by rearranging the formula:
τ = G * γ
=> τ = (80 x 10^9 N/m²) * 0.36 = 28.8 x 10^9 N/m²
The force F on the nail is equal to the weight w of the picture, and it can be calculated from the shear stress:
τ = F / A
=> F = τ * A = (28.8 x 10^9 N/m²) * (1.767 x 10^-6 m²) = 50.89 N.
Since weight w = m * g, where m is mass and g is the acceleration due to gravity (approximately 9.81 m/s²), we can find the mass m:
m = w / g = (50.89 N) / (9.81 m/s²) = 5.19 kg.
So, the mass of the picture is approximately 5.19 kilograms.
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A ball of mass 0.500 kg is carefully balanced on a shelf that is 2.70 m above the ground. What is its gravitational potential energy
Answer:
The gravitational potential energy of the ball is 13.23 J.
Explanation:
Given;
mass of the ball, m = 0.5 kg
height of the shelf, h = 2.7 m
The gravitational potential energy is given by;
P.E = mgh
where;
m is mass of the ball
g is acceleration due to gravity = 9.8 m/s²
h is height of the ball
Substitute the givens and solve for gravitational potential energy;
PE = (0.5 x 9.8 x 2.7)
P.E = 13.23 J
Therefore, the gravitational potential energy of the ball is 13.23 J.
The half-life of a radioactive isotope is 210 d. How many days would it take for the decay rate of a sample of this isotope to fall to 0.58 of its initial rate?
It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.
1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.
2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.
3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.
4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.
5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.
6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".
7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).
8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).
9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.
10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.
11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).
12. Evaluating the expression, we find: t ≈ 546.
13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.
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