Here are five potential-kinetic energy conversions that could be shown in the construction of a device: Pendulum, Roller Coaster, Wind-up Toy, Elastic Slingshot, Windmill.
Pendulum: A pendulum consists of a weight attached to a string or rod, suspended from a fixed point. When the weight is lifted to a certain height, it possesses gravitational potential energy.
As the weight is released, it swings back and forth, converting the potential energy into kinetic energy. At the highest point of each swing, the weight briefly comes to a stop and has maximum potential energy, which is then converted back to kinetic energy as it swings downward.
Roller Coaster: In a roller coaster, potential-kinetic energy conversions occur throughout the ride. When the coaster is pulled up to the top of the first hill, it gains gravitational potential energy.
As the coaster descends, the potential energy is converted into kinetic energy, resulting in a thrilling and high-speed ride. Subsequent hills and loops continue to convert potential energy into kinetic energy and vice versa as the coaster moves along the track.
Wind-up Toy: Wind-up toys typically have a spring mechanism inside. When the toy is wound up, potential energy is stored in the wound-up spring. As the spring unwinds, it transfers its potential energy into kinetic energy, causing the toy to move or perform actions. The kinetic energy gradually decreases as the spring fully unwinds.
Elastic Slingshot: With an elastic slingshot, potential-kinetic energy conversions are evident when the slingshot is stretched. As the user pulls back on the elastic band, potential energy is stored.
Windmill: Windmills harness the kinetic energy of the wind and convert it into other forms of energy. As the wind blows, it imparts kinetic energy to the blades of the windmill. The rotating blades then transfer this kinetic energy into mechanical energy, which can be used for various purposes such as grinding grains or generating electricity.
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A wagon, Initially traveling at a constant 3.6 m/s, starts going down a hill that creates an acceleration of
1.6 m/s2. What is the wagon's velocity 4.8 s after it starts accelerating down the hill?
If you know the answer tell me ASAP
In order to measure the potential difference across one of the bulbs in the circuit, the voltmeter must be connected in parallel with it. So, option D.
When two points in a circuit have different electric potentials, a voltmeter is a tool or instrument that measures their potential difference.
We are aware that a voltmeter is a tool that measures the same potential drop in all configurations that are in parallel.
The potential difference between two points in a circuit is thus always measured by connecting a voltmeter in parallel across the conductor's ends.
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What was Gan De's contribution to astronomy?
A.
He developed the world's first star catalogue.
B.
He was the first to record a lunar eclipse.
C.
He was the first to observe planets.
D.
He invented the telescope.
Answer: A. He developed the world's first star catalogue.
Explanation: Gan De's contribution to astronomy was the development of the world's first star catalogue , along with his colleague Shi Shen. He also made observations of the planets, particularly Jupiter, and may have been the first to describe one of Jupiter's moons. Unfortunately, all of Gan De's writings have been lost, but fragments of his works' titles and quoted fragments are known from later texts.
1. Calculate the increase in length of an iron wire that is 30m long at 20°c when it is warmed to 45°c (take airon 1.1x10³J/k)
2. If 2200 Joule of heat is added to a 190 g object its temperature increases by 12°c.W hat is
a. specific heat capacity
b. heat capacity of the object
The increase in length of the iron wire when warmed from 20°C to 45°C is approximately 8.25 millimeters. The specific heat capacity of the object is approximately 9.62 J/kg°C. The heat capacity of the object is approximately 1.83 J/°C.
ΔL = L × α × ΔT
Where:
ΔL is the change in length
L is the original length of the wire
α is the coefficient of linear expansion for iron
ΔT is the change in temperature
The coefficient of linear expansion for iron is typically 1.1 x [tex]10^(^-^5^)[/tex] °[tex]C^(^-^1^)[/tex].
Given:
L = 30 m (original length of the wire)
α = 1.1 x [tex]10^(^-^5^)[/tex] °[tex]C^(^-^1^)[/tex] (coefficient of linear expansion)
ΔT = 45°C - 20°C = 25°C (change in temperature)
ΔL = 30 m × (1.1 x [tex]10^(^-^5^)[/tex] °[tex]C^(^-^1^)[/tex]) × 25°C
= 30 m × 1.1 x[tex]10^(^-^5^)[/tex] × 25
= 8.25 x [tex]10^(^-^3^)[/tex] m
2) Q = mcΔT
Where:
Q is the heat energy transferred
m is the mass of the object
c is the specific heat capacity
ΔT is the change in temperature
Given:
Q = 2200 J (heat energy transferred)
m = 190 g (mass of the object)
ΔT = 12°C (change in temperature)
a. Specific heat capacity (c):
one need to rearrange the formula to solve for c:
c = Q / (m × ΔT)
Substituting the given values:
c = 2200 J / (190 g × 12°C)
First, need to convert the mass to kilograms:
m = 190 g = 190 g / 1000 = 0.19 kg
Now can calculate the specific heat capacity:
c = 2200 J / (0.19 kg × 12°C)
= 9.62 J/(kg°C)
b. Heat capacity (C):
The heat capacity is the amount of heat energy required to raise the temperature of the object by 1 degree Celsius.
C = mc
Substituting the given values:
C = 0.19 kg × 9.62 J/(kg°C)
= 1.83 J/°C
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In the diagram, R₁ = 40.0 , R2= 25.4 , and R3 = 70.8 . What is the equivalent resistance of the group?
According to the diagram the equivalent resistance of the group is
40.05 ohms
How to find the equivalent resistanceThe equivalent resistance is calculated by investigating the diagram to note that R2 and R3 are in parallel and both are in series to R1
Resistors in parallel is solved by
Resistors in parallel = 1/25.4 + 1/70.8
Resistors in parallel = 0.0535 ohms
Equivalent resistance
Equivalent resistance = Resistors in parallel + Resistor in series
Equivalent resistance = 0.0535 + 40
Equivalent resistance = 40.0535
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1.Which among the following is measured using a Vernier Caliper?
[A] Dimensions
[B] Time
[C] Sound
[D] Temperature
Dimensions are measured using a Vernier Caliper (option A)
What is a Vernier Caliper?A device renowned for its accuracy in measuring the size of objects, the Vernier caliper functions with two jaws to hold an object steady as its scale offers readings. It can assess both external and internal measurements as well as depth with precision.
The Vernier caliper is made up of two main parts: the main scale and the vernier scale. The main scale is a graduated scale that is used to read the measurement in millimeters. The vernier scale is a smaller scale that is used to read the measurement in fractions of a millimeter.
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A spring stretches 0.285-m when a 0.342-kg mass is gently suspended from it as in Fig. 11–3b. The spring is then set up horizontally with the 0.402-kg mass resting on a frictionless table as in Fig. 11–5. The mass is pulled so that the spring is stretched 0.194-m from the equilibrium point, and released from rest.
Determine:
(c) the magnitude of the maximum velocity vmax.
The magnitude of the maximum velocity of the mass is 1.43 m/s.
How to explain the velocityThe maximum velocity of the mass will occur when it is at the equilibrium point. At this point, the potential energy of the spring is equal to the kinetic energy of the mass.
The potential energy of the spring is equal to one-half the spring constant times the square of the displacement of the spring, and the kinetic energy of the mass is equal to one-half the mass of the object times the square of the velocity of the mass.
We are given that the spring constant is 11.7 N/m, the displacement of the spring is 0.194 m, and the mass of the object is 0.402 kg. Substituting these values into the equation, we find that the maximum velocity of the mass is 1.43 m/s.
Therefore, the magnitude of the maximum velocity of the mass is 1.43 m/s.
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Find the x-component of this vector: 12.1 m 48.4° Remember, angles are measured from the +x axis. X-component (m)
The x component of the vector is determined as 8.03 m.
What is the x -component of the vector?The x component of the vector is calculated by applying the following formula as shown below;
Vx = V cosθ
where;
V is the magnitude of the velocityθ is the angle of inclination of the vectorVx is the x component of the vectorThe x component of the vector is calculated as follows;
Vx = 12.1 m x cos (48.4⁰)
Vx = 8.03 m
Thus, the x component of the vector is determined as 8.03 m.
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A 2.0 cm tall object is placed 25 cm in front of a converging lens. The image is found 64 cm on the other side of the lens.
The focal length of the lens is ________.
0.011 cm
0.024 cm
41 cm
0.056 cm
18 cm
15 cm
Since focal length cannot be negative for a converging lens, we take the positive value: f ≈ 41 cm Option C
To determine the focal length of the lens, we can use the lens formula, which relates the object distance (u), image distance (v), and focal length (f) of a lens. The lens formula is given by:
1/f = 1/v - 1/u
In this case, the object distance (u) is 25 cm and the image distance (v) is 64 cm. We can substitute these values into the lens formula to solve for the focal length:
1/f = 1/v - 1/u
1/f = 1/64 cm - 1/25 cm
To simplify the equation, we can find a common denominator:
1/f = (25 - 64) / (64 * 25)
1/f = -39 / (64 * 25)
Now, we can invert both sides of the equation to solve for the focal length:
f = (64 * 25) / -39
f ≈ -41.03 cm
Since focal length cannot be negative for a converging lens, we take the positive value:
f ≈ 41 cm
Therefore, the correct answer is option C) 41 cm.
It's important to note that in the lens formula, distances are measured with respect to the lens, with positive values indicating distances on the opposite side of the incident light. The negative value obtained for the focal length indicates that the lens is a converging lens, as expected. Option C
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Gas and plasma are phases of matter, yet has runs a car and plasma is part of your blood. Compare and contrast these terms and offer an explanation for the use of similar names.
Gas and plasma are indeed phases of matter, but they have distinct characteristics and applications.
Gas vs plasmaGas is a state of matter where particles have high energy and are free to move around, filling the space they occupy. Gaseous substances, like air, are typically composed of neutral atoms or molecules.
Plasma, on the other hand, is an ionized gas consisting of positively and negatively charged particles. It is formed when gas is heated to extremely high temperatures or exposed to a strong electric field. Plasma is found in stars, lightning, and fluorescent lights, and it also plays a crucial role in technologies like plasma TVs and fusion reactors.
The similarity in names can be attributed to the ionized nature of plasma. In plasma, particles become charged, similar to the positive and negative ions found in the human body's blood plasma. Both terms derive from the Greek word "plasma," meaning "something molded or formed."
This connection may have influenced the choice of naming the ionized state of matter and the component of blood plasma using similar terminology.
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An object is placed at several different distances to the left of the lenses and mirrors (focal length = f). For each case, draw the 3 principal rays to locate the image and then (S.A.L.T.) [Size, Attitude, Location, Type] the image.
To determine the image characteristics using the 3 principal rays and SALTS (Size, Attitude, Location, Type), we'll consider both lenses and mirrors separately. Here's how you can analyze each case:
Lenses:
Place an object at different distances to the left of a lens with a focal length (f).
a) Object placed beyond 2f:
In this case, the object is placed far beyond twice the focal length of the lens.
Principal ray 1: A ray parallel to the principal axis will pass through the focal point on the opposite side.
Principal ray 2: A ray passing through the optical center will continue in a straight line without any deviation.
Principal ray 3: A ray passing through the focal point on the object side will emerge parallel to the principal axis.
The image will be formed on the opposite side of the lens, between the focal point and twice the focal length.
SALTS:
Size: The image will be smaller than the object.
Attitude: The image will be inverted.
Location: The image will be located between the focal point and twice the focal length.
Type: The image will be real.
b) Object placed at 2f:
In this case, the object is placed at twice the focal length of the lens.
Principal ray 1: A ray parallel to the principal axis will pass through the focal point on the opposite side.
Principal ray 2: A ray passing through the optical center will continue in a straight line without any deviation.
Principal ray 3: A ray passing through the focal point on the object side will emerge parallel to the principal axis.
The image will be formed on the opposite side of the lens at twice the focal length.
SALTS:
Size: The image will be the same size as the object.
Attitude: The image will be inverted.
Location: The image will be located at twice the focal length.
Type: The image will be real.
c) Object placed between f and 2f:
In this case, the object is placed between the focal point and twice the focal length of the lens.
In this case, the object is placed far beyond twice the focal length of the mirror.
Principal ray 1: A ray parallel to the principal axis will reflect through the focal point on the same side.
Principal ray 2: A ray passing through the focal point on the object side will reflect parallel to the principal axis.
Principal ray 3: A ray passing through the center of curvature will reflect back along the same path.
The image will be formed on the opposite side of the mirror, between the focal point and twice the focal length.
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If you know the answer please tell me ASAP
3. Fulcrum left
Explanation:
What are the similarities and differences between these data sets in terms of their centers and their variability?
Data Set A: 12, 15, 18, 18, 22, 29
Data Set B: 13, 17, 17, 19, 20, 34
Select from the drop-down menus to correctly complete the statements.
Comparing the centers of the data sets, the median for Data Set A is Choose...
Choose.
Set A is Choose... the mean for Data Set B.
less than
equal to
greater than
the median for Data Set B. The mean for Data
4
a hand pump is used to inflate a ball, the pump piston does 24 J of work on the air to compress it. the air in the pump loses 7 J of heat to the surroundings. what is the change in thermal energy of the air??
A Thermal energy of the air is 17 J of heat to the surroundings.
Thus, Thermal energy is produced by materials whose molecules and atoms vibrate more quickly as a result of a rise in temperature.
The atoms and molecules that make up matter are always in motion. The increase in temperature caused by heating a substance causes these particles to accelerate and collide.
The energy that arises from a heated substance is referred to as thermal energy. The more the substance's thermal energy and the more its particles travel at higher temperatures.
Thus, A Thermal energy of the air is 17 J of heat to the surroundings.
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(c)
A metal, X has a work function of 2.0 eV.
Explain the underlined statement.
If X is illuminated with light of wavelength 4.5 x 10-7 m, calculate the:
cut-off wavelength;
maximum energy of the liberated electrons;
stopping potential.
[h=6.6 x 10-34 J s, c = 3.0 x 108 m s¹, 1 eV = 1.6 x 10-19 J
e = 1.6 × 10-¹⁹ C]
(ii)
(a)
(B)
(Y)
The underlined statement refers to the work function of a metal, X, which is a measure of the minimum energy required to liberate an electron from the surface of the metal. In other words, if the energy of the incident light is equal to or greater than the work function, electrons can be ejected from the metal's surface.
(i) To calculate the cutoff wavelength, we can use the equation:
E = hc/λ
where E is the energy of a photon, h is the Planck's constant (6.6 x 10^(-34) J s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength of light.
Since we want to find the cutoff wavelength, we need to determine the energy of a photon that corresponds to the work function of the metal, X. We can use the equation:
E = work function = 2.0 eV = 2.0 x 1.6 x 10^(-19) J
Now we can rearrange the equation to solve for λ:
λ = hc/E
Substituting the values:
λ = (6.6 x 10^(-34) J s) * (3.0 x 10^8 m/s) / (2.0 x 1.6 x 10^(-19) J)
Calculating this expression will give us the cutoff wavelength.
(ii) (a) To calculate the maximum energy of the liberated electrons, we can use the equation:
E = hc/λ
Using the given wavelength of 4.5 x 10^(-7) m, we can substitute it into the equation to find the energy.
(B) To calculate the stopping potential, we can use the equation:
eV_stop = E - work function
where e is the elementary charge (1.6 x 10^(-19) C), V_stop is the stopping potential, E is the energy of a photon corresponding to the given wavelength, and the work function is given as 2.0 eV. Solving for V_stop will give us the stopping potential.
(Y) It seems that there is no specific information or question provided for (Y). Please provide additional context or information for me to assist you further with (Y).
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Question 2 of 10
Which of the following represents a beta particle?
O A. e
OB. Y
O C. a
O D. He
Obiects 1 and 2 attract each other with a electrostatic force of 36.0 units. If the distance separating Objects 1 and 2 is tripled, then the new electrostatic force will be
__ units.
Objects 1 and 2 attract each other with an electrostatic force of 36.0 units. If the distance separating Objects 1 and 2 is tripled, then the new electrostatic force will be four units.
Coulomb's law can be expressed as:
F = k × (q1 × q2) / r²
In which:
F = electrostatic force
k = electrostatic constant (k = 9 × 10⁹ N·m²/C²)
q1 and q2 = the charges of the objects
r = distance between the objects
Let's consider that the initial electrostatic force in between objects 1 and 2 is 36.0 units.
F1 = 36.0 units
Next, if the distance is considered between the objects is tripled, the new distance (r') changes into three times the initial distance (r):
r' = 3 × r
To determine the new electrostatic force (F'), replacement r' into Coulomb's law:
F' = k × (q1 × q2) / (r')²
Place r' = 3r:
F' = k × (q1 × q2) / (3r)²
= k × (q1 × q2) / 9r²
The new force will be one-ninth (1/9) of the initial force since the electrostatic force (F') is directly proportional to (q1 q2) and inversely proportional to r2.
F' = (1/9) × F1
= (1/9) × 36.0
= 4.0 units
Thus, objects 1 and 2 attract each other with an electrostatic force of 36.0 units. If the distance separating Objects 1 and 2 is tripled, then the new electrostatic force will be 4 units.
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An astronaut has a total mass of 110 kg.
On the moon, he climbs into his spacecraft, 5 m up a ladder.
His GPE increases by 880 J.
What is the strength of gravity on the moon?
The strength of gravity on the moon is approximately 1.6 J/kg.
The change in gravitational potential energy (GPE) is given by the equation:
ΔGPE = m * g * Δh
where ΔGPE is the change in gravitational potential energy, m is the mass of the object, g is the strength of gravity, and Δh is the change in height.
In this case, the astronaut's GPE increases by 880 J as he climbs up the ladder by 5 m. We can rewrite the equation as:
880 J = (110 kg) * g * (5 m)
To find the strength of gravity on the moon (g), we can rearrange the equation:
g = 880 J / (110 kg * 5 m)
g = 1.6 J/kg
Therefore, the strength of gravity on the moon is approximately 1.6 J/kg.
It's important to note that the value of gravity on the moon is significantly lower than that on Earth. The moon has about one-sixth the gravity of Earth, which means objects weigh less on the moon compared to Earth. This lower gravity is due to the moon's smaller mass and smaller radius compared to Earth.
As a result, astronauts experience a different gravitational environment on the moon, which affects their movements and the energy required to perform tasks such as climbing.
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Please tell me the answer ASPA
Answer:
both objects are negatively charged.
please answer all the three question i am not sure of my answer i have final exam it would mean alot for u to help
Answer:
3 : Presence of a catalyst and Temperature
4 : correct, nothing needed to change
5 : Le Chatelier's principle states that when an equilibrium system is subjected to a disturbance or stress, it will undergo a shift in the direction that counteracts the impact of the stress, ultimately reestablishing a new state of equilibrium.
A car travels a distance of 120 km in 4 hours. What is its average speed in kilometers per hour?
Answer:
60 kilometers per hr
Explanation:
A spring stretches 0.294-m when a 0.360-kg mass is gently suspended from it as in Fig. 11–3b. The spring is then set up horizontally with the 0.431-kg mass resting on a frictionless table as in Fig. 11–5. The mass is pulled so that the spring is stretched 0.250-m from the equilibrium point, and released from rest.
Determine:
(a) the spring stiffness constant k.
The spring constant k based on the information is 12.0 N/m.
How to calculate the valueFrom the information, a spring stretches 0.294-m when a 0.360-kg mass is gently suspended from it as in Fig. 11–3b. The spring is then set up horizontally with the 0.431-kg mass resting on a frictionless table.
The spring constant k is the force required to stretch or compress the spring by a unit distance. In this case, the spring is stretched by 0.294 m when a 0.360 kg mass is suspended from it.
This means that the force exerted by the spring is equal to the weight of the mass, which is 0.360 kg x 9.8 m/s^2 = 3.53 N.
Therefore, the spring constant k is:
= 3.53 N/0.294 m
= 12.0 N/m.
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A car has a displacement of 150 kilometers to the south in 5 hours. What is its velocity in kilometers per hour?
Type the correct answer in the box. Spell all words correctly.
Mention the term
refers to having a generalized (and biased) belief about a particular group of people.
In social psychology, a stereotype is a generalized belief about a particular category of people.
What is stereotype ?A stereotype can be described as the accepted, condensed, and essentialist opinion with regards to certain population.
I should be nted hat his can be related to gender identity, race as well as ethnicity, country, however there are other things that an be used frequently used to stereotype groups. Stereotypes are pervasively present in both the larger social structure and culture.
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Gas and plasma are phases of matter, yet gas runs a car and plasma is part of your blood. Compare and contrast these terms and offer an explanation for the use of similar names.
Plasma lacks a precise form or volume, much like gas. It completes the empty space. Even though it is in the gaseous form, there is a difference because some of the particles are plasma-ionized.
High-energy particles are free to move around and fill the area they inhabit in the state of matter known as gas.
Neutral atoms or molecules often make up gaseous substances like air.
The ionised gas known as plasma, on the other hand, contains both positively and negatively charged particles.
It develops when a gas is subjected to an intense electric field or heated to incredibly high temperatures.
Plasma is a substance that may be found in stars, lightning, and fluorescent lights. It is also an essential component of many modern technology, like plasma TVs and fusion reactors.
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What is the result of two displacement vectors having opposite directions? Question 6 options: The resultant is the sum of the two displacements, having the same direction as the smaller vector. The resultant is the sum of the two displacements, having the same direction as the larger vector. The resultant is the difference of the two displacements, having the same direction as the smaller vector. The resultant is the difference of the two displacements, having the same direction as the larger vector.
The resultant of two displacement vectors having opposite directions is the difference of the two displacements, having the same direction as the smaller vector.
When two displacement vectors have opposite directions, it means they are pointing in opposite ways. In other words, one vector is in the opposite direction of the other. To find the resultant of these vectors, we need to subtract one vector from the other.
If we consider two displacement vectors, let's say vector A and vector B, and they have opposite directions, we can represent them as A and -B.
To find the resultant, we subtract vector B from vector A: A - (-B) or A + B.
The resultant will have the same direction as the smaller vector. This is because when we subtract a larger vector from a smaller vector, the resultant will have the direction of the smaller vector.
Therefore, the correct option is: "The resultant is the difference of the two displacements, having the same direction as the smaller vector."
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Find the position and velocity of a particle at t = 1.98 s if the particle is initially moving east at a speed of 20.4 m/s and experiences an acceleration of magnitude 4.40 m/s2, directed west.
Magnitude and direction of the position.
magnitude ---blank---
direction ---Select---
Magnitude and direction of the velocity.
magnitude ---blank---
direction ---select---
To find the position and velocity of a particle at a specific time, we can use the equations of motion.
Given:
Initial velocity (u) = 20.4 m/s (east)
Acceleration (a) = -4.40 m/s² (west)
Time (t) = 1.98 s
To find the position (displacement) of the particle at time t, we can use the equation:
s = ut + (1/2)at²
s = (20.4 m/s)(1.98 s) + (1/2)(-4.40 m/s²)(1.98 s)²
s = 40.392 m + (1/2)(-4.40 m/s²)(3.9204 s²)
s = 40.392 m - 8.6914 m
s ≈ 31.7006 m
To find the velocity of the particle at time t, we can use the equation:
v = u + at
v = (20.4 m/s) + (-4.40 m/s²)(1.98 s)
v = 20.4 m/s - 8.712 m/s
v ≈ 11.688 m/s
Therefore, the velocity of the particle at t = 1.98 s is approximately 11.688 m/s to the east.
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What is the value of acceleration in the following conditions
when a body comes at its initial position after motion
When a body comes to its initial position after motion, its velocity becomes zero, but the value of acceleration can vary depending on the specific conditions of the motion.
If the body comes to rest smoothly and gradually, the acceleration is zero. This means that there is no net force acting on the body, and it is not experiencing any acceleration. The body's velocity decreases over time until it reaches zero, and it returns to its initial position without any further acceleration.
However, if the body comes to its initial position abruptly, the situation is different. In this case, the body experiences a sudden change in velocity, and the acceleration can be nonzero.
For example, if a body is moving with a certain velocity and suddenly hits an obstacle or encounters a collision that brings it to a stop, the acceleration during the collision will be nonzero. The body experiences a rapid deceleration as it comes to rest, and this deceleration represents a negative acceleration.
In general, when a body comes to its initial position after motion, the value of acceleration can vary depending on the specific circumstances of the motion. It can be zero if the body comes to rest smoothly and gradually, or it can be nonzero if there is a sudden change in velocity leading to deceleration or acceleration.
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Ex) A wire has resistance R. Another wire, of the same material, has half the length and half the diameter of the first wire. The resistance of the second wire is?
The resistance of the second wire is twice the resistance of the first wire R₂ = 2R₁
Understanding ResistanceThe resistance of a wire is directly proportional to its length and inversely proportional to the cross-sectional area.
Let:
R₁ = resistance of the first wire
R₂ = resistance of the second wire
L₁ = length of the first wire
L₂ = length of the second wire
r₁ = radius of the first wire
r₂ = radius of the second wire
Given:
L₂ = L₁/2
r₂ = r₁/2
A₂ = A₁/4
Since resistance is inversely proportional to the cross-sectional area, which is proportional to the square of the radius.
Now, we can use the formula for resistance:
R = (ρL) / A
where
ρ is the resistivity,
L is the length,
A is the cross-sectional area.
For the first wire:
R₁ = (ρL₁) / A₁
For the second wire:
R₂ = (ρL₂) / A₂
Substituting the relationships we derived earlier:
R₂ = (ρ(L₁/2)) / (A₁/4)
R₂ = (ρL₁) / (A₁/2)
R₂ = 2(ρL₁) / A₁
Since ρL₁/A₁ is equal to R₁ (the resistance of the first wire), we can substitute:
R₂ = 2R₁
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5. Ametal block increases in temprature from 15°c to 60°c when supplied with 13500 joule of heat energy. a. Calculate the heat capacity of the metal. b. Calculate the specific heat capacity of the metal if this sample has a mass of 0.75kg.
The specific heat capacity of the substance is defined as the amount of heat energy supplied to the substance to increase the temperature of the substance by 1°C. The SI unit of specific heat is J/Kg.°C.
The heat energy, q = mC×ΔT, where m is the mass of the substance. C is the specific heat capacity of the material. ΔT is the change in temperature.
From the given,
a) heat supplied, q = 13500J
Initial temperature,T₁ = 15°C
Final temperature, T₂ = 60°C
Specific heat capacity, C=?
q = mCΔT
13500 = C(T₂ - T₁)
13500/(60-15) = C
13500/45 = C
C = 300 J/Kg.°C
Thus, the specific heat capacity is 300J/Kg.°C.
b) mass of the substance = 0.74kg
q = mCΔT
13500 = 0.75×C×(60-15)
13500/(0.75×45) = C
C = 400 J/Kg.°C
Thus, the specific heat capacity with heat energy of 13500 J is 400J/kg.°C.
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