The diameter of the sphere can be solved using the relationship between the tension in the string, the linear density of the string, and the frequency of the standing waves.
This relationship is given by the equation:
f = (n/2L) * sqrt(T/u)
where f is the frequency of the standing wave, n is the number of the harmonic, L is the length of the string, T is the tension in the string, and u is the linear density of the string.
Before the sphere was submerged, the tension in the string was equal to the weight of the sphere, or T = (2.1 kg) (9.8 m/s^{2}) = 20.58 N.
After the sphere was submerged, the tension in the string was reduced by the buoyant force of the water, which is equal to the weight of the water displaced by the sphere. The volume of the sphere is given by:
V = (4/3) * pi * (d/2)^{3}
where d is the diameter of the sphere. The weight of the water displaced is equal to the volume of the sphere times the density of water, or:
Fb = (4/3) * pi * (d/2)^{3} * (1000 kg/m^{3}) * (9.8 m/s^{2})
The tension in the string after the sphere was submerged is equal to the weight of the sphere minus the buoyant force, or:
T' = 20.58 N - (4/3) * pi * (d/2)^{3} * (1000 kg/m^{3}) * (9.8 m/s^{2})
Since the frequency of the fifth harmonic with the sphere submerged is equal to the frequency of the third harmonic before the sphere was submerged, we can set the two equations equal to each other and solve for d:
(5/2L) * sqrt(T'/u) = (3/2L) * sqrt(T/u)
Squaring both sides and rearranging terms gives:
(25/9) * (T'/T) = (u/u)
Substituting the expressions for T and T' and simplifying gives:
(25/9) * [(20.58 N - (4/3) * pi * (d/2)^{3} * (1000 kg/m^{3}) * (9.8 m/s^{2}))/(20.58 N)] = 1
Solving for d gives:
d = 2 * [(9/25) * (20.58 N)/(4 * pi * (1000 kg/m^{3}) * (9.8 m/s^{2})) - (1/3)]^{(1/3)}
d = 0.117 m
Therefore, the diameter of the sphere is 0.117 m, or 11.7 cm.
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A man has a mass of 60. 1 kilograms. He jumps from the ground onto a 177 meter building and then dives off of it and comes to a rest at the bottom of a 18. 5 meter excavation. By how much will gravitational energy change in joules?
The change in gravitational potential energy is approximately 93,640 joules.
The change in gravitational potential energy can be calculated using the formula, ΔPE = mgΔh, where ΔPE is the change in gravitational potential energy, m is the mass of the man, g is the acceleration due to gravity, and Δh is the change in height.
The change in height, Δh = 177 m + (-18.5 m) = 158.5 m.
The mass of the man is given as 60.1 kilograms, and the acceleration due to gravity is approximately 9.81 meters per second squared. The change in gravitational potential energy.
ΔPE = (60.1 kg)(9.81 m/s^2)(158.5 m) ≈ 93,640 J
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A woman walks 200m east and then 100m south. Find the total distance travelled and then find the resultant displacement.
Answer:
300m
Explanation:
It is very simple.
200m+100m= 300m
Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the 45 kg object at various locations as shown on the diagram below.
The potential energy at each point:
PE₁ = 1764 J
PE₂ = 1323 J
PE₃ = 0 J
PE₄ = 441 Jh
The kinetic energy at each point:
KE at point 1 = 0KE at point 2 = 1764 - 1323 JKE at point 2 = 441 JKE at point 3 = 1764 JKE₄ = 1219.7 JTo find the mechanical energy at each point:
ME₁ = 1764 JME₂ = 1764 JME₃ = 1764 JME₄ = 1764 JThe height at point 4, h = 1.23 m
What are the potential energy, kinetic energy, and mechanical energy of the object at each point?
To calculate the potential energy, kinetic energy, and mechanical energy of the object at each point, we will need to use the following formulas:
Potential energy (PE) = mgh, where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and h is the height above a reference point.
Kinetic energy (KE) = 0.5mv^2, where m is the mass of the object and v is its velocity.
Mechanical energy (ME) = PE + KE
Given:
Mass of the object (m) = 45 kg
Point 1: h = 4 m
Point 2: h = 3 m
Point 3: h = 0 m
Point 4: v = 5.2 m/s
To find the potential energy at each point:
PE₁ = mgh1 = 45 kg x 9.8 m/s^2 x 4 m
PE₁ = 1764 J
PE₂ = mgh2 = 45 kg x 9.8 m/s^2 x 3 m
PE₂ = 1323 J
PE₃ = mgh3 = 45 kg x 9.8 m/s^2 x 0 m
PE₃ = 0 J
PE₄ = mgh4 = 45 kg x 9.8 m/s^2 x h
PE₄ = 441 Jh
KE at point 1 = 0
KE at point 2 = 1764 - 1323 J
KE at point 2 = 441 J
KE at point 3 = 1764 J
To find the kinetic energy at point 4:
KE₄ = 0.5mv^2 = 0.5 x 45 kg x (5.2 m/s)^2
KE₄ = 1219.7 J
To find the mechanical energy at each point:
ME₁ = PE₁ + KE
ME₁ = 1764 J + 0 J = 1764 J
Since the mechanical energy is conserved (ignoring friction and air resistance), we can set ME₁ = ME₂ = ME₃ = ME₄
Solving for h:
ME₁ = ME₄
1764 J = 441 Jh + 1219.7 J
h = (1764 J - 1219.7 J) / (441 J)
h = 1.23 m
Therefore, at point 4, the object has a velocity of 5.2 m/s and a height of 1.23 m.
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A charged cloud system produces an electric field in the air near the earth surface. When a particle (q=-2. 0x10^-9) is acted on by a downward electrostatic force of 3. 0x10^-6 N when placed in this field, determine the magnitude of the electric field
The correct option is 4, the gravitational and electrostatic force, respectively, exerted on a proton placed in this field are: 2.9 × [tex]10^{-17}[/tex]N and 1.64 × [tex]10^{-26}[/tex]N.
Electrostatic force on charge particle,
3 × [tex]10^{-6}[/tex]N
Charge on a particle,
q = 16.2 × [tex]10^{-19}[/tex]C
Calculation of gravitational force:
F = qE
3 × [tex]10^{-6}[/tex] = 16.2 × [tex]10^{-9}[/tex]E
E = 3 × [tex]10^{-6}[/tex] / 16.2 × [tex]10^{-9}[/tex]
= 3 × [tex]10^3[/tex] / 16.2
Electrostatic force on proton,
= qE = 1.6 ×[tex]10^{-19}[/tex] × 3 × [tex]10^3[/tex] / 16.2
= 2.9 × [tex]10^{-17}[/tex]N
The gravitational force on the proton,
= mass of proton × acceleration due to gravity
= 1.67 × [tex]10^{-27}[/tex] × 9.8
= 1.64 × [tex]10^{-26}[/tex]N
Hence, the gravitational and electrostatic force, respectively, exerted on a proton placed in this field are:
2.9 × [tex]10^{-17}[/tex]N and 1.64 × [tex]10^{-26}[/tex]N
The electrostatic force, also known as the Coulombic force, is a fundamental force of nature that governs the interactions between electrically charged particles. This force arises from the attraction or repulsion between electric charges, which can be positive or negative. Like charges repel each other, while opposite charges attract.
Electrostatic force plays a crucial role in a wide range of physical phenomena, including the behavior of atoms and molecules, the functioning of electronic devices, and the behavior of charged particles in electric and magnetic fields. It is also responsible for the behavior of lightning, the spark from static electricity, and the attraction between a comb and hair. The electrostatic force is one of the four fundamental forces of nature, along with gravity, the strong nuclear force, and the weak nuclear force.
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Complete Question: -
A charged cloud system produces an electric field in the air near the earth's surface. A particle of charge 16.2 × [tex]10^{-19}[/tex]C is acted on by a downward electrostatic force of 3 × [tex]10^{-6}[/tex]N when placed in this field. The gravitational and electrostatic force, respectively, exerted on a proton placed in this field are
(1) 1.64 × [tex]10^{-26}[/tex]N, 2.4 × [tex]10^{-16}[/tex]N
(2) 1.64 × [tex]10^{-26}[/tex]N, 2.9 × [tex]10^{-16}[/tex]N
(3) 1.56 × [tex]10^{-18}[/tex]N, 2.4 ×[tex]10^{-16}[/tex]N
(4) 2.9 × [tex]10^{-17}[/tex]N, 1.64× [tex]10^{-26}[/tex]N
The light from the furthest galexy every seen (galaxy hd1) has traveled for 13. 463 billions light years to reach us. How far is this in meters?
The light from Galaxy HD1 is believed to have traversed 1.273 10 26 metres.
To convert the distance traveled by the light from Galaxy HD1 from light-years to meters, we can use the following conversion factor:
1 light-year = 9.461×10^15 meters
Therefore, the distance traveled by the light from Galaxy HD1 is:
13.463 billion light-years × 9.461×10^15 meters/light-year = 1.273×10^26 meters
So, the distance traveled by the light from Galaxy HD1 is approximately 1.273×10^26 meters, which is an incredibly large distance. It is important to note that this distance represents the comoving distance, which takes into account the expansion of the universe over time.
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Compare the gravitational force between earth and mars in the gravitational force between a newborn baby in a doctor the greater forces between which pair?
A newborn infant and a doctor are pulled apart by much less gravitational force than the distance between Earth and Mars.
The gravitational force between Earth and Mars can be calculated using the formula F = G(m1m2)/r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers. The mass of Earth is about 5.97 x 10^24 kg, the mass of Mars is about 6.39 x 10^23 kg, and the average distance between them is about 225 million km. Using these values and the formula, we can calculate that the gravitational force between Earth and Mars is about 2.7 x 10^22 N.
On the other hand, the gravitational force between a newborn baby and a doctor can be calculated using their masses and the distance between them. Assuming an average newborn baby mass of 3.5 kg and an average doctor mass of 75 kg, and a distance of 1 meter between them, we can calculate that the gravitational force between them is about 2.2 x 10^-8 N.
Clearly, the gravitational force between Earth and Mars is much greater than the force between a newborn baby and a doctor. The greater forces are between the larger and more massive objects, such as planets or stars, due to their greater masses and distances.
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Determine the molar mass of a gas if the volume of 0. 05 g of the gas is 50cc at 27°c and 76cm Hg pressure
If the volume of 0. 05 g of the gas is 50cc at 27°c and 76cm Hg pressure the molar mass of the gas is approximately 81.97 g/mol.
To determine the molar mass of the gas, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the given values to the appropriate units. The volume is given in cc, which is equivalent to mL, so we can convert it to m^3:
V = 50 cc = 50 x 10^-6 m^3
The temperature is given in degrees Celsius, so we need to convert it to Kelvin:
T = 27°C + 273.15 = 300.15 K
The pressure is given in cm Hg, so we need to convert it to Pa:
P = 76 cm Hg x (1 m/100 cm) x (133.32 Pa/1 cm Hg) = 101325.12 Pa
Now we can solve for the number of moles of gas:
n = PV/RT
where R = 8.314 J/(mol·K) is the gas constant.
n = (101325.12 Pa) x (50 x 10^-6 m^3) / (8.314 J/(mol·K) x 300.15 K)
n = 0.000610 mol
Finally, we can calculate the molar mass of the gas:
molar mass = mass / moles
Since the mass of the gas is given as 0.05 g, we have:
molar mass = 0.05 g / 0.000610 mol
molar mass = 81.97 g/mol
Therefore, the molar mass of the gas is approximately 81.97 g/mol.
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How long will it take a 500w heater to melt 100grams of ice at 0degrees celsius
Ice has a 333J/g latent heat of fusion.it will take approximately 66.8 seconds for a 500W heater to melt 100 grams of ice at 0 degrees Celsius. .To deliver a required amount of energy, l
At 0 degrees Celsius, how can ice melt?Liquid water freezes at temperature below 32°F (0°C); this temperature is known as the water freezing point. Normal water ice melts or transforms from a solid into a liquid (water) at temperatures over 32°F (0°C); 32°F (0°C) is indeed the melting point.
where:
Q = energy required (in joules)
m = mass of ice (in grams)
Lf = latent heat of fusion for water (334 J/g)
Substituting the given values, we get:
Q = 100 g * 334 J/g = 33400 J
The rate at which the heater provides energy is given by its power, which is 500W.
To calculate the time it takes to melt the ice, we can use the formula:
t = Q / P
where:
t = time (in seconds)
Q = energy required (in joules)
P = power of the heater (in watts)
Substituting the given values, we get:
t = 33400 J / 500 W = 66.8 seconds
What happens at Celsius's absolute zero?In fact, the lowest temperature that can be imagined is absolute zero. In absolute zero, neither heat nor motion are present. Absolute zero is found at a temperature of about 0 kelvin, or -273.15 degrees Celsius, and -460 degrees Fahrenheit.
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If earth was suddenly removed from the solar system what would happen to the moon? :
a- The moon would fall toward earths former location
b- he moon would move straight out of the solar system
c- The moon would continue to move in its current orbit
d- The moon would move into a new orbit under the influence of the sun
Without experiencing a major change in its orbit, the moon would keep revolving around the sun in the same direction.
If the Earth was suddenly removed from the solar system, the moon would continue to move in its current orbit. This is because the moon's orbit is not only influenced by the gravitational pull of the Earth, but also by the gravitational pull of the sun. The gravitational force of the sun on the moon is much stronger than the gravitational force of the Earth on the moon, as the sun is much more massive than the Earth.
Therefore, the moon would continue to orbit around the sun in its current path, without any significant change in its orbit. However, the absence of the Earth would cause significant changes in the rest of the solar system, as the gravitational interactions between the planets would be altered.
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Hhhhhhhhhhhhhhhhhhhhjj
Answer:
grrr I don't know either grrr
Calculate the wavelength for a sound wave with a frequency of 485 Hz. That has a sound wave in air has a frequency of 420 Hz
The wavelength for a sound wave with a frequency of 485 Hz. That has a sound wave in the air has a frequency of 420 Hz is 70.7cm and 81.7cm.
Wavelength = speed of sound/frequency
The speed of sound is approximately 343 meters per second.
For a sound wave with a frequency of 485 Hz, the wavelength would be:
wavelength = 343 m/s / 485 Hz = 0.707 m or 70.7 cm
For a sound wave in air with a frequency of 420 Hz, the wavelength would be:
wavelength = 343 m/s / 420 Hz = 0.817 m or 81.7 cm.
Wavelength is a fundamental concept in physics that refers to the distance between two consecutive points on a wave that is in phase, meaning that they are at the same point in their respective cycles. It is usually denoted by the Greek letter lambda (λ).
Wavelength is an important property of all types of waves, including electromagnetic waves (such as light), sound waves, and even waves in water. In general, the wavelength of a wave is inversely proportional to its frequency, which is the number of cycles that occur per unit of time. This means that waves with a higher frequency have a shorter wavelength, while waves with a lower frequency have a longer wavelength.
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Pablo lifts a bag of flour 0.8 m from the floor to a table. He lifted the bag using a force of 20 N. How much work did Pablo do on the bag of flour?
The amount of work done by Pablo is 16 J.
Work done problemThe work done by Pablo on the bag of flour is given by the formula:
work = force x distance x cos(theta)
where force is the magnitude of the force applied, distance is the distance moved by the object, and theta is the angle between the direction of the force and the direction of the displacement. In this case, the angle between the direction of the force and the direction of the displacement is 0 degrees (since Pablo lifted the bag straight up), so cos(theta) = 1. Substituting the given values, we get:
work = 20 N x 0.8 m x 1 = 16 J
Therefore, Pablo did 16 J of work on the bag of flour.
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The "hang time" of a punt is measured to be 4.30 s
.If the ball was kicked at an angle of 68.0 ∘ above the horizontal and was caught at the same level from which it was kicked, what was its initial speed?
t^2=10.97 sin(68)-3.05cos(68)/4.905cos(68)
t=2.2164
10.97/cos68 x 2.21= vo
I got v0=13.25
13.25/1000=.0133 x 3600=47.88 kh/m(which is wrong)
13.25 m/s = 47.88 km/h was roughly how fast the punt was moving at the time.
What, in physics, is speed, and what is its unit?The rate at which distance and time change is what is meant by speed. It has the aspect of temporal and spatial distance. The combination of a fundamental units of distance and time is what is described as the System of units ( si of speed. As a result, the SI unit for speed is the meter per second.
Describe velocity and speed.In contrast to velocity, which describes the speed and direction of the an object's movement, speed is the rate of movement along a path. Instead, velocity is a vector while speed is a scalar quantity.
t = (2 * v0 * sin) g
where (9.81 m/s2) is the acceleration caused by gravity.
In order to find t, we must solve for it as follows: t = (2 * v0 * sin) / g 4.30 ≈ (2 * v0 * sin68) / 9.81 v0 = (4.30 * 9.81) / (3 ) * sin68)
0.194 = 13.25 m/s
We may multiply this by 3.6 to get the speed in km/h: 13.25 m/s * 3.6 ≈ 47.88 km/h
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The initial speed 13.25 m/s = 47.88 km/h was roughly how fast the punt was moving at the time.
Speed in physics is measured in what unit?Speed refers to the rate at which distance and time change. It has a temporal and spatial distance component. The System of units (s of speed) is the amalgamation of fundamental units of time and distance. Consequently, the meter per second is the SI unit for speed.
Depict speed and speed :Speed is the rate of movement along a path, in contrast to velocity, which describes the speed and direction of an object's movement. Speed, on the other hand, is a scalar quantity while velocity is a vector.
t = (2 × v₀ × sin) g
where (9.81 m/s2) is the acceleration caused by gravity.
In order to find t, we must solve for it as follows:
t = (2 × v₀ × sin) / g 4.30 ≈ (2 × v₀ × sin 68) / 9.81 v₀
= (4.30 × 9.81) / (3 ) × sin 68)
0.194 = 13.25 m/s
We may multiply this by 3.6 to get the speed in km/h:
13.25 m/s × 3.6 ≈ 47.88 km/h
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Select the correct answer from each drop-down menu.
Jason is collecting evidence at a crime scene. He finds a bullet casing and unused ammunition. What should he look for on the casing itself? What will the unused ammunition tell him?
Jason should look for markings called__1__ on the casing. The unused ammunition will help determine if the casing was from the same__2__ as the unused ammunition.
Reset
Next
1. Rifling, casting, impression
2. Store, gun, lot
Answer:
Impression & Gun
Explanation:
Consider this question posed at the beginning of this task:
Will two charged objects (sticky tape) create electric force fields that allow them to interact without touching?
Did the investigation answer the question? Explain whether the investigation gave enough evidence to support the idea that invisible electric force fields exist.
The investigation presented did offer proof in favor of the existence of imperceptible electric force fields.
What is electric force?The force between two charged objects is the electric force, sometimes referred to as the Coulomb force. The interaction of charged particles produces this fundamental force of nature. The magnitudes of the charges on the two objects and the separation between them define the strength of the electric force.
The tape was observed to interact without touching when it was charged by rubbing the tape against one another. The formation of an electric field surrounding the charged tape, which pulls on other nearby charged items, can be used to explain this interaction.
Even though the electric field surrounding the charged tape was not explicitly measured or quantified, the observed interaction between the tape offers a weak indirection for its presence. Hence, the investigation did offer sufficient proof to back up the existence of undetectable electric force fields.
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Find the altitude of Earth’s geostationary orbit.
The mass of the Earth is 5.97 x 1024 kg.
The radius of Earth is 6.38 x 106 m.
Altitude of Earth's geostationary orbit is approximately 35,786 km above the surface of the Earth.
What is Geostationary?
Geostationary refers to an object in orbit around the Earth that appears to remain fixed in the same position above the Earth's surface. Specifically, a geostationary orbit is an orbit in which a satellite orbits the Earth at the same rate that the Earth rotates, so that the satellite appears to remain stationary relative to a fixed point on the Earth's surface.
The altitude of Earth's geostationary orbit can be found using the formula:
h = R(3/2) * √(M/m)
where:
h is the altitude of the geostationary orbit
R is the radius of the Earth
M is the mass of the Earth
m is the mass of the satellite
For a geostationary orbit, the satellite has a period of 24 hours, which means it orbits the Earth once every 24 hours. This requires the satellite to be at an altitude where its orbital period matches the Earth's rotational period, and this altitude is known as the geostationary orbit.
For a geostationary satellite, the mass of the satellite is negligible compared to the mass of the Earth, so we can assume that m is much smaller than M.
Plugging in the given values, we get:
h = (6.38 x 10^6 m) * (3/2) * √(5.97 x 10^24 kg / m)
h = 35,786 km
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The thermal energy of a system increases by 600 j, and 1400 j of heat is added to the system. how much work did the system do? responses a. 600 j b. 800 j c. 1400 j d. 2000 j
The correct answer is B. The system did 800 J of work.
ΔU = Q - W
we are given that ΔU = 600 J and Q = 1400 J.
W = Q - ΔU
W = 1400 J - 600 J
W = 800 J
Thermal energy is a type of energy that is related to the temperature of a system or object. It is a form of kinetic energy that results from the movement of particles in a substance. The faster the particles move, the higher the temperature and the greater the thermal energy of the substance.
In physics, thermal energy is often associated with heat transfer between two objects that are at different temperatures. This transfer of energy can occur through conduction, convection, or radiation. For example, when you touch a hot stove, the thermal energy from the stove is transferred to your hand, causing a sensation of heat.
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what are the differences in your experimental results between the perfectly elastic and inelastic collisions?
The main difference between perfectly elastic and inelastic collisions is that In a perfectly elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, the total kinetic energy of the system decreases.
Perfectly elastic collisions result in no loss of kinetic energy, whereas inelastic collisions result in a loss of kinetic energy. Collisions in which the kinetic energy is conserved are known as perfectly elastic collisions. Two billiard balls colliding are an example of a perfectly elastic collision because they have the same mass, and there is no deformation of the ball. As a result, in a perfectly elastic collision, both momentum and kinetic energy are conserved.In contrast, in an inelastic collision, kinetic energy is not conserved.
In an inelastic collision, two or more bodies come together and stick to one another after colliding. When two cars collide, for example, they do not bounce off each other; instead, they become deformed and stick together. A loss of kinetic energy is present in inelastic collisions because the deformation causes some of the energy to be converted to heat, sound, and other forms of energy that are not associated.
Therefore, the differences in the experimental results between perfectly elastic and inelastic collisions are due to the fact that inelastic collisions cause kinetic energy to be lost, while perfectly elastic collisions do not cause kinetic energy to be lost.
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The man is pushing this boulder to the right, but it will not move. Which of the following statements correctly describes the net force?
a)The net force is acting upward.
b) The net force is acting to the right.
C) The net force is zero, and all forces are balanced.
D) The net force is acting to the left.
Answer : The man is pushing this boulder to the right, but it will not move, The net force is acting to the left. The correct answer is option D
The net force acting on the boulder is the vector sum of all forces acting on the boulder. In this case, since the man is pushing the boulder to the right, there is an applied force to the right.
However, if the boulder is not moving, the net force must be zero, meaning that there must be an equal and opposite force acting to the left. Therefore, the correct statement is: The net force is acting to the left.
To understand this, we must consider the two components of net force: magnitude and direction. The magnitude of the net force is determined by how hard the man is pushing the boulder, while the direction is determined by the vector sum of all forces acting on the boulder.
Therefore, the correct statement is: The net force is acting to the left.
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Pablo and Jacob are running a half marathon. Jacob is d=54. 9m
behind Pablo, and both are running at the same speed, v0=3. 98m/s
. At a particular moment, Jacob begins to accelerate forward at a constant rate of a=0. 054m/s2
Jacob will catch up to Pablo in approximately 31.8 seconds.
What is constant rate?A constant rate is a fixed or unchanging speed at which a process occurs. It is a measurement of how much something changes in a given amount of time. For example, if a car is traveling at a constant rate of 60 miles per hour, it will cover 60 miles in one hour, regardless of any changes in speed or direction.
What is a constant rate example?An example of constant rate is the speed of a car traveling on a highway with no traffic or other obstacles. As long as the car maintains a steady speed, the rate of its movement remains constant. Another example could be the rate at which a chemical reaction proceeds under stable conditions.
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What happens to the capacitance of a parallel plate capacitor when it is connected to a battery and dielectric is inserted?
(pls help fast it's urgent)
Answer:
After the dielectric is inserted the capacitance is increased hence the stored energy is also increased . It may be noted here that since voltage between the capacitor V0 is constant the electric field between the plates also remains constant .
a 4.50 cm tall object is placed in front a convex mirror with a focal length of -(5.25 a) cm. if the magnification is 1/(2 b), what is the distance from the object to the mirror? give your answer in centimeters (cm) and with 3 significant figures
The distance between the object and the mirror is 13.96 cm, given to 3 significant figures.
The given data are as follows:Object height, h1= 4.50 cmFocal length of the convex mirror, f = −(5.25a) Magnification, m = 1/(2b)We are supposed to find the distance between the object and the mirror, u using the mirror formula. We can use the formula,1/f = 1/u + 1/vSince the mirror is convex, the focal length f is negative.
Therefore, substituting the values in the formula, we get,1/(-5.25a) = 1/u + 1/v⇒ −0.1905 = 1/u + 1/v…… (1)The magnification of an object is given by,m = −v/u where, m is the magnification, u is the distance of the object from the mirror and v is the distance of the image from the mirror. Substituting the values of m and solving for v, we get,v = m×u= (1/(2b))×u…… (2)
We are now supposed to solve the above equations to find the value of u. To do that, we have to substitute equation (2) into (1). On substituting, we get,−0.1905 = 1/u + 1/[(1/(2b))×u]Simplifying the above equation and cross multiplying, we get,(1/(2b))u − 0.1905u = −1On further simplification and solving for u, we get,u = 13.96 cm…… (3).
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A diverging mirror has a focal length of 20cm. An object is placed 30 cm from the mirror. Determine the image distance
The image distance is 60 cm if An object is placed 30 cm from the diverging mirror has a focal length of 20cm.
What is diverging mirror ?A concave mirror, also known as a converging mirror, has an inwardly recessed reflecting surface (away from the incident light). Concave mirrors focus light inward to a single focal point. They are used to concentrate light. Concave mirrors, unlike convex mirrors, produce different image types depending on the distance between the object and the mirror.
The mirrors are referred to as "converging mirrors" because they collect light that falls on them and refocus parallel incoming rays toward a focus. This is due to the fact that light is reflected at different angles at different spots on the mirror due to the fact that the normal to the mirror surface varies at each spot.
use mirror formula
[tex]\frac{1}{f}[/tex] = [tex]\frac{1}{v}[/tex] + [tex]\frac{1}{u}[/tex]
The image distance is 60 cm
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a wire carrying more electrons will transfer more energy than a wire giving fewer electrons. is this statement accurate? explain!
Answer:
Yes because provided the current is the same.
Amy wishes to measure the specific heat capacity of a piece of metal. She places the 75 g piece of metal in a pan of boiling water, then drops it into a cup holding 50 g of water at 22°C. The metal and the water come to an equilibrium temperature of 25°C.
a. Calculate the heat gained by the water.
b. Calculate the heat lost by the metal.
c. Calculate the specific heat of the metal.
Answer:
QL = heat lost = Sm * Mm * ΔTm
QL = Sm * 75 g * (212 - 25) = 14,000 Sm heat lost by metal
QG = 1 cal/gm deg C * 50 g * (25 - 22) = 150 cal / gm deg C gained water
Since heat loss = heat gained
Sm = 150 / 14,000 = .010 cal / gm deg C
D. Volume
10. If a tricycle drove to a passenger's house that is 20 meters away from the station
in 10 minutes. What is the speed of the tricycle?
The speed of the tricycle while going to passenger's home from the station is 0.03m/s.
The equation of motion says, V = D/T where, V is the speed, D is the distance covered and T is the time taken. Here it is given that the tricycle takes 20 minutes to reach a passenger's home that is 20m away from the station, So, putting the value in the standard form of the values,
10 minutes = 600 seconds.
Speed =distance/time
Speed = 20/600
Speed = 0.03 m/s.
So, the speed of the tricycle is 0.03m/s.
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Hi please help me solve this question… I’m confused…
Answer:
To calculate the work done by the teenager, we need to know the force applied and the distance moved.
Since we don't know the force applied, we can assume that it's equal to the weight of the teenager. The weight of the teenager can be calculated by multiplying their mass by the acceleration due to gravity, which is approximately 9.81 m/s^2:
weight = mass * acceleration due to gravity
weight = 46 kg * 9.81 m/s^2
weight = 451.26 N
The distance moved is equal to the height of 44 steps:
distance = height of 1 step * 44 steps
distance = 20 cm * 44
distance = 880 cm or 8.8 m
Now we can calculate the work done by the teenager using the formula:
work = force * distance * cos(theta)
where theta is the angle between the force and the direction of movement. Since the teenager is moving vertically upward, the angle theta is 0 degrees, and the cos(0) is equal to 1. Therefore, we can simplify the formula to:
work = force * distance
Plugging in the values we have calculated, we get:
work = 451.26 N * 8.8 m
work = 3977.488 J
Therefore, the work done by the teenager to get to your room is approximately 3977.5 joules.
A 0.250 kg toy car moving with a speed of .860 m/s collided with a wall. The figure shows the force exerted on the car by the wall over the course of the collision. What is the magnitude of the velocity, or final speed of the car in the collision?
Answer:
We can use the impulse-momentum theorem to solve this problem, which states that the change in momentum of an object is equal to the impulse applied to it. The impulse is given by the area under the force vs. time graph, which is shown in the figure.
First, we need to find the initial momentum of the car. Since the car is moving only in the x-direction, we can use the equation:
p_initial = m*v_initial
where p_initial is the initial momentum, m is the mass of the car, and v_initial is the initial velocity of the car. Plugging in the given values, we get:
p_initial = (0.250 kg)(0.860 m/s) = 0.215 kgm/s
Next, we need to find the change in momentum of the car, which is equal to the area under the force vs. time graph. We can approximate this area by dividing it into two triangles and a rectangle, as shown in the figure. The total area can be found as follows:
area = (1/2)(20 N)(0.002 s) + (20 N)(0.004 s) + (1/2)(10 N)(0.002 s)
= 0.06 Ns
Finally, we can use the impulse-momentum theorem to find the final momentum of the car, which is given by:
p_final = p_initial + impulse
where impulse is the area under the force vs. time graph. Plugging in the values, we get:
p_final = 0.215 kgm/s + 0.06 Ns = 0.275 kg*m/s
Since the mass of the car doesn't change during the collision, we can use the equation for momentum to find the final velocity of the car:
p_final = m*v_final
Solving for v_final, we get:
v_final = p_final / m = 0.275 kg*m/s / 0.250 kg = 1.1 m/s
Therefore, the magnitude of the velocity, or final speed of the car in the collision, is 1.1 m/s.
Explanation:
a few images below to understand.
A car traveling with an initial speed of 25 m/s decelerates at −5 m/s2 to a complete stop. What best approximates the distance the car travels during its deceleration?
Faults, folding ridges, mountains, valleys and volcanic arc are formed when the plates move because ????
Plate tectonics can result in the formation of faults, folding ridges, mountains, valleys, and volcanic arcs, among other geological features.
Plate tectonics is the scientific theory that explains how the Earth's lithosphere (its solid outermost layer) is broken up into several large plates that move relative to each other over the underlying asthenosphere (its partially molten layer). When plates move, they can interact with one another in a variety of ways, including colliding, spreading apart, and sliding past one another. Depending on the type of interaction and the characteristics of the plates involved, these interactions can produce a wide range of geological features.When plates move apart, magma from the earth's mantle can arise to fill the gap, forming new crust and forming mid-ocean ridges like the Mid-Atlantic Ridge. This is referred to as seafloor spreading.
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