Answer:
According to "http://ww2010.atmos.uiuc.edu" Diffraction is the slight bending of light as it passes around the edge of an object.
Some examples of Light Defraction would be..
-CD reflecting rainbow colours
-Sun appears red during sunset
-From the shadow of an object
The law of conservation of angular momentum states that if no external force acts on an object, then its angular momentum does not change. true or false
Answer:
the answer is false.
Explanation:
i took the test and it is false trust me!!!!!!!!!
the mass of the velociraptor and cage together is 175 kg. What is the gravitational potential energy added when when the velociraptor and cage is lifted from the ground to a height of 9 m?
The gravitational potential energy added when the velociraptor and cage is lifted from the ground to a height of 9 m is approximately 15,998.95 joules.
What is Potential Energy?
Potential energy is a form of energy that is stored in an object due to its position or configuration in a system. It is the energy that an object has the potential to possess, or the ability to do work, as a result of its position or state.
The gravitational potential energy (GPE) added when the velociraptor and cage is lifted from the ground to a height of 9 m can be calculated using the formula:
GPE = mgh
Where m is the mass of the velociraptor and cage, g is the acceleration due to gravity (approximately 9.81 m/\(s^{2}\)), and h is the height lifted.
Given that the mass of the velociraptor and cage together is 175 kg, and the height lifted is 9 m, we can substitute these values into the formula:
GPE = mgh
GPE = (175 kg) x (9.81 m/\(s^{2}\)) x (9 m)
GPE = 15,998.95 J (joules)
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In a double-slit interference experiment, assuming that the distance from the location of the double slit to the location of the screen remains fixed, explain what happens to the double-slit interference pattern that appears on the screen if we:
a. increase the wavelength of the laser illuminating a particular, fixed double-slit.
b. decrease the separation of the double-slit (i.e., replace the original double slit witha smaller-separation double-slit) while keeping the illumination unchanged.
Two blocks are attached by a string as shown. The blocks are released from rest and
allowed to move freely. The sloped ramp angle is θ = 30⁰. Find the coefficient of friction
on the blocks (assume they have the same coefficient), assuming the blocks have the
same mass, and given that the blocks travel a distance of 0.50 m in a time of 0.935 s.
The coefficient of friction between the two blocks is 0.194.
The problem involves finding the coefficient of friction between two blocks of equal mass attached by a string that moves over a sloped ramp with an angle of 30 degrees. The blocks start from rest and are allowed to move freely. The distance traveled by the blocks is 0.50 m, and the time taken to travel this distance is 0.935 s. To solve the problem, we need to consider the forces acting on the system of blocks. The forces acting on the blocks are the gravitational force, the tension in the string, and the frictional force. As the blocks are moving up the ramp, the force of gravity is pulling them down. The tension in the string is pulling the blocks up the ramp. The frictional force is opposing the motion of the blocks and is acting in the opposite direction to the tension in the string.
To determine the coefficient of friction, we can use the equations of motion to find the acceleration of the blocks. Once we have the acceleration, we can use Newton's Second Law to find the net force acting on the blocks. We can then use the force of friction to find the coefficient of friction. Using the equations of motion, we can find the acceleration of the blocks:
a = 2d/t^2
where d is the distance traveled by the blocks and t is the time taken to travel the distance. Plugging in the given values, we get:
a = 2(0.50 m)/(0.935 s)^2 = 1.15 m/s^2
Next, we can use Newton's Second Law to find the net force acting on the blocks:
ΣF = ma
where ΣF is the sum of the forces acting on the blocks. Plugging in the known forces, we get:
T - mg sin θ - μmg cos θ = ma
where T is the tension in the string, m is the mass of the blocks, g is the acceleration due to gravity, θ is the angle of the ramp, and μ is the coefficient of friction.
We can simplify this equation by substituting mg sin θ for the component of the weight of the blocks that is acting down the ramp and mg cos θ for the component of the weight that is acting perpendicular to the ramp:
T - mg sin θ - μmg cos θ = ma
T - mg(1/2) - μmg(√3/2) = ma
We can also use the equation for the tension in the string:
T = 2mg sin θ
Substituting this into the equation for net force, we get:
2mg sin θ - mg(1/2) - μmg(√3/2) = ma
Simplifying and solving for μ, we get:
μ = (2gsinθ - a)/(2gcosθ)
Substituting the given values, we get:
μ = (2(9.81 m/s^2)sin 30° - 1.15 m/s^2)/(2(9.81 m/s^2)cos 30°) = 0.194
Therefore, the coefficient of friction between the two blocks is 0.194.
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Two equal magnitude electric charges are separated by a distance d. The electric potential at the midpoint between these two charges is zero. A student considering this situation says: "The electric field at the midpoint between the two charges will be zero also, since the two charges are opposite in sign, so the fields will equal but opposite, and add to zero." There is something wrong with the student's statement. Identify any problem(s) and explain how to correct it/them.
Answer:
The charges under study are of the same sign
The calculation of the electric field for each charge separately, there is no relationship between the charges
Explanation:
Let's start by writing the equation for the electric field
E = k q / r²
where q is the charge under analysis and r the distance from this charge to a positive test charge.
When analyzing the statement the student has some problems.
* The charges under study are of the same sign, it does not matter if positive or negative.
* The calculation of the electric field for each charge separately, there is no relationship between the charges for the calculation of the electric field.
* What is added is the interaction of the electric field with the positive test charge, in this case each field has the opposite direction to the other, so the vector sum gives zero
What are examples of water on Earth that are part of the water cycle
Find the acceleration due to gravity on planet Fergie which has a mass of 6.23 * 10^23 kg and a radius of 5.79* 10^7 m
Answer:
The acceleration due to gravity on the planet Fergie is 0.0123 m/s^2.
Explanation:
We want to find the acceleration due to gravity on the planet Fregie. Let it be g m/s^2.
Now, the acceleration due to gravity is defined through the following equation:
\(mg = GMm/R^2\)
where m is the mass of an object on the surface of the planet, M is the mass of the planet, R is the radius of the planet, and G is the universal Gravitational constant.
Subsituting values for M = 6.23*10^23, R = 5.79*10^7, G = 6.67*10^(-11), we get
g = 0.0123 m/s^2.
Thus the acceleration due to gravity on the planet Fergie is 0.0123 m/s^2.
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Question 1
In basketball, how many points is a free throw worth?
A. Zero a free throw determines possession only
B. One
C. Two
D. Three
Which is the best example of reusing?
repairing a stove instead of buying a new one
wearing a pair of pants made from cotton
buying a toy packaged in paper instead of plastic
placing a glass bottle in the recycling bin
Answer:
ITS A repairing a stove instead of buying a new one not D
Explanation:
i dont know why the dude above me has 5 stars its wrong and I got proof ;) for the future edge ppl
Answer:
A) repairing a stove instead of buying a new one
Explanation:
GOT IT RIGHT :DDD
A uniform electric field is directed upward and has a magnitude of 24 N/C. A charge of -6 C is placed in this
field.
The direction of the force on the charge placed in the electric field is upward.
True or False
The statement" The direction of the force on the charge placed in the electric field is upward" is false because the direction of the force on a negative charge (-6 C) placed in an upward-directed uniform electric field of magnitude 24 N/C would be downward.
The direction of the force on a charged particle placed in an electric field is determined by the charge of the particle and the direction of the electric field. In this case, a charge of -6 C is placed in an electric field directed upward with a magnitude of 24 N/C.
The force on a charged particle in an electric field can be calculated using the formula:
F = q * E
Where F is the force, q is the charge of the particle, and E is the electric field.
Since the charge q in this case is negative (-6 C) and the electric field E is directed upward, we can substitute the values into the formula:
F = (-6 C) * (24 N/C)
F = -144 N
The negative sign in the force value indicates that the force is in the opposite direction to the electric field. Therefore, the force on the charge placed in the electric field is downward, not upward.
The force on a negative charge is always opposite to the direction of the electric field. This is because negative charges experience an attractive force towards positive charges, and electric fields are directed from positive charges to negative charges.
Therefore, the statement "The direction of the force on the charge placed in the electric field is upward." is false.
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Two equal resistors of resistance x ohm each are connected in parallel, and the resultant combination is connected in series with another resistor of resistance x ohm. Calculate the effective resistance of the combination
The effective resistance of the combination when two resistors are connected in series is 2+x²/x.
The resistance is a quantity that offers obstruction to the current flow and the unit of resistance is the ohm. The resistors are connected in series and parallel. The effective resistance of series connections, R(eff) = R₁+R₂+...+Rₙ. The effective resistance of parallel connections are, 1/R(eff) = 1/R₁+1/R₂+.....+1/Rₙ.
From the given,
the parallel resistance of two-ohm x, the effective resistance,
1/R(eff) = 1/x+1/x = 2/x.
The effective resistance in a series combination of resistors, 2/x, and x are,
R(eff) = R₁+R₂ = 2/x + x = 2+x²/x.
Hence, the effective resistance is 2+x²/x.
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Two blocks, M = 14.2 kg and m = 4.73 kg, are connected via a massless rope. They are being pushed up a frictionless hill, with a slope of 15.80, with a constant force in the direction of the incline, such that there is a total acceleration of 2.53 m/s2 for the system
Slope is rise over run, meaning the ratio of the change in height to the change in horizontal distance. So a slope of 15.80 corresponds to an angle of ascension θ of
tan(θ) = 15.80 → θ ≈ 86.38°
The order of the blocks (i.e. whether the large one is pulling the smaller one up or vice versa) does not matter, since friction is not a concern. So if we take the connected blocks as a single mass, by Newton's law we have a net force acting parallel to the incline of
∑ F = P - (M + m) g sin(θ) = (M + m) a
(see the attached free body diagram)
where
P = magnitude of the push
g = 9.80 m/s²
a = 2.53 m/s²
and M and m are the given masses.
Then the system requires a push of
P = (M + m) (a + g sin(θ))
P = (14.2 kg + 4.73 kg) (2.53 m/s² + (9.80 m/s²) sin(86.38°))
P ≈ 233 N
If you have to find the tension in the rope, consider the free body diagram for one of the blocks. By Newton's second law, the net parallel force acting on, say, the larger block (if it's being pulled by the rope) is
∑ F = T - M g sin(θ) = M a
where
T = tension in the rope
Then
T = M (a + g sin(θ))
T = (14.2 kg) (2.53 m/s² + (9.80 m/s²) sin(86.38°))
T ≈ 175 N
A meter stick has only two forces acting on it, of equal sizes at the ends that are in opposite directions. (I have magically turned gravity Off.) Is the stick in equilibrium? Explain your answer.
Answer:
Explanation:
Equilibrium is a state in which the algebraic sum of all forces acting on an object is zero. Thus the object has no force acting on it. The types are: stable, unstable and neutral equilibrium. While a torque is a turning force which are equal but acts in an opposite direction. When applied to on object, it constitute a turning effect. Example is the force applied on a tap, handle wheel of a car etc.
In the given question, the condition stated shows that the stick would experience a torque, thus not in equilibrium. Since the forces at its ends are in opposite directions, then it continues to rotate about its axis.
An object has a mass of 450g. What is the gravitational force of the object by earth?
Answer:
4.41N or 4.5N (check explanation)
Explanation:
450g = 0.45kg
F = ma
Using 10m/s² = 10(0.45) = 4.5N
Using 9.8m/s² = 9.8(0.45) = 4.41N
Can you use an adjustable gas lift leg (Similar to office chair) on the moon?
a farmer grows a bushel of wheat and sells it for $1. the miller turns the wheat into flour and then sells the flour to a baker for $3. The baker uses the flour to make bread and sells the bread to an engineer for $6. the engineer eats the bread. What is the value added by each person ? what is the bread's contribution to GDP ?
The value added by the baker is $3. The bread's contribution to GDP is the final sale price of the bread, which is $6
In this scenario, each person involved in the production and sale of the bread adds value to the final product. The concept of value added refers to the increase in the market value of a product at each stage of production.
The farmer grows the wheat and sells it for $1. The value added by the farmer is $1.
The miller processes the wheat into flour, increasing its value. The miller sells the flour to the baker for $3, so the value added by the miller is $3 - $1 = $2.
The baker uses the flour to make bread, further adding value to the product. The baker sells the bread to the engineer for $6, so the value added by the baker is $6 - $3 = $3.
The engineer consumes the bread, but since no further economic value is added, there is no additional value added by the engineer.
The bread's contribution to GDP (Gross Domestic Product) is the final sale price of the bread, which is $6. GDP measures the total value of all goods and services produced within a country's borders, and the sale of the bread represents the final output of the production chain.
Overall, the value added at each stage contributes to the final price of the bread, and the final sale price of the bread represents its contribution to GDP.
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Part 3 Waves on a string-with a loose end The reflected
wave interferes with the original wave and creates standing wave composed of
nodes and antinodes if the frequency is just right: Instead of a node an antinode
will always exist at the loose end: (This happens because the phase of the wave
is not inverted upon reflection from loose end and therefore always constructively
interfere at that position:) Draw and measure the frequency of the 1st harmonic
(node near driver end followed by an antinode on loose end) Settings: amplitude:
0.05 cm tension: high damping: none turn on: Loose End What fraction of a
wavelength is this? Hz Click Restart' to observe the standing wave. 2. Predict the
frequencies of several higher harmonics: Use the wave simulator to test each of
your calculated harmonics Draw and label the standing waves for each of the
harmonics you discovered: Divide each higher harmonic by the first harmonic:
Are the higher harmonics even-number or odd-number multiples of the first
harmonic?
The first harmonic of the standing wave on a string with a loose end represents half a wavelength.
The fraction of a wavelength represented by the first harmonic is 1/2.
The higher harmonics of a standing wave on a string with a loose end are odd-number multiples of the first harmonic.
1. The first harmonic of a standing wave on a string with a loose end occurs when there is a node near the driver end and an antinode at the loose end. To measure the frequency of the first harmonic, we need to determine the fraction of a wavelength represented by this standing wave.
The first harmonic of the standing wave on a string with a loose end represents half a wavelength.
The first harmonic of a standing wave on a string with a loose end consists of a node near the driver end and an antinode at the loose end. This configuration creates the simplest standing wave pattern.
In a standing wave, a node is a point where the amplitude of the wave is always zero, representing a point of minimum displacement. An antinode, on the other hand, is a point of maximum displacement, where the amplitude is at its highest.
Since the loose end does not invert the phase of the wave upon reflection, the reflected wave and the original wave constructively interfere at the loose end, resulting in an antinode.
In the first harmonic, there is exactly half a wavelength between the node near the driver end and the antinode at the loose end.
Therefore, the fraction of a wavelength represented by the first harmonic is 1/2.
2. To predict the frequencies of higher harmonics, we can use the relationship that the frequency of each harmonic is a multiple of the frequency of the first harmonic. The higher harmonics can be calculated as follows:
Second Harmonic: The second harmonic consists of two nodes and one additional antinode compared to the first harmonic. The fraction of a wavelength for the second harmonic is 1/2 * 2 = 1. Thus, the second harmonic has a frequency that is twice that of the first harmonic.
Third Harmonic: The third harmonic consists of three nodes and two additional antinodes compared to the first harmonic. The fraction of a wavelength for the third harmonic is 1/2 * 3 = 1.5. Thus, the third harmonic has a frequency that is three times that of the first harmonic.
Fourth Harmonic: The fourth harmonic consists of four nodes and three additional antinodes compared to the first harmonic. The fraction of a wavelength for the fourth harmonic is 1/2 * 4 = 2. Thus, the fourth harmonic has a frequency that is four times that of the first harmonic.
In general, the higher harmonics of a standing wave on a string with a loose end are odd-number multiples of the first harmonic.
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An 8.0 Kg mass is placed at = 3 where should a 10 Kg mass be placed along the − so that the center of mass will be located ay = 4.5?
Answer:
Therefore, the 10 kg mass should be placed at x = 5.7 m along the x-axis to achieve a center of mass located at y = 4.5 m.
Explanation:
To find the position along the x-axis where a 10 kg mass should be placed such that the center of mass is located at y = 4.5, we can use the formula for the center of mass:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
Here, m1 and x1 represent the mass and position of the 8 kg mass, respectively. m2 is the mass of the 10 kg mass, and we need to find x2, its position.
Given:
m1 = 8 kg
x1 = 3 m
x_cm = unknown (to be found)
m2 = 10 kg
y_cm = 4.5 m
Since the center of mass is at y = 4.5, we only need to consider the y-coordinate when calculating the center of mass position along the x-axis.
To solve for x2, we can rearrange the formula as follows:
x2 = (x_cm * (m1 + m2) - m1 * x1) / m2
Substituting the given values:
x2 = (x_cm * (8 kg + 10 kg) - 8 kg * 3 m) / 10 kg
Simplifying:
x2 = (x_cm * 18 kg - 24 kg*m) / 10 kg
Now, we can set the y-coordinate of the center of mass equal to 4.5 m and solve for x_cm:
4.5 m = (8 kg * 3 m + 10 kg * x2) / (8 kg + 10 kg)
Simplifying:
4.5 m = (24 kg + 10 kg * x2) / 18 kg
Multiplying both sides by 18 kg:
81 kg*m = 24 kg + 10 kg * x2
Subtracting 24 kg from both sides:
10 kg * x2 = 81 kg*m - 24 kg
Dividing both sides by 10 kg:
x2 = (81 kg*m - 24 kg) / 10 kg
Simplifying:
x2 = 8.1 m - 2.4 m
x2 = 5.7 m
(brainlest?) ples:(
Answer:
the 10 kg mass should be placed at x = -2.4 m to achieve a center of mass at y = 4.5 m.
Explanation:
To find the position along the x-axis where the 10 kg mass should be placed so that the center of mass is located at y = 4.5, we can use the principle of the center of mass.
The center of mass of a system is given by the equation:
x_cm = (m1x1 + m2x2) / (m1 + m2),
where x_cm is the x-coordinate of the center of mass, m1 and m2 are the masses, and x1 and x2 are the positions along the x-axis.
Given:
m1 = 8 kg,
x1 = 3 m,
m2 = 10 kg,
y_cm = 4.5 m.
To solve for x2, we need to find the x-coordinate of the center of mass (x_cm) by using the y-coordinate:
y_cm = (m1y1 + m2y2) / (m1 + m2),
where y1 and y2 are the positions along the y-axis.
Rearranging the equation and substituting the given values:
4.5 = (83 + 10y2) / (8 + 10).
Simplifying the equation:
4.5 = (24 + 10*y2) / 18.
Multiplying both sides by 18:
81 = 24 + 10*y2.
Rearranging the equation:
10*y2 = 81 - 24,
10*y2 = 57.
Dividing both sides by 10:
y2 = 5.7.
Therefore, the y-coordinate of the 10 kg mass should be 5.7 m.
To find the x-coordinate of the 10 kg mass, we can use the equation for the center of mass:
x_cm = (m1x1 + m2x2) / (m1 + m2).
Substituting the given values:
x_cm = (83 + 10x2) / (8 + 10).
Since the center of mass is at x_cm = 0 (the origin), we can solve for x2:
0 = (83 + 10x2) / (8 + 10).
Rearranging the equation:
83 + 10x2 = 0.
24 + 10*x2 = 0.
10*x2 = -24.
Dividing both sides by 10:
x2 = -2.4.
Assume you push a 20 kg child in a little red wagon with a force of 100 N. However, the dirt and rocks below the wheels
create a frictional force of 25 N. What is the acceleration on the wagon and child?
A. 1.25 m/s2
B.3.75 m/s2
C. 5 m/s2
D. 0.2 m/s2
Answer:
a
Explanation:
Which of the following is the most appropriate description of an electric current?
the fastest tennis service by a man is 246,2 km.hr-1 by Andy Roddick of the United States of America during a match in London in 2004. Calculate the ball's momentum if it has a mass of 58 g?
Answer:
Approximately \(3.967\; {\rm kg\cdot m\cdot s^{-1}}\).
Explanation:
Convert velocity to the standard units (meters per second):
\(\begin{aligned}v &= 246.2 \; {\rm km \cdot h^{-1}} \\ &= 246.2 \; {\rm km \cdot h^{-1}}\times \frac{1\; {\rm h}}{3600\; {\rm s}} \times \frac{1000\; {\rm m}}{1\; {\rm km}} \\ &\approx 68.389\; {\rm m\cdot s^{-1}}\end{aligned}\).
Convert mass to standard units (kilograms):
\(\begin{aligned} m &= 58\; {\rm g} \\ &= 58\; {\rm g} \times\frac{1\; {\rm kg}}{1000\; {\rm g}}\\ &= 0.058\; {\rm kg}\end{aligned}\).
When an object of mass \(m\) travels at a velocity of \(v\), momentum of that object would be \(p = m\, v\). In standard units, the momentum of this tennis ball would be:
\(\begin{aligned}p &= m\, v \\ &\approx (0.058\; {\rm kg})\, (68.389\; {\rm m\cdot s^{-1}}) \\ &\approx 3.967\; {\rm kg \cdot m\cdot s^{-1}}\end{aligned}\).
Was the Big Bang a loud explosion? Why?
Answer:
bc it was a universal explosion and It started the future
Explanation:
FACTS
Answer:
i wouldn't believe so.
Explanation:
because there was no room or air for the sound to move through. this is because of immense heat and the amount of hyperactive neutrons, electrons and protons clouding everywhere. This would mean that even if there was sound it would a. not travel far or b. go in a completely different direction than expected.
how were the outer planets formed?
Answer:
All planets including the outer larger planets were formed at the same time somewhere around 4.5 Billion years ago.
Explanation:
the young sun drove away most of the gas from the inner solar system, leaving behind the rocky cores also known as the terrestrial planets.
Air at 273K and 1.01x10³Nm2 pressure contains 2.70x1025 molecules per cubic meter. How many molecules per cubic meter will there be at a place where the temperature is 223K and pressure is 1.33x10 Nm-2
The molecules of O2 that are present in 3.90 L flask at a temperature of 273 K and a pressure of 1.00 atm is 1.047 x 10^23 molecules of O2
Step 1: used the ideal gas equation to calculate the moles of O2
that is Pv=n RT where;
P(pressure)= 1.00 atm
V(volume) =3.90 L
n(number of moles)=?
R(gas constant) = 0.0821 L.atm/mol.K
T(temperature) = 273 k
by making n the subject of the formula by dividing both side by RT
n= Pv/RT
n=[( 1.00 atm x 3.90 L) /(0.0821 L.atm/mol.k x273)]=0.174 moles
Step 2: use the Avogadro's law constant to calculate the number of molecules
that is according to Avogadro's law
1 mole = 6.02 x10^23 molecules
0.174 moles=? molecules
by cross multiplication
the number of molecules
= (0.174 moles x 6.02 x10^23 molecules)/ 1 mole =1.047 x 10^23 molecules of O2
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A pipe drips at 155 mL/min.
Express this is units of gallons/day.
1. 2.34 gal/day
2. 15.7 gal/day
3. 942 gal/day
4. 58.9 gal/day
5. 223 gal/day
6. 377 gal/day
7. 0.223 gal/day
We have that the total pipe drip of \(X=155 mL/min.\) expressed in gallons/day is
\(X=58.96gal/day\)
From the Question we are told that
Pipe Drip\(=155 mL/min.\)
Generally
We have that for mL to gallons conversion
\(1mL=0.000264172\)
And
A minute to day con version is
\(1min=0.000694444\)
Therefore
\(X=155 mL/min.\)
\(X=155(\frac{0.000264172}{0.000694444})\)
\(X=58.96gal/day\)
In conclusion
The total pipe drip of \(X=155 mL/min.\) expressed in gallons/day is \(X=58.96gal/day\)
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You exert a 138 N push the leftmost of two identical blocks of mass 244 g connected by a spring of stiffness 605 kg/s2. After pushing the block a distance 15 cm, you release it; by this time the rightmost block has moved a distance 5 cm. (a) What is the energy in the oscillations between the blocks
Answer:
the energy in the oscillations between the blocks is 3.025 J
Explanation:
Given the data in the question;
Force f = 138 N
stiffness of spring k = 605 kg/s²
mass of block = 202 g = 0.202 kg
pushing the block a distance 15 cm, the rightmost block has moved a distance 5 cm
i.e
x₁ = 15 cm
x₂ = 5cm
the energy in the oscillations between the blocks will be;
E\(_A\) = E\(_B\) = \(\frac{1}{2}\)k( Δx )²
we substitute
= \(\frac{1}{2}\) × k( 15 - 5 )² × 10⁻⁴
= \(\frac{1}{2}\) × 605 × ( 10 )² × 10⁻⁴
= \(\frac{1}{2}\) × 605 × 100 × 10⁻⁴
= 3.025 J
Therefore, the energy in the oscillations between the blocks is 3.025 J
An object is thrown into the air going 80m/s. How high does it go?
Four point charges q 1
,q 2
,q 3
and q 4
are placed at the corners of the square of side a, as shown in figure. The potential at the centre of the square is: (Given : q 1
=1×10 −8
C,q 2
=−2×10 −8
C,q 3
=3×10 −8
C,q 4
=2×10 −8
C,a=1m).
The potential at the center of the square is 507 V. Option (a) is correct answer.
The electric potential at a distance r from a point charge q is given by:
V = kq/r
where k is the Coulomb constant.
In this case, the charges q₂ and q₄ are negative, so the potentials due to these charges will be negative. The charges q₁ and q₃ are positive, so the potentials due to these charges will be positive. The potential at the center of the square is given by:
\(V = \dfrac{kq_1}{a} + \dfrac{kq_2}{\sqrt{2}a} + \dfrac{kq_3}{a} + \dfrac{kq_4}{\sqrt{2}a}\)
Plugging in the values of the charges and the distance a, we get:
\(V = \dfrac{9 \times 10^9 \times 1 \times 10^{-8}}{1} + \dfrac{9 \times 10^9\times -2\times 10^{-8}}{\sqrt{2}\times 1} + \dfrac{9 \times 10^9\times 3 \times 10^{-8} }{1} + \dfrac{9 \times 10^9 \times 2 \times 10^{-8} }{\sqrt{2} \times 1}\)
Simplifying this expression,
V = 507 V
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--The complete question is, Four point charges q1 ,q2 ,q3 and q4 are placed at the corners of the square of side a, as shown in figure. The potential at the centre of the square is: (Given: q1 =1×10^−8 C , q2 =−2×10^−8 C, q3 =3×10^−8 C, q4 =2×10^−8C, a=1m).
a. 507 V
b. 607 V
c. 550 V
d. 650 V--
The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.40 the weight of the object is 4.2
The frictional force of an object is the product of the normal force and coefficient of kinetic friction. Here the frictional force acting on the object is 16.4 N.
What is frictional force?
Frictional force is a kind of force acting on a body to resist it from motion. Thus, the direction of the force will be in negative with the magnitude. Frictional force is the product of coefficient of friction and the normal force.
The normal force acting on the object of mass 4.2 Kg is N = mg
N = 4.2 Kg × 9.8 m/s² = 41.16 N
Frictional force = ц N
= 0.40 × 41.16 N
= 16.4 N.
Therefore, the frictional force acting between the surface of the object and the floor is 16.4 N
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Your question is incomplete. But your complete question probably was:
The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.40 the weight of the object is 4.2 kg. What is the frictional force of the object?
One of the waste products of a nuclear reactor is plutonium-239 . This nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus , the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is and is entirely converted to kinetic energy of the helium and uranium nuclei. The mass of the helium nucleus is , while that of the uranium is (note that the ratio of the masses is 4 to 235).
(a) Calculate the velocities of the two nuclei, assuming the plutonium nucleus is originally at rest.
(b) How much kinetic energy does each nucleus carry away
Answer:
a) \( v_{U-235} = 2.68 \cdot 10^{5} m/s \)
\(v_{He-4} = -1.57 \cdot 10^{7} m/s\)
b) \( E_{He-4} = 8.23 \cdot 10^{-13} J \)
\( E_{U-235} = 1.41 \cdot 10^{-14} J \)
Explanation:
Searching the missed information we have:
E: is the energy emitted in the plutonium decay = 8.40x10⁻¹³ J
m(⁴He): is the mass of the helium nucleus = 6.68x10⁻²⁷ kg
m(²³⁵U): is the mass of the helium U-235 nucleus = 3.92x10⁻²⁵ kg
a) We can find the velocities of the two nuclei by conservation of linear momentum and kinetic energy:
Linear momentum:
\( p_{i} = p_{f} \)
\( m_{Pu-239}v_{Pu-239} = m_{He-4}v_{He-4} + m_{U-235}v_{U-235} \)
Since the plutonium nucleus is originally at rest, \(v_{Pu-239} = 0\):
\( 0 = m_{He-4}v_{He-4} + m_{U-235}v_{U-235} \)
\( v_{He-4} = -\frac{m_{U-235}v_{U-235}}{m_{He-4}} \) (1)
Kinetic Energy:
\( E_{Pu-239} = \frac{1}{2}m_{He-4}v_{He-4}^{2} + \frac{1}{2}m_{U-235}v_{U-235}^{2} \)
\( 2*8.40 \cdot 10^{-13} J = m_{He-4}v_{He-4}^{2} + m_{U-235}v_{U-235}^{2} \)
\( 1.68\cdot 10^{-12} J = m_{He-4}v_{He-4}^{2} + m_{U-235}v_{U-235}^{2} \) (2)
By entering equation (1) into (2) we have:
\( 1.68\cdot 10^{-12} J = m_{He-4}(-\frac{m_{U-235}v_{U-235}}{m_{He-4}})^{2} + m_{U-235}v_{U-235}^{2} \)
\( 1.68\cdot 10^{-12} J = 6.68 \cdot 10^{-27} kg*(-\frac{3.92 \cdot 10^{-25} kg*v_{U-235}}{6.68 \cdot 10^{-27} kg})^{2} +3.92 \cdot 10^{-25} kg*v_{U-235}^{2} \)
Solving the above equation for \(v_{U-235}\) we have:
\( v_{U-235} = 2.68 \cdot 10^{5} m/s \)
And by entering that value into equation (1):
\(v_{He-4} = -\frac{3.92 \cdot 10^{-25} kg*2.68 \cdot 10^{5} m/s}{6.68 \cdot 10^{-27} kg} = -1.57 \cdot 10^{7} m/s\)
The minus sign means that the helium-4 nucleus is moving in the opposite direction to the uranium-235 nucleus.
b) Now, the kinetic energy of each nucleus is:
For He-4:
\(E_{He-4} = \frac{1}{2}m_{He-4}v_{He-4}^{2} = \frac{1}{2} 6.68 \cdot 10^{-27} kg*(-1.57 \cdot 10^{7} m/s)^{2} = 8.23 \cdot 10^{-13} J\)
For U-235:
\( E_{U-235} = \frac{1}{2}m_{U-235}v_{U-235}^{2} = \frac{1}{2} 3.92 \cdot 10^{-25} kg*(2.68 \cdot 10^{5} m/s)^{2} = 1.41 \cdot 10^{-14} J \)
I hope it helps you!