Answer:
the magnitude of the electrostatic force between these two charged particles is 4.32 x 10^-28 N.
Explanation:
F = k * (q1 * q2) / r^2
where:
F is the electrostatic force
k is the Coulomb's constant (9 x 10^9 Nm^2/C^2)
q1 and q2 are the charges of the particles
r is the distance between the particles
Plugging in the given values:
q1 = 8 x 10^-19 C
q2 = 4.8 x 10^-19 C
r = 1.2 x 10^-4 m
k = 9 x 10^9 Nm^2/C^2
we can calculate the electrostatic force:
F = (9 x 10^9 Nm^2/C^2) * (8 x 10^-19 C) * (4.8 x 10^-19 C) / (1.2 x 10^-4 m)^2
F = 4.32 x 10^-28 N
The electrostatic force between these two particles is therefore calculated to be **1.44x10⁻¹⁴ N**1 using Coulomb's equation of electrostatic force.
COULOMB LAW BE DEFINED?With a force proportional to the product of the charges and inversely proportional to the square of the distance between them, Coulomb's law states that like charges repel and opposite charges attract. There is a formula that may be used to calculate the force between two point charges. Charles-Augustin de Coulomb created Coulomb's law in 1785
The electrostatic force between two charges is inversely proportional to the square of the distance between them and directly proportional to the product of their magnitudes1.
The centers of the two tiny charged particles in this example are separated by a distance of **1.2x10⁻⁴ meter**, with charges of **8x10⁻¹⁹** and **4.8*10⁻¹⁹**, respectively.
F is the electrostatic force
k is the Coulomb's constant (9 x 10⁹ Nm²C²)
q1 and q2 are the charges of the particles
r is the distance between the particles
Plugging in the given values:
q1 = 8 x 10⁻¹⁹ C
q2 = 4.8 x 10⁻¹⁹C
r = 1.2 x 10⁻⁴ m
k = 9 x 10₉ Nm²/C²
we can calculate the electrostatic force:
F = (9 x 10⁹Nm²/C²) * (8 x 10⁻¹⁹ C) * (4.8 x 10⁻¹⁹ C) / (1.2 x 10⁻⁴ m)²
The electrostatic force between these two particles is therefore calculated to be **1.44x10⁻¹⁴N**1 using Coulomb's equation of electrostatic force.
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Can u please help with first two tasks
Workbook:complete physics for Cambridge secondary first
Electromagnetic induction is a phenomenon in physics that occurs when a varying magnetic field produces an electric current or voltage in a conductor. It was first discovered by Michael Faraday in the early 19th century and is now a fundamental principle of modern electrical technology.
When a conductor, such as a wire, is moved through a magnetic field, or when the magnetic field itself changes, a voltage is induced across the ends of the conductor. The magnitude of the induced voltage is proportional to the rate of change of the magnetic field and the number of turns of wire in the coil.
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a) A 0.250-kg toy car is propelled by a compressed spring. The car follows a track that rises above the starting point. The spring is compressed 6.00 cm and has a force constant of 450.0 N/m. Find the speed of the car when it reaches 0.110 m above the starting point.
b) Estimate the power expended by a child raising a 0.25-kg toy 0.75 m in 2.0 s. Convert your answer to horsepower (1 ℎp = 746w)
Answer:
a) To solve for the speed of the car, we can use the conservation of energy equation:
(1/2)mv^2 = mgh - (1/2)kx^2
where m is the mass of the car, v is the speed of the car, g is the acceleration due to gravity, h is the height of the car above the starting point, k is the spring constant, and x is the distance the spring is compressed.
Plugging in the given values, we get:
(1/2)(0.250 kg)v^2 = (0.250 kg)(9.81 m/s^2)(0.110 m) - (1/2)(450.0 N/m)(0.0600 m)^2
Solving for v, we get:
v = 1.23 m/s
Therefore, the speed of the car when it reaches 0.110 m above the starting point is 1.23 m/s.
b) To estimate the power expended by a child raising a 0.25-kg toy 0.75 m in 2.0 s, we can use the work-energy theorem:
W = ΔE = mgh
where W is the work done, m is the mass of the toy, g is the acceleration due to gravity, h is the height the toy is raised, and ΔE is the change in energy.
Plugging in the given values, we get:
W = (0.25 kg)(9.81 m/s^2)(0.75 m) = 1.84 J
Next, we can use the definition of power:
P = W/t
where P is power, W is work, and t is time.
Plugging in the given values, we get:
P = 1.84 J / 2.0 s = 0.92 W
Finally, we can convert watts to horsepower:
1 hp = 746 W
0.92 W = 0.92 / 746 hp = 0.0012 hp
Therefore, the power expended by a child raising a 0.25-kg toy 0.75 m in 2.0 s is approximately 0.0012 hp.
On Earth the gravitational field strength is 10N/kg. What would be the weight of someone on Earth who had a mass of 75kg?
750N/kg
750N
75N
7500kg
The weight of someone on Earth with a mass of 75kg is 750N.
option B.
What would be the weight of someone on Earth?The weight of someone on Earth is calculated using Newton's second law of motion.
W = mg
where;
m is the massg is acceleration due to gravityFor the mass is 75kg and the gravitational field strength on Earth is 10N/kg.
W = 75 kg x 10 N/kg
W = 750 N
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The surfaces of a lipid bi-layer forming the membrane around a cell with a radius of 1.5 μm has a residual charge qr = 9.1×10-15 C on outside of the bi-layer, and the same amount of negative charge on the inside. What is the force in pN (×10-12 N) on a singly-charged positive ion (q =1.6 ×10-19 C) located on the outer surface of this membrane? Hint: Use F = q E = q (σ/e) with σ = qr/A = qr/ (4π r2) and εo = 8.85 x 10-12 F·m-1.
I mean if it will be anything the asnwer would be 23^90'200
A block of wood weighing 15 N rest on top of the table. How mush force is exerted by the table on the blockso that it will remainat rest. Explain your answer
The force exerted by the table on the block to keep it at rest is equal in magnitude but opposite in direction to the force exerted by the block on the table.
This is due to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.Therefore, the force exerted by the table on the block is 15 N, the weight of the block. This is because the block is at rest and not accelerating, which means that the net force acting on it must be zero.
Since the force of gravity acting on the block is 15 N and it is not accelerating, the force exerted by the table on the block must also be 15 N but in the opposite direction, which balances out the gravitational force.
In summary, the force exerted by the table on the block to keep it at rest is 15 N, which is equal in magnitude but opposite in direction to the force exerted by the block on the table.
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why does pure water increase in volume when heated
Answer:
Pure water increases in volume when heated due to the phenomenon of thermal expansion. When water is heated, the kinetic energy of its molecules increases, causing them to move faster and spread out. This increased molecular movement leads to an increase in the average distance between water molecules, resulting in an expansion of the water.
Explanation:
.......
Which list of components creates a circuit through which an electric current can flow?
A. a battery, insulated wires, a buzzer, and an open switch
B. a generator, two light bulbs, and an open switch
C. a generator, a light bulb, and a closed switch
D. a battery, insulated wires, and a buzzer
A circuit requires a complete loop through which an electric current can flow. Therefore, The correct answer is Option(D).
A battery provides the source of the electric potential difference, and insulated wires allow the current to flow from the battery to the buzzer. The buzzer completes the loop back to the battery. An open switch, such as in options A and B, would break the circuit and prevent the flow of electric current. A closed switch, such as in option C, would complete the circuit. However, option C does not provide a complete circuit with a source of electric potential difference, and therefore cannot create a sustained flow of electric current.
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If the wave pictured above oscillates up and down 25 time in 10
seconds, what is the frequency?
Answer:
Frequency = 25 / 10 = 2.5 Hz
Explanation:
If the wave oscillates up and down 25 times in 10 seconds, then the frequency can be calculated as follows:
Frequency = Number of oscillations / Time
In this case, the number of oscillations is 25, and the time is 10 seconds. Therefore, the frequency is:
Frequency = 25 / 10 = 2.5 Hz
So the frequency of the wave is 2.5 Hertz, which means it completes 2.5 cycles or oscillations in one second.
String is wrapped around an object of mass M = .5 kg and the moment of inertia I = .02 kg*m^2. You pull the string with your hand straight up with some constant force F such that the center of the objects does not move up or down, but the object spins faster and faster. This is like a yo-yo; nothing but the vertical string touches the object. When your hand is a height y = .22 m above the floor, the object has an angular speed of w = 15 radians/s. When your hand has risen to a height of y = .73 m above the floor, what is the angular speed of the object? Your answer must be numeric and not contain the symbol F.
The angular speed of the object when your hand has risen to a height of y = 0.73 m above the floor is approximately 26.83 radians/s.
What is Mass?
Mass is a fundamental property of matter that quantifies the amount of matter in an object. It is a scalar quantity that describes the resistance of an object to acceleration when subjected to an external force. The mass of an object is a measure of the total amount of material or substance that it contains, and it is usually expressed in kilograms (kg) or other appropriate units.
The final potential energy is given by:
PE_final = m * g * y_final
where y_final is the final height of the object above the floor.
Setting the initial mechanical energy equal to the final mechanical energy and rearranging the equation, we get:
g = 9.8 m/[tex]s^{2}[/tex] (acceleration due to gravity)
(1/2) * 0.02 * [tex](15)^{2}[/tex]^2 + 0.5 * 9.8 * 0.22 = (1/2) * 0.02 * [tex]w_final ^{2}[/tex] + 0.5 * 9.8 * 0.73
w_final = sqrt((2 * ((1/2) * 0.02 * (15)^2 + 0.5 * 9.8 * 0.22 - 0.5 * 9.8 * 0.73)) / 0.02)
Plugging in the given values and solving for w_final, we get:
w_final ≈ 26.83 radians/s (rounded to two decimal places)
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A blue train of mass 50 kg moves at 4 m/s toward a green train of 30 kg initially at rest. The trains collide. After the collision the green train moves with a speed of 3 m/s. What is the final momentum of the green train?
A. 200 kgm/s
B. 90 kgm/s
C. 20 kgm/s
D. 110 kgm/s
If the adhesive force between solid molecules and liquid molecules is relatively weak, the phenomenon of non infiltration will be formed. True or false?
If the adhesive force between solid molecules and liquid molecules is relatively weak, the phenomenon of non infiltration will not be formed. False.
What is non-infiltration about?If the adhesive force between solid molecules and liquid molecules is relatively weak, the phenomenon of infiltration (or wetting) will be formed, as the liquid will spread out over the surface of the solid.
Non-infiltration is a phenomenon where a liquid is unable to wet or spread over the surface of a solid due to the strong adhesive force between the solid and liquid molecules. Instead of spreading out, the liquid will form droplets on the surface of the solid.
Non-infiltration is the opposite of infiltration (or wetting), where a liquid is able to spread over the surface of a solid due to a weak adhesive force.
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An atom with four protons and four electrons is in equilibrium. An electron is added. What is the overall charge of the atom?
The overall charge of the atom after an electron is added is -1.
An ion is an atom or molecule that has an unequal number of protons and electrons, resulting in a net electrical charge. Atoms are normally electrically neutral because the number of protons, which carry a positive charge, is equal to the number of electrons, which carry a negative charge. However, when an atom gains or loses one or more electrons, it becomes an ion with a net electrical charge.
When an atom loses one or more electrons, it becomes a positively charged ion, or cation, since the number of positively charged protons is greater than the number of negatively charged electrons. On the other hand, when an atom gains one or more electrons, it becomes a negatively charged ion, or anion, since the number of negatively charged electrons is greater than the number of positively charged protons.
An atom with four protons and four electrons is electrically neutral since the number of positively charged protons equals the number of negatively charged electrons. When an electron is added to the atom, the number of electrons becomes five, while the number of protons remains at four. This results in a net negative charge on the atom, since the extra electron carries a negative charge.
Therefore, the overall charge of the atom after an electron is added is -1.
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5. How mach work is repuried to increase the speed of 4kg object from 20m/s to 40m/s
URGENT 50 POINTS
Show all Steps of your work.
7. Mohammed whose mass is 50kg swings back and forth on a long vine makes an angle 45 from the vertical resting position. His friend Abdella notices in amazement that he makes 30 complete swings in 2.0 minuies.
(a) What is the frequency (in hertz) of Tarzan's swing?
(b) What is the period of oscillation?
(c) How long is the vine he is using?
(d) Calculate the Restoring force on Mohammed?
The frequency of oscillation of the swing is 0.25 Hz.
The time period of oscillation of the swing is 4 s.
The length of the vine of the swing is 3.97 m.
The restoring force acting on Mohammed is 692.9 N.
Mass of Mohammed, m = 50 kg
Angle made by the vine with the vertical, θ = 45°
Number of complete swings made by Mohammed, n = 30
Time taken for this swing, t = 2 minutes = 120 seconds
a) The frequency of the swing is defined as the number of complete oscillations in one second.
So, the frequency of oscillation of the swing is,
f = n/t
f = 30/120
f = 0.25 Hz
b) The time period of oscillation of the swing is,
T = 1/f
T = 1/0.25
T = 4 s
c) The expression for the time period is given by,
T = 2π√(l/g)
T² = 4π² x (l/g)
l/g = T²/4π²
Therefore, the length of the vine of the swing is,
l = T²g/4π²
l = 4² x 9.8/4 x (3.14)²
l = 3.97 m
d) The restoring force acting on Mohammed,
F = mg sinθ
F = 50 x 9.8 x sin 45°
F = 490 x 1/√2 = 490/1.414
F = 692.9 N
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What is the period, in seconds, of this mass?
The period (in second) of the 0.95 Kg mass, given that it has an amplitude of 0.21 m and an angular velocity of 9.5 rad/s is 0.66 second
How do i determine the period of the mass?From the question given above, the following data were obtained:
Mass (m) = 0.95 KgAmplitude (A) = 0.21 mAngular frequency (ω) = 9.5 rad/sPi (π) = 3.14Period (T) =?The period of the mass can be obtained as shown below:
ω = 2π/ T
9.5 = (2 × 3.14) / T
9.5 = 6.28 / T
Cross multiply
9.5 × T = 6.28
Divide both sides by 9.5
T = 6.28 / 9.5
T = 0.66 second
Thus, from the above calculation, we can conclude that the period of the mass is 0.66 second
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Find the Peukert constants n and λ for Peukert’s equation for following two measurements available from a constant current discharge experiment of a battery : (i) (t1, I1) = (10, 25) (ii) (t2, I2) = (4,45)
The battery Peukert constants, n and, are around 1.223 and 2.486, respectively.
How many Peukerts can fit?Wilhelm Peukert, a German physicist, proposed Peukert's law in 1897, which quantifies a battery's capacity in terms of the rate of discharge. The battery's useful capacity reduces as the rate of discharge rises. The supplied capacity decreases as discharge rate increases.
C = I⁽⁻ⁿ⁾ * t * λ
log(C) = -n * log(I) + log(λ) + log(t)
log(C1) = -n * log(I1) + log(λ) + log(t1)
log(C1) = -n * log(25) + log(λ) + log(10)
Similarly, for the second measurement, we have:
log(C2) = -n * log(I2) + log(λ) + log(t2)
log(C2) = -n * log(45) + log(λ) + log(4)
log(C1) - log(C2) = -n * (log(25) - log(45)) + log(10/4)
Simplifying, we get:
log(C1/C2) = n * log(45/25) + log(2.5)
Substituting the values, we get:
log(25/45) = n * log(45/25) + log(2.5)
Solving for n, we get:
n = (log(25/45) - log(2.5)) / log(45/25)
n = 1.223
log(C1) = -1.223 * log(25) + log(λ) + log(10)
log(C1) = -1.223 * 1.39794 + log(λ) + 1
Solving for log(λ), we get:
log(λ) = log(C1) + 1.223 * 1.39794 - 1
log(λ) = log(25) + 1.223 * 1.39794 - 1
log(λ) = 0.39794
Therefore, λ = 2.486.
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Explain why sound wave travel faster in liquids than in gases
Answer:
Sound travels faster in liquids than in gases because molecules are more tightly packed. In fresh water, sound waves travel at 1,482 meters per second (about 3,315 mph). That's well over 4 times faster than in air!
Explanation:
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How does the ecotourism industry act as an ecosystem service that benefits tourists, the people that live in the area, and the people that work in the industry?
It promotes enjoyable experiences for both guests and hosts; It lessens the negative effects of tourism on the environment; It increases local residents' access to work and financial prospects; It promotes conservation by offering financial advantages in its direction.
What is ecotourism?The World Tourism Organization defines ecotourism as all forms of nature-based travel in which visitors' primary interests are in observing and appreciating the environment as well as the local cultures that are still practiced in natural settings.
Here are a few instances of ecotourism:
Visit places where there is nature (think of the flora, animals, and resources)discovering the heritage of the local culture.Ecologically sound wilderness excursions.volunteering or watching nature.trips devoted to environmental preservation efforts, like beach clean-ups.Learn more about ecotourism here:
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Sources of error could have come from friction that may result in energy losses during the collision, The gliders may not be perfectly elastic, which means that some energy may be lost during the collision
are these errors random or systematic errors?
Sources of error could have come from small amounts of friction, and glider 2 could have not been totally at rest. These errors are systematic errors.
Are these errors random or systematic?
Answer:
The first set of errors, which include friction and imperfect elasticity, are systematic errors because they arise from consistent factors that affect the measurements in a predictable way. These errors will be present in every trial of the experiment and will cause a consistent deviation from the true value.
The second set of errors, which include small amounts of friction and the initial velocity of glider 2, are also systematic errors because they arise from consistent factors that affect the measurements in a predictable way. These errors will also be present in every trial of the experiment and will cause a consistent deviation from the true value.
Explanation:
What new question occurred to scientists after they discovered that the
ocean floor was not flat?
O A. Are there bathtubs that have shapes similar to that of the Mid-
Atlantic Ridge?
OB. Why is the ocean floor not flat and smooth like the bottom of a
bathtub?
C. How much cable will it take to go from North America to England?
OD. How deep is the ocean?
Answer:
b
Explanation:
The answer is B. Why is the ocean floor not flat and smooth like the bottom of a bathtub?
Scientists were surprised to find that the ocean floor was not a flat and featureless plain, but rather had mountains, valleys, and other geological features. This discovery raised questions about how these features formed and what processes were involved. Scientists began to investigate the causes of these features, such as plate tectonics and volcanic activity, and how they might have shaped the ocean floor over millions of years. Understanding the complex and dynamic nature of the ocean floor has since become an important area of study in earth science and oceanography.
A sound wave travelling at 330m/s has a frequency of 220Hz. What is its wavelength?
Answer: 1.5 meters.
Explanation:
Wavelength is equal to λ = v/f. We are given the following:
v = 330 m/s
f = 220 Hz
We can plug this in to find the wavelength.
[tex]wavelength = \frac{330}{220} \\wavelength = 1.5 m[/tex]
What is the weight of a body of mass 12kg?
math
Determine if the function below is continuous.
graph of a piecewise function, with 2 pieces. The first piece is a line that starts at negative infinity and goes through point (-4,5) and ends with an open dot at (1,0). The second piece is a line that starts with a closed dot at (1,-1), goes through point (2,1) and continues to infinity.
A. not continuous at x = 1
B. not continuous at x = 0
C. not continuous at x = -1
D. continuous
The function is not continuous at x=1, so the answer is A.
At x=1, the two pieces of the function meet. The first piece ends with an open dot at (1,0), meaning that the function is not defined at $x=1$. The second piece starts with a closed dot at (1,-1), meaning that the function is defined at x=1 and takes the value -1 there.
Since the function is not defined at x=1, it cannot be continuous at that point. Therefore, the function is not continuous overall.
* Find out the force between the wires 150 cm long and I'm apart) used to connect the battery of a car to the motor? [Note: The Current in the wires in 200 ampere)
Answer:
The force between the wires used to connect the battery of a car to the motor can be calculated using the equation F = I*L, where F is the force, I is the current, and L is the length of the wires. In this case, the force would be calculated as F = 200A * 0.15m = 30N.
Observe the distance between the compressions shown in the image. What do you notice about the sound waves in front of the truck compared to the sound waves behind the truck? Was your prediction correct?
The sound waves in front of the truck compared to the sound waves behind the truck is using Doppler effect.
The prediction is correct.
What is the doppler effect?The Doppler effect or Doppler shift is described as the apparent change in frequency of a wave in relation to an observer moving relative to the wave source.
The apparent frequency heard by the listener differs from the frequency of the source of sound when there is relative motion between the source and listener.
The perceived frequency increases as the source and the listener go closer together, and it decreases as they get farther apart. It's called the Doppler effect.
The wave-fronts move closer as the source and listener approach closer to each other. Thus, the observed frequency is greater than the actual.
The pitch depends on frequency, greater is the pitch
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A 60.6 kg weight-watcher wishes to climb a mountain to work off the equivalent of a large piece of chocolate cake rated at 720 (food) Calories. How high must the person climb? The acceleration due to gravity is 9.8 m/s 2 and 1 food Calorie is 103 calories. Answer in units of km.
The height the weight-watcher needs to climb to work off the equivalent of the chocolate cake is 0.5225 km.
What is the height of the person?The height the weight-watcher needs to climb to work off the equivalent of the chocolate cake is calculated as follows;
P.E = mgh
Where;
m is the mass of the objectg is the acceleration due to gravityh is the height.720 Calories x 103 calories/1 food Calorie = 74,160 calories
74,160 calories = 310285.44 J
h = P.E/mg
h = (310285.44) / (60.6 x 9.8)
h = 522.5 m
h = 0.5225 km
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By how much do you stretch your 0.600-cm diameter nylon rope when you hang 23.0m
below a rock outcropping. Assume your mass is 75.0 kg and your nylon rope has Young’s modulus of 5.00 × 10^9 N/m^2.
Answer:
To solve for the amount of stretch in the nylon rope, we can use the equation for the elongation (stretch) of a rope under tension:
ΔL = FL / AE
where ΔL is the change in length of the rope, F is the force on the rope, L is the original length of the rope, A is the cross-sectional area of the rope, and E is the Young's modulus of the rope.
First, we need to find the force on the rope. This is equal to the weight of you and the rope:
F = mg = (75.0 kg + mass of rope)g
Next, we need to find the cross-sectional area of the rope. The diameter of the rope is given as 0.600 cm, so the radius is 0.300 cm = 0.00300 m. Therefore, the cross-sectional area is:
A = πr^2 = 2.83 × 10^-6 m^2
Now we can plug in the given values and solve for ΔL:
ΔL = FL / AE = [(75.0 kg + mass of rope)g](23.0 m) / [(2.83 × 10^-6 m^2)(5.00 × 10^9 N/m^2)]
We can simplify this expression by using the fact that the mass of the rope is much smaller than your mass, so we can assume that the force on the rope is equal to your weight:
ΔL = (mg)(23.0 m) / (A E) = (75.0 kg)(9.81 m/s^2)(23.0 m) / [(2.83 × 10^-6 m^2)(5.00 × 10^9 N/m^2)]
Solving for ΔL, we get:
ΔL = 0.068 cm
Therefore, the nylon rope stretches by approximately 0.068 cm when you hang 23.0 m below a rock outcropping.
what’s the answer for this
Suppose the metal sample in Figure 10.2 is immersed in water, is cubical with side 3.0 cm, and has a mass of 54 g.
The force of buoyancy acting on the sample is 2.65 N.
If the sample's supporting string is cut, it will float to the surface of the water.
How to calculate bouyant force?a. The buoyant force acting on the sample can be calculated using the formula Fb = ρVg, where ρ is the density of water, V is the volume of the submerged part of the sample, and g is the acceleration due to gravity. Since the sample is immersed in water, its volume is equal to the volume of water it displaces, which can be calculated using the formula V = l × w × h, where l, w, and h are the dimensions of the submerged part of the sample. Since the sample is cubical, all sides have the same length of 3.0 cm. Thus, the submerged part of the sample has a volume of V = 3.0 cm × 3.0 cm × 3.0 cm = 27.0 cm³ = 0.027 m³. The density of water is ρ = 1000 kg/m³, and the acceleration due to gravity is g = 9.81 m/s². Therefore, the buoyant force acting on the sample is:
Fb = ρVg = 1000 kg/m³ × 0.027 m³ × 9.81 m/s² ≈ 2.65 N
b. The sample will float to the surface of the water if its supporting string is cut. This is because the buoyant force acting on the sample is greater than its weight, which means that there is a net upward force on the sample. This net force causes the sample to accelerate upward, and it will continue to accelerate until it reaches the surface of the water. At the surface, the upward force is balanced by the weight of the sample, and it will float on the water.
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Complete question:
2. Suppose the metal sample in Figure 10.2 is immersed in water, is cubical with side 3.0 cm, and has a mass of 54 g. a. Calculate the buoyant force acting on the sample. b. Describe the behavior of the sample if its supporting string is cut. Explain how you arrive at your answer. balance arm water metal sample water overflow can beaker Figure 10.2 MEASUREMENTS
The center of gravity of a 5.00 kg irregular object is shown in (Figure 1). You need to move the center of gravity 1.60 cm to the left by gluing on a 1.50 kg mass, which will then be considered as part of the object.
Where should the center of gravity of this additional mass be located?
The moment of the weight of the 1.50 kg mass about the CG of the 5.00 kg object will be considered as part of the object.
The center of gravity of the additional 1.50 kg mass should be located 1.60 cm to the right of the current CG of the 5.00 kg object.
What is the moment ?
We can use the principle of moments to determine the location of the center of gravity of the additional 1.50 kg mass that needs to be glued on.
The principle of moments states that the sum of the moments of all the forces acting on an object is equal to the moment of the resultant force about any point. In this case, we can take moments about the current center of gravity (CG) of the 5.00 kg object to determine the location of the center of gravity of the additional 1.50 kg mass.
The moment of a force about a point is given by the product of the magnitude of the force and the perpendicular distance from the point to the line of action of the force. Since the gravitational force acting on the masses is the only force acting on the system, we can take moments of the weight of each mass about the CG of the 5.00 kg object.
The moment of the weight of the 5.00 kg object about its CG is zero, since the CG is the point about which the object is in rotational equilibrium. Therefore, we only need to consider the moment of the weight of the 1.50 kg mass about the CG of the 5.00 kg object.
The distance between the CG of the 5.00 kg object and the desired new CG is 1.60 cm to the left, so we need to find the distance between the current CG and the new CG. Let x be the distance from the current CG to the new CG.
The moment of the weight of the 1.50 kg mass about the current CG is:
(1.50 kg)(9.81 m/s²)(x) = 14.72x Nm
The moment of the weight of the 1.50 kg mass about the new CG is:
(1.50 kg)(9.81 m/s²)(1.60 cm + x) = 14.72x + 23.54 Ncm
Setting these two moments equal, we have:
14.72x Nm = 14.72x + 23.54 Ncm
Converting the units, we get:
0.1472x m = 0.2354 m
x = 1.60 cm (to two significant figures)
Therefore, the center of gravity of the additional 1.50 kg mass should be located 1.60 cm to the right of the current CG of the 5.00 kg object.
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