A concave mirror of radius of curvature 10 cm is placed 30 cm from a thin convex lens of focal length 15 cm. Find the location and magnification of a small bulb sitting 50 cm from the lens by using the algebraic method.

Answers

Answer 1

To find the location and magnification of the small bulb using the algebraic method, we can apply the lens mirror formula and the magnification formula.

Given data:

Radius of curvature of the concave mirror (R) = -10 cm (negative sign indicates concave shape)

Distance between the concave mirror and the convex lens (d) = 30 cm

Focal length of the convex lens (f) = 15 cm

Distance of the small bulb from the convex lens (u) = 50 cm

Step 1: Find the image formed by the convex lens.

Using the lens formula, 1/f = 1/v - 1/u, where v is the image distance, we can rearrange the formula to solve for v:

1/v = 1/f - 1/u

1/v = 1/15 - 1/50

1/v = (50 - 15) / (15 * 50)

1/v = 35 / (15 * 50)

v = (15 * 50) / 35

v ≈ 21.43 cm

The image formed by the convex lens is located approximately 21.43 cm from the lens.

Step 2: Find the final image location using the concave mirror.

To find the final image location, we need to consider the image formed by the convex lens as the object for the concave mirror. The distance between the convex lens and the concave mirror is given as 30 cm. Therefore, the object distance for the concave mirror (u') is equal to 30 - 21.43 = 8.57 cm.

Using the mirror formula, 1/f = 1/v' - 1/u', where v' is the final image distance, we can rearrange the formula to solve for v':

1/v' = 1/f - 1/u'

1/v' = 1/(-10) - 1/8.57

1/v' = (-8.57 + 10) / (-10 * 8.57)

1/v' = 1.43 / (-10 * 8.57)

v' = (-10 * 8.57) / 1.43

v' ≈ -60 cm

The final image formed by the concave mirror is located approximately 60 cm in front of the mirror. The negative sign indicates that the image is virtual.

Step 3: Find the magnification.

The magnification (M) can be calculated using the formula:

M = -(v' / u')

M = -(-60 / 8.57)

M ≈ 7

The magnification of the image is approximately 7.

Therefore, the location of the final image formed by the small bulb is approximately 60 cm  in front of the concave mirror, and the magnification of the image is approximately 7.

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Related Questions

This refers to the ability of the joints to move through a full range of motion

Answers

Answer:

Flexibility is the ability of a joint or series of joints to move through an unrestricted, pain free range of motion. ... These soft tissues include: muscles, ligaments, tendons, joint capsules, and skin.

Explanation:

Determine the velocity and acceleration of the peg A which is confined between the vertical guide and the rotating slotted rod.
a) Cannot be determined from the given information
b) Velocity is constant, acceleration is zero
c) Velocity is increasing, acceleration is constant
d) Velocity is decreasing, acceleration is zero

Answers

a) Cannot be determined from the given information. The reason for this is that we are not provided with any information about the speed of the rotating slotted rod or any other forces acting on the peg.

Without this information, it is impossible to determine the velocity or acceleration of the peg A. Velocity is the rate of change of position over time, while acceleration is the rate of change of velocity over time. Without knowing the speed of the rotating slotted rod or any other external forces acting on the peg, we cannot determine its velocity or acceleration. Therefore, option a) is the correct answer.
Your answer: a) Cannot be determined from the given information. To accurately determine the velocity and acceleration of peg A confined between the vertical guide and the rotating slotted rod, additional information such as the dimensions, rotational speed of the rod, and initial conditions are required. Without these specifics, it's impossible to establish the precise behavior of peg A within the system.

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7 points
Lynn is walking up a hill with a horizontal distance of 20m and a vertical
distance of 12m. What is her displacement at the top?*
16.9m
23.3m
26.4m
34.5m
Other:

Answers

Answer:

displacement = 23.32m___________________FOLLOW ME

What's the Closest Planet to Earth?

Answers

The closest planet to Earth is Venus. Venus is the second planet from the sun and is the brightest natural object in the night sky after the moon.

It is often referred to as the Earth's twin because it is similar in size, mass, and composition. In terms of distance, Venus is the closest planet to Earth, with an average distance of 41 million kilometers or 25 million miles.

Venus is known for its thick atmosphere which consists mostly of carbon dioxide and traps heat, making it the hottest planet in our solar system. The temperature on the planet's surface can reach up to 460°C or 860°F, which is hot enough to melt lead.

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What is asexual reproduction?
List the various and describe four types of asexual reproduction.
What is sexual reproduction?
Why is sexual reproduction beneficial?

Answers

Answer:

there are a number of types of asexual reproduction including fission, fragmentation, budding, vegetative reproduction, spore formation and gamogenesis. Spore formation occurs in plants, and some algae and fungi, and will be discussed in additional concepts

the production of new living organisms by combining genetic information from two individuals of different types (sexes). In most higher organisms, one sex (male) produces a small motile gamete which travels to fuse with a larger stationary gamete produced by the other (female)

The advantages of sexual reproduction: produces genetic variation in the offspring. the species can adapt to new environments due to variation, which gives them a survival advantage. a disease is less likely to affect all the individuals in a population.

Explanation:

Which option is an example of an object that has potential energy followed by an object that has kinetic energy?

Answers

A ball held over a person's head | a ball rolling on the floor is an example of an object that has potential energy followed by an object that has kinetic energy.

What is Kinetic energy?

This is the type of energy possessed by a body by virtue of its motion or movement.

The rolling ball therefore has kinetic energy while a ball being held over a person's head has potential energy which is the energy possessed by a body by virtue of its position.

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Jamie wanted to see what kitchen cleaner worked best for cleaning her counters. He used Lysol, Clorox, Pinesol, and just water. For each cleaner, he put 5 milliliters of grape juice on the counter, sprayed the cleaner, and wiped it with one paper towel.

Independent Variable (IV):

Answers

Explanation:

Independent Variables are constants. They do not affect the result of the experiment.

In this problem, Jamie used Lysol, Clorox, Pinesol, and just water for cleaning her kitchen counter. For each cleaner, he put 5 milliliters of grape juice on the counter, sprayed the cleaner, and wiped it with one paper towel.

It means, the cleaning products like Lysol, Clorox, Pinesol, water did not depend on anything. They remain constant throughout the experiment. Also, paper towel comes under Independent Variables.

Answer:

No need for explanaxition

Explanation:

Independent variable : Lysol, Clorox, Pinesol, and just plain water. Dependent variable : How clean the counter is Constant : the amount of cleaning product and the brand of the paper towel

write the function in terms of unit step functions. find the laplace transform of the given function. f(t) = 5, 0 ≤ t < 2 −4, t ≥ 2

Answers

The Laplace transform of the given function f(t) is \(5/s - 5/s * e^{(-7s)} - 3/s * e^{(-7s)}.\)

What is Laplace transform?

The Laplace transform is an integral transform that converts a function of time (commonly denoted as f(t)) into a function of a complex variable s (commonly denoted as F(s)). It is named after the French mathematician Pierre-Simon Laplace, who introduced this mathematical tool.

The given function can be expressed using unit step functions as follows:f(t) = 5[u(t) - u(t - 7)] - 3[u(t - 7)]Here, u(t) represents the unit step function.

To find the Laplace transform of f(t), we can apply the linearity property of the Laplace transform. The Laplace transform of the unit step function u(t - a) is 1/s * e^(-as), where 'a' is a constant.

Using the linearity property, the Laplace transform of f(t) can be calculated as:L{f(t)} = L{5[u(t) - u(t - 7)] - 3[u(t - 7)]}= 5 * L{u(t) - u(t - 7)} - 3 * L{u(t - 7)}Applying the Laplace transform to each term:L{u(t)} = 1/sL{u(t - 7)} = 1/s * e^(-7s)

Therefore,L{f(t)} = \(5 * (1/s - 1/s * e^{(-7s)}) - 3 * (1/s * e^{(-7s)})= 5/s - 5/s * e^{(-7s)} - 3/s * e^{(-7s)}\)So, the Laplace transform of the given function f(t) is \(5/s - 5/s * e^{(-7s)} - 3/s * e^{(-7s)}.\)

Therefore, the Laplace transform of the given function f(t) is \(5/s - 5/s * e^{(-7s)} - 3/s * e^{(-7s)}.\)

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A car moving east at a velocity of 16.0 m/s collides with a stationary truck with exactly twice the mass. If the two vehicles lock together, calculate the velocity of their combined mass immediately after collision

Answers

Answer:

5.33ms-¹

Explanation:

that is the procedure above

A car moving east at a velocity of 16.0 m/s collides with a stationary truck with exactly twice the mass.

TRUE or FALSE

A front door peephole is a convex lens.

Answers

Answer:

it is Trueeeee

Consider a car at rest. We can conclude that the downward gravitational pull of the Earth on the car and the upward contact force of the Earth on it are equal and opposite because: A) The two forces form an interaction pair B) The net force on the car is zero C) Neither of the above?

Answers

We can say that the downward gravitational pull of the Earth on the car and the upward contact force of the Earth on it are equal and opposite because the two forces form an interaction pair.

According to Newton's Third Law of Motion, for every action force, there is an equal and opposite reaction force. In the case of the car at rest, the action force is the gravitational force exerted on the car by the Earth, which is directed downwards. The reaction force is the contact force exerted on the car by the Earth, which is directed upwards.

Since these two forces are equal and opposite, we can conclude that the net force on the car is zero. Mathematically, we can represent this as:

F_gravity = -F_contact

where F_gravity is the gravitational force exerted on the car by the Earth, and F_contact is the contact force exerted on the car by the Earth.

By adding the two forces, we get:

F_net = F_gravity + F_contact = 0

This means that the car is in a state of equilibrium, and there is no net force acting on it.

In conclusion, we can conclude that the downward gravitational pull of the Earth on the car and the upward contact force of the Earth on it are equal and opposite because the two forces form an interaction pair. This relationship is explained by Newton's Third Law of Motion, which states that every action force has an equal and opposite reaction force. Since the net force on the car is zero, it is in a state of equilibrium.

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The map shows Earth's ocean conveyor belt. What effect does the ocean conveyor belt have on coastal climates

Answers

The ocean conveyor belt is a global system of deep and surface ocean currents that circulate water around the world. It is driven by differences in water density, temperatures, and salinity.

What is salinity ?

Salinity is the measure of the amount of dissolved salts in a given volume of water. It is typically expressed as parts per thousand (ppt) or parts per million (ppm). Salinity can be found in most bodies of water, including oceans, rivers, and lakes. Salinity levels can vary greatly depending on the source of the water, the amount of rainfall, and other factors. In general, the higher the salinity, the more difficult it is for organisms to survive in the water. High salinity levels can also affect the taste and smell of the water, and can be an indicator of water pollution. Salinity can also be an important factor for many human activities, such as agriculture, industry, and navigation.

The ocean conveyor belt has a huge effect on coastal climates by transporting heat from the tropics to higher latitudes, where it is released into the atmosphere. This helps warm coastal climates, resulting in milder winters and cooler summers. It also helps to reduce the effects of extreme weather events such as droughts and floods, by moderating temperatures and redistributing moisture.

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Which of these results in kinetic energy of an object? (1 point)
Oposition
O motion
O mass
volume

Answers

Motion I’m pretty sure

Answer:

B. Motion

Explanation:

Kinetic energy is a property of a moving object or particle and depends on the motion and its mass.

Hope this helps!

Alan and Monica tested how fertilizer X affected the growth of a plant. Alan and Monica put 100 grams of fertilizer X in pot 1. They put 0 grams of fertilizer X in pot 2.
What is pot 2 called in science?
A.
a test group
B.
a data group
C.
an observational group
D.
a control group

Answers

Answer:

D.

a control group

Explanation:

In a scientific experiment such as the one above, there is an experimental group and a control group. The experimental group is the group that receives the treatment while the control group does not receive any treatment. The control group helps the researcher to observe if the treatment had any significant effect.

In this case, it will help Alan and Monica to determine if fertilizer X actually had an effect on the plant. Therefore, the pot with o grams of fertilizer in it is the control group.

A body of mass 3 kg and volume 4 x 10^m' is hung from a balance
graduated in Newton. What is the reading of the balance when the
body is
a. In air;
b. Fully immersed in water
immersed in water.​

Answers

Answer:

it's b I guess not sure

Explanation:

The reading of the balance for a body with mass 3kg and volume 4 × 10⁻⁴ in air and when fully immersed in water are 29.4N and 25.5N, respectively.

What is weight?

The weight of an object is the force which is acting on the object due to the influence of gravity. Weight is a vector quantity because it has both the magnitude and direction. The gravitational force acts on the object.

The reading of the balance when the body is in air, W = mg = (3) × (9.8) = 29.4 N

The reading of the balance when the body is fully immersed in water is:

F = mg − ρgV = (3) × (9.8) − (1000) × (9.8) × (0.0004) = 25.5 N

Therefore, the reading of the balance in the given conditions are 29.4N and 25.5N.

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Henry is at the state fair. At one booth he throws a 0.70 kg ball forward with a velocity of 22.0 m/s in order to hit a 0.15 kg bottle sitting on a shelf. When the ball makes contact the bottle goes flying forward at 29.0 m/s. What is the velocity of the ball after it hits the bottle?

Answers

The velocity of the ball after it hits the bottle is 15.8 m/s

Let m₁ represent the mass of the ball, m₂ the mass of the bottle, u₁ the velocity of ball before impact, u₂ the velocity of bottle before impact, v₁ the velocity of ball after impact and v₂ the velocity of bottle after impact.

Given that:

m₁ = 0.7 kg, m₂ = 0.15 kg, u₁ = 22 m/s, u₂ = 0, v₂ = 29

momentum before impact = momentum after impact, hence:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

0.7(22) + 0.15(0) = 0.7v₁ + 0.15(29)

0.7v₁ = 11.05

v₁ = 15.8 m/s

Therefore the velocity of the ball after it hits the bottle is 15.8 m/s

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a ball is at rest in frame s'. what is the speed of the ball in frame s? express your answer in meters per second.

Answers

The ball moves with a velocity of v' = 0 in frame S when u = v = 5 m/s and There is no value of v that would result in the ball having a minimum velocity in frame S'.

How fast is the specified direction moving?

Speed in a certain direction is referred to as velocity. Velocity provides information on how quickly or slowly an object is travelling in a certain direction.

In order to determine in which reference frame the ball moves faster, we need to compare the velocity of the ball in both frames S and S'. We can use the Galilean transformation equations to relate the velocities in the two frames:

v' = v - u

0 = v - u

v = u

So the ball moves with a velocity of u in frame S, in the direction opposite to the motion of frame S'.

0 = v - u

v' = v - u

v' = -u

So the ball moves with a velocity of -u in frame S', in the direction opposite to the motion of frame S.

0 = v - v'

v = v'

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Question:

In which reference frame, Sor S', does the ball move faster? 10 m/s 4 m/s in s 2. Frame S' moves relative to frame S as shown. a. A ball is at rest in frame S'. What are the speed and direction of the ball in frame S? -5 m/s b. A ball is at rest in frame S. What are the speed and direction of the ball in frame S'? 3. Frame S' moves parallel to the x-axis of frame S. a. Is there a value of v for which the ball is at rest in S'? If so, what is v? If not, why not? 5 m/s Velocity 4 in S 3 b. Is there a value of v for which the ball has a minimum speed in S'? If so, what is v? If not, why not?

What would happen to a current in a circuit if the resistance is multiplied by four

Answers

Answer:

The current would be multiplied by 1/4, meaning it is reduced by 3/4 of itself.

Explanation:

This is because when the resistance increases, the current decreases along with it.

I’m positive that answer is correct

is climbing stairs work done​

Answers

Answer:

The work you did in climbing the stairs is the force you applied (your weight) times the distance you moved upward (the height of the stairs.) So yes, climbing stairs is work done.

Explanation:

Hope this helped, nya~ :3

Which statement explains why 49 is a perfect square?

Answers

It’s the product of 7 x 7. The square root of 49 is 7

Answer:

It’s the product of 7 x 7. The square root of 49 is 7

Explanation:

It’s the product of 7 x 7. The square root of 49 is 7

Conversion Chart Temperature °C= 5/9 (°F - 32) Time 60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day Mass 1 pound = 16 ounces 1 ounce = 28.35 grams 1000 milligrams = 1 gram 1000 grams = 1 kilogram Length 1 mile = 1.6 kilometers 1 inch = 2.54 centimeters 100 centimeters = 1 meter 1000 meters = 1 kilometer Conversions for temperature, time, mass, and length.
1. 46,756,790 mg = _______ kg
2. 5.6 hours = ________ seconds
3. 13.5 cm = ________ inches
4. 47 °F = _______ °C

Answers

46,756,790 mg = 46.75679 kg

5.6 hours = 20,160 seconds

13.5 cm = 5.315 inches

47 °F = 8.333 °C

To convert milligrams (mg) to kilograms (kg), we divide the value by 1,000,000 (since there are 1,000,000 milligrams in a kilogram). Therefore, 46,756,790 mg divided by 1,000,000 equals 46.75679 kg.

To convert hours to seconds, we multiply the value by 3,600 (since there are 3,600 seconds in an hour). Therefore, 5.6 hours multiplied by 3,600 equals 20,160 seconds.

To convert centimeters (cm) to inches, we divide the value by 2.54 (since there are 2.54 centimeters in an inch). Therefore, 13.5 cm divided by 2.54 equals 5.315 inches.

To convert Fahrenheit (°F) to Celsius (°C), we use the formula °C = 5/9 (°F - 32). Plugging in the value 47 °F into the formula, we get °C = 5/9 (47 - 32), which simplifies to °C = 5/9 (15) = 75/9 ≈ 8.333 °C.

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A 40,000kg rocket traveling at 220 m/s expels 300kg worth of gases at what velocity?

Answers

Hi there!

We can use the conservation of momentum to solve.

\(m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'\)

m1 = mass of rocket (40,000 kg)

m2 = mass of gas (300 kg)

v1, v2 = INITIAL velocities of rocket and gas (0 m/s)

v1' = FINAL velocity of rocket (+220 m/s, assuming UP to be positive)

v2' = FINAL velocity of gas (- ? m/s, DOWNWARD so negative)

This is an example of a "recoil" collision, so:

\(0 = m_1v_1' + m_2(v_2')\)

Set the two equal:

\(m_2(-v_2') = m_1v_1'\)

Plug in the givens:

\(300(-v_2') = (40,000)(220)\\\\\)

\(\v_2 = \boxed{-29,333.33 m/s}\)\(v_2 = \boxed{-29,333.33 m/s}\)

How can you confirm/show that decay is exponential? (when talking about damped oscillations) What is responsible for the damping force? Why?

Answers

Answer:

Following are the solution to this question:

Explanation:

In this question, it is usually designing the question with difference calculus but instead demonstrate there is an empirical term for both the answer of a nonlinear equation is the decay, Throughout the preliminary training programs, the origin of a damping word is usually resistance or Rossiter.

Magnesium Oxide Reaction

Answers

Answer:

When magnesium reacts with oxygen, it produces light bright enough to blind you temporarily. Magnesium burns so bright because the reaction releases a lot of heat. As a result of this exothermic reaction, magnesium gives two electrons to oxygen, forming powdery magnesium oxide (MgO).

Answer:

Mg+O2 -----MgO

balanced equation

2Mg+O2-------2MgO

An airplane travels for 2.5 hours at an average rate
of 130 miles per hour. Use the distance formula, d=rt, to find how
far the plane travels.

Answers

The plane travels a distance of 325 miles if the airplane travels for 2.5 hours at an average speed of 130 miles per hour. Using the distance formula (d = rt), we can calculate the distance.

To find the distance traveled by the airplane, we can use the distance formula, which is represented as d = rt. In this formula, "d" represents the distance, "r" represents the rate or speed at which the object is traveling, and "t" represents the time taken for the travel.

Given that the airplane travels for 2.5 hours at an average rate of 130 miles per hour, we can substitute these values into the formula. The rate of the airplane is 130 miles per hour, and the time taken is 2.5 hours.

Using the formula, we can calculate the distance traveled as follows:

d = rt

d = 130 mph × 2.5 hours

Multiplying the rate (130 mph) by the time (2.5 hours) gives us:

d = 325 miles

Therefore, the airplane travels a distance of 325 miles during the 2.5 hours of travel at an average rate of 130 miles per hour.

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Which of the following best explains what creates this convection current?
options:

The rotation of Earth makes the air above it rotate, but not the same over land and water.


Because of its mass, Earth's gravity creates a high pressure area over both the land and water.


Salt in the ocean makes it more dense than the land, so its gravity pulls more on the air above it.


During the evening, the land cools off more quickly than the water. The cooler land cools the air above it, while the warmer water warms the air above it. These differences in air temperature create the convection.

Which of the following best explains what creates this convection current?options:The rotation of Earth

Answers

Answer:

During the evening, the land cools off more quickly than the water. The cooler land cools the air above it, while the warmer water warms the air above it. These differences in air temperature create the convection.

Explanation:

sorry I took forever

help me please and thank uuuu

help me please and thank uuuu

Answers

Answer:

45° should be the correct one

Answer:

45° should be the correct one

Explanation:

A vertical piston-cylinder device initially contains 0.1 m^3 of air at 400 K and 100 kPa. At this initial condition, the piston is resting on a stop. The piston-cylinder device is connected to a supply line with air at 400 K and a pressure of 500 kPa. The valve between the supply line and the piston-cylinder device is opened and is left open until the pressure in the piston-cylinder device reaches 500 kPa. The piston is observed to start moving when the pressure in the cylinder is 200 kPa and the piston continues to rise until it reaches a second stop. At the second stop, the piston-cylinder volume is 0.2 m^3 . The final temperature and pressure in the piston-cylinder device are 440 K and 500 kPa, respectively. Determine the heat transfer to or from the piston-cylinder device for the filling process Determine heat transfer (kJ) during the entire process.

Answers

Answer:

\(Q=-38.15kJ\)

Explanation:

From the question we are told that

Piston-cylinder initial Volume of air \(v_1=0.1 m^3\)

Piston-cylinder initial temperature \(T_1=400k\)

Piston-cylinder initial pressure \(P_1= 100kpa\)

Supply line temperature\(T_s=400k\)

Supply line pressure \(P_s= 500kpa\)

Valve  final pressure \(P_v=500kpa\)

Piston movement pressure \(P_m=200kpa\)

Piston-cylinder final Volume of air\(v_2=0.2 m^3\)

Piston-cylinder final temperature \(T_2=440k\)

Piston-cylinder final pressure \(P_2= 500kpa\)

Generally the  equation for conservation of mass is mathematically given by

\(Q=m_2 \mu_2-m_1 \mu_1 +W-(m_2-m_1)h\)

where

Initial moment

\(m_1=\frac{p_1 V_1}{RT_1}\)

\(m_1=\frac{100*0.1}{0.287*400}\)

\(m_1=8.7*10^-^2kg\)

Final moment

\(m_2=\frac{p_2 V_2}{RT_2}\)

\(m_1=\frac{500*0.3}{0.287*440}\)

\(m_1=79*10^{-2}kg\)

Work done by Piston movement pressure

\(W=Pd\)

\(W=P(v_2-v_1)\)

\(W=200(0.2-0.1))\)

\(W=20000J\)

Heat function

\(h=cT_1\)

\(h=1.005(400)\)

\(h=402\)

Therefore

\(Q=(0.792*0.718(440)-0.0871*0.718(400)+20-(0.792-0.087)*402))\)

\(Q=-38.15kJ\)

It is given mathematically that the system lost  or dissipated Heat of

\(Q=-38.15kJ\)

Two 1-kg objects, C and D, increase in temperature by the same amount, but the
thermal energy transfer of object C is greater than the thermal energy transfer of
object D. If object C has a specific heat of 235 J/kg-K, which material might object
D be made of?
(A) aluminum
(B) brass
(C) iron
(D) lead

Answers

The object D is made up of material Lead. The correct option is D.

What is specific heat?

The specific heat is the amount of heat required to change the temperature by 1°C. It is denoted by C.

Two 1-kg objects, C and D, increase in temperature by the same amount, but the thermal energy transfer of object C is greater than the thermal energy transfer of object D. The object C has a specific heat of 235 J/kg-K.

Q = m C ΔT

Qc > Qd

The energy transfer is proportional to specific heat.

Specific heat of D must be less. The possible material with specific heat less than the given value is for Lead material.

Thus, the correct option is D.

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two identical speakers that face each other and that are separated by a distance of emit a constant tone in phase. you stand in line with the speakers such that your right ear is exactly halfway between the two speakers, resulting in your left ear being closer to one speaker than the other. you notice that what you hear in your right ear is loud, but in your left ear you hear almost nothing. given that your hearing is fine in both ears and the distance between your ears is , what are the two lowest frequencies that the speakers could possibly be emitting?

Answers

This is an example of a standing wave interference pattern, where sound waves interfere constructively at certain points and destructively at others.

The distance between the speakers is not given, so we'll call it d. We'll also call the distance from each speaker to your ears x and y, respectively. Using the formula for the path difference for constructive interference, we have:

path difference = mλ, where m is an integer and λ is the wavelength of the sound wave.

For the first case, m = 0 (since the distance from the midpoint between the speakers to your right ear is an exact multiple of the wavelength), so the path difference is zero. For the second case, m = 1 (since the distance from the midpoint between the speakers to your left ear is one-half of a wavelength more than an exact multiple of the wavelength), so the path difference is λ/2. Equating these two expressions for the path difference, we get:

λ/2 = d sinθ, where θ is the angle between the line connecting the two speakers and the line connecting your left ear to the midpoint between the speakers.

Since the speakers are facing each other, the angle between them is 180 degrees, so sinθ = sin(180 - θ) = sinθ. Therefore:

λ = 2d sinθ.

The two lowest frequencies correspond to the longest wavelengths that fit between the speakers, which occur when the wavelength is twice the distance between the speakers (i.e., one full wavelength fits between them) and four times the distance between the speakers (i.e., two full wavelengths fit between them). Therefore:

λ1 = 2d, f1 = v/λ1 = v/2d,

λ2 = 4d, f2 = v/λ2 = v/4d,

where v is the speed of sound.

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