Answer:
the stone's final speed just before hitting the ground is: v = √(2 × 9.81 × 90) m/s = √(1765.8) m/s = 42.0 m/s.
A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is 1000 N
and the angle between the two ropes is 50 ∘
. Assume both players pull with the same force.
Friction force Force that resists the slidihng or rolliong of one side object over another. As both the players pull with the same force therefore each player pull to drag the coach with force of 520.83
What is Friction?
Friction force on the given sled is 1000 N.
Angle between the two ropes dragging by the players is 50 Celcius.
Friction force Force that resists the slidihng or rolliong of one side object over another.
Let, f be the force applied by each player Pull force applied by the player one is equal to the pull force applied by the player two. Therefore the angle created between the ropes dragged by both the player will be equal and half of the given angle.
Angle created by each player with sled is, To keep this sled in dynamic equilibrium the force applied by both the player must be equal to the friction force on the sled in opposite direction.
Therefore, Hence, each player pull to drag the coach with force of 520.83.
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A pendulum bob of mass 5 kg is displaced from the vertical until it is 0.25 m above its lowest point. Upon release, it rises to a height of 0.24 m on the other side. How much energy was lost due to friction? Assuming half the total energy loss takes place during the downward swing, with what speed does the bob pass though its lowest point?
The energy lost due to friction is 0.49 J. And the speed of the bob passing through its lowest point will be 2.19 m/s.
What is the conservation of energy?The mass is 5 kg and the heights are h₁ 0.25 m and h₂ = 0.24. And the difference in the height is given as,
h₁ - h₂ = 0.25 - 0.24
h₁ - h₂ = 0.01
The energy loss due to friction is given as,
Energy loss = mgh₁ - mgh₂
Energy loss = mg (h₁ - h₂)
Energy loss = 5 x 9.8 x 0.01
Energy loss = 0.49 J
The energy lost due to friction is 0.49 J.
The velocity is given as,
KE = mgh₁ - E / 2
(1/2) x 5 x v² = 5 x 9.8 x 0.25 - 0.49 / 2
2.5v² = 12.25 - 0.245
v² = 4.802
v = 2.19 meters per second
The speed of the bob passing through its lowest point will be 2.19 m/s.
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what is kinematics?
;-;
Answer:
The branch of mechanics concerned with the motion of objects without reference to the forces which cause the motion.
(iii) The area of the piston is 5.0 x 10-³m². Calculate the weight that is added to the piston.(the initial pressure is 105000 and the final is 140000, the air decreases from 860 cm3 to 645cm3)
The weight added to the piston is 175 N.
What is the weight that is needed?
The weight that is added to the piston can be calculated using the Ideal Gas Law, which states that PV = nRT
where;
P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature.Since the initial pressure, volume, and temperature are known, we can use the Ideal Gas Law to find the number of moles of gas, n.
Then, we can use the equation for pressure force, to find the weight added to the piston.
F = PA
where;
A is the area of the piston, .First, we'll find the initial number of moles of gas:
P1V1 = nRT
n = P1V1 / RT
T = 298 K is the temperature (room temperature)
n = (105000 Pa x 860 cm^3) / (8.31 J/mol.K x 298 K)
Next, we'll find the final number of moles of gas:
P2V2 = nRT
n = P2V2 / RT
n = (140000 Pa x 645 cm^3) / (8.31 J/mol.K x 298 K)
Now, we have the number of moles of gas for both the initial and final conditions, and we can calculate the change in number of moles of gas, ∆n:
∆n = n2 - n1
Finally, we can use the equation for pressure force to find the weight added to the piston:
F = PA
∆F = P2A - P1A
∆F = (140000 Pa - 105000 Pa) x 5.0 x 10^-3 m^2
∆F = 35000 Pa x 5.0 x 10^-3 m^2
∆F = 175 N
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Which is an accurate statement about two objects that have the same average kinetic energy?
Each object has the same amount of potential energy.
Each object has the same mass.
Both objects are made of the same material.
Both objects are at the same temperature.
Answer:
both objects are at the same temperature
Explanation:
kinetic energy is not affected or is independent of temperature
(3 of 5)
Referring to the two questions above, the transit detection method relies on the difference
between the flux when the planet is transiting versus when it is off to the side. The larger
the difference, the better chance astronomers have of detecting the planet. For which of
the above is the transit detection method more likely to detect the planet?
O The configuration in question 1.
O The configuration in question 2
O Both are the same, so there is no dependence on planet size.
Answer: The configuration in question 2
Explanation:
Answer:
The configuration in question 1 (correct)
Explanation:
Could you please help with the attached question?
the work done by the ball is 38.72 J.
define work done ?
In physics, work is defined as the product of force and displacement. It is a measure of the energy transferred when a force is applied over a distance, resulting in the displacement of an object. Mathematically, work is represented by the formula:
Work = Force x Distance x Cos(theta)
where Force is the applied force, Distance is the displacement of the object, and theta is the angle between the force and the displacement vectors. The unit of work is the Joule (J), which is equivalent to one Newton-meter (N·m). Work can be positive, negative, or zero, depending on the direction of the force and displacement. If the force is in the same direction as the displacement, work is positive, and if the force is in the opposite direction to the displacement, work is negative. If the force and displacement are perpendicular, the work is zero.
Work = Force x Distance x Cos(theta)
where:
Force = 484 N (given)
Distance = 8 cm = 0.08 m (given)
Cos(theta) = 1 (since the force and displacement are in the same direction)
Plugging in the values, we get:
Work = 484 N x 0.08 m x 1
Work = 38.72 Joules (J)
Therefore, the work done by the ball is 38.72 J.
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POSSIBLE POINTS: 1
Based on what you have learned from this project so far, describe the relationship between mass and gravitational force (the size of the gravity force
vectors). You should use directly proportional or inversely proportional in your answer. Use at least three complete sentences to justify your answer
(explain why you think what you think).
Answer:
F = G * (m1 * m2) / r^2
Explanation:
The relationship between mass and gravitational force is directly proportional. This means that as the mass of an object increases, the magnitude of the gravitational force acting on it also increases. The exact relationship can be described using Newton's law of universal gravitation, which states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.
This relationship can be expressed mathematically as:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
This relationship makes intuitive sense: larger objects have a greater ability to pull other objects towards them, so the gravitational force they exert is stronger. On the other hand, as the distance between two objects increases, the gravitational force between them decreases, because the pull is spread out over a larger area.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
Two blocks are connected by a string as shown. The inclination of the ramp is theta = 35 degrees while the masses of the blocks are m1=2.1kg and m2=11kg. Friction is negligible.Part (a): What is the magnitude of the acceleration of each block in m/s^2?Part (b): What is the tension in the rope in newtons?
(a) The acceleration of each block is zero. (b) The tension in the rope is 97.7 N.
(a) The forces acting on each block are,
For m1,
F_net = T - mg*sin(35)
For m2,
F_net = mg*sin(35) - T
Since the two blocks are connected by a rope, they will have the same acceleration.
T - mgsin(35) = mgsin(35) - T
T = mg*sin(35)
Substituting this value of T,
F_net = T - mg*sin(35)
F_net = mgsin(35) - mgsin(35)
F_net = 0
Therefore, the net force acting on each block in the direction of motion is zero.
(b) To find the tension in the rope,
T = mg*sin(35)
T = (2.1 kg + 11 kg)9.81 m/s^2sin(35)
T = 97.7 N
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To pick up a few staples from the table, a student wrapped copper wire around a nail and connected it to a battery. She was able use this device to pick up all staples. How was this possible?
A. The current moving through the wire made the nail into an electromagnet.
B. The staples are responding to the wire because it was made of copper.
C. The electricity from the wire was arcing to the staples.
D. The protons in the staples and are attracted to the electrons in the wire.
Answer:
The correct answer is A. The current moving through the wire made the nail into an electromagnet.
An electromagnet is created when a current is passed through a wire. The flow of electrons creates a magnetic field, which can attract or repel other magnetic objects. In this case, when the student wrapped the copper wire around the nail and connected it to a battery, the flow of electrons created a magnetic field around the nail. This magnetic field allowed the student to pick up the staples because they were attracted to the nail, which was now acting as an electromagnet.
TRUE OR FALSE: Increasing the time of impact during a collision increases the force experienced by the object.
Answer: True
Explanation:
This equation is known as the ideal gas law, and it can be used to predict the behavior of many gases at relatively low pressure. From this equation, you can see that as the temperature of a gas increases,.
From the ideal gas law equation ([tex]PV = nRT[/tex]), you can see that as the temperature of a gas increases, either the pressure (P) or the volume (V) of the gas must increase in order to maintain a constant number of moles (n) and a constant gas constant (R).
This can be explained by the kinetic theory of gases, which states that the temperature of a gas is proportional to the average kinetic energy of its molecules. As the temperature increases, the molecules move faster and collide with the walls of the container more frequently and with greater force, increasing the pressure. Alternatively, the molecules can also move further apart, increasing the volume of the gas. In other words, as the temperature of a gas increases, the gas will expand and/or its pressure will increase, assuming the volume or the number of moles of gas are held constant. This relationship is important for many practical applications, such as in the design of engines, refrigeration systems, and industrial processes.
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A moving object has
kinetic energy
velocity.
speed.
all of these
It has all of these. everything has kinetic energy, it is moving so it will have both speed and velocity as well.
Returning to the scene of the (possible) crime, you estimate that the bathtub in which Polly was found contained around 0.3 m3 (around 80 gallons), which corresponds to 300 kg (since the density of water is 1000 kg/m3), of water as you scoop the water out of the tub. The temperature of this water is 7oC. You assume that the water was initially at its lowest temperature, 2oC, which you find by turning on the cold tap only.
With these measurements, first determine the amount of heat that transferred from Polly and the external environment to warm the cold water. The specific heat of water is about 4186 J/(kgoC). Give your answers in units of kilojoules (kJ).
This indicates that to increase the temperature of the water in the bathtub from 2°C to 7°C, roughly 62,760 kJ of heat energy were added.
What is the water's temperature?While scientists typically use the Centigrade (or Celsius) scale, where water freezes at 0 degrees and boils at 100 degrees, we typically measure temperature in the United States using the Fahrenheit scale, where water freezes at 32 degrees and boils at 212 degrees.
According to the data given, the bathtub once held 300 kg of water at 2°C.
we can use the specific heat capacity of water and the formula:
Q = m * c * ΔT
The specific heat capacity of water is 4.184 J/(g°C), or 4184 J/(kg°C). Therefore, the amount of heat energy absorbed by the water is:
Q = 300 kg * 4184 J/(kg°C) * (7°C - 2°C)
Q = 62,760 kJ
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They include cash,
accounts receivable, notes receivable,
inventory and prepaid expenses. Step 8
explains each one in detail.
1.
You are the owner of an appliance store.
Choose four categories from above and
explain how that asset may fit into your
business. For example, if I owned a
company that installed furnaces, my
inventory would include different types of
furnaces and air conditioners as well as
controls to operate them. Accounts
receivable would include the installations
we did but have not been paid for yet.
As the owner of an appliance store, the following four categories of assets could apply to my business:
What are the categories of assets that could apply to my business?Cash: Cash is the most liquid asset and represents the money that the business has on hand or in the bank. As an appliance store owner, cash can be used to pay for business expenses such as rent, utilities, employee wages, and inventory purchases.
Accounts receivable: Accounts receivable represents the money that customers owe to the business for goods or services that have been sold but not yet paid for. In the context of an appliance store, accounts receivable would include sales made on credit, where customers are allowed to take the appliances and pay for them at a later date.
Inventory: Inventory represents the goods that the business has on hand to sell to customers. For an appliance store, inventory would include appliances such as refrigerators, washing machines, dryers, and ovens. The value of the inventory can fluctuate depending on market demand, changes in technology, and other factors.
Prepaid expenses: Prepaid expenses represent the costs that the business has paid in advance for goods or services that will be used in the future. In the context of an appliance store, prepaid expenses may include things like rent payments, insurance premiums, and maintenance contracts. By prepaying for these expenses, the business can ensure that it has access to the resources it needs to operate efficiently.
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Water has a specific heat of 4184 Jkg⋅∘C. How much energy is needed to increase the temperature of a kilogram of water5∘C?
The specific heat capacity of water is 4184 and it needs 20920J energy to increase the temperature of a kilogram of water 5 degree celcius.
The amount of heat required to raise the temperature of one gramme of a substance by one degree Celsius. Specific heat is usually measured in calories or joules per gramme per Celsius degree. Water, for example, has a specific heat of 1 calorie (or 4.186 joules) per gramme per Celsius degree.
A substance's specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of that substance by 1oC. (or 1K). The SI unit of measurement is joule per kilogramme per kelvin (Jkg-1K-1).
By using the equation:-
Q= mCΔmCΔTT
(where, Q= energy, m= mass of the sample, C= specific heat of the sample and delta T is the change in temperature).
[tex]Q= 1kg*4184J*(5-0)= 20920J.[/tex]
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HELPPPP
i need this done quickly
Answer:
F(Net) = F(a) + F(g) + F(f) + FN.
W
Question 9
1 pts
The initial vertical velocity (Vyi) needed to raise your center of mass from an initial
height (yi) of 1.2 m to a peak height (yf) of 1.8 m is
The initial vertical velocity needed to raise the center of mass from 1.2 m to a peak height of 1.8 m is approximately 3.43 m/s.
What is the initial velocity?The initial vertical velocity needed to reach a peak height can be calculated using the equation of motion for a projectile under constant gravity:
Vyi = √(2 * g * (yf - yi))
where:
g is the acceleration due to gravity (approximately 9.8 m/s^2)yi is the initial height (1.2 m)yf is the peak height (1.8 m)Plugging in the values, we get:
Vyi = √(2 * 9.8 * (1.8 - 1.2))
Vyi = √(2 * 9.8 * 0.6)
Vyi = √(11.76)
Vyi = 3.43 m/s
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an object or is placed close to a thin converging lens. The diagram represents three way from the top of all passing through that lens.
Which option is correct A, B, C or D?
The type of image produced by the converging lens when object O is at that position will be virtual and enlarged, Option D.
What is a virtual and enlarged image?A virtual image is an image that is formed when light rays do not actually converge at a single point, but instead appear to converge when they are extended backwards. A virtual image is typically created by objects that are behind a lens or mirror that diverts the light rays in such a way that they appear to come from a different location.
An enlarged image, on the other hand, refers to a visual representation that has been magnified or made larger than the original size of the object being viewed.
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Which of the following substances would allow an electric current to flow through it easily?(1 point)
Responses
glass
aluminum (Al)
rubber
carbon (C)
Aluminum (Al) allows an electric current to flow through it easily. The correct option is B.
What is electrical conductivity?Electricity is the flow of electric charge through a conductor. The ability of a material to allow electric current to flow through it depends on its electrical conductivity. Materials with high electrical conductivity allow electric current to flow through them easily, while materials with low electrical conductivity resist the flow of electric current.
Here in the Question,
Option A: Glass is a poor conductor of electricity and has very low electrical conductivity. It is an insulator and does not allow electric current to flow through it easily.
Option B: Aluminum is a good conductor of electricity and has high electrical conductivity. It allows electric current to flow through it easily.
Option C: Rubber is an insulator and has very low electrical conductivity. It does not allow electric current to flow through it easily.
Option D: Carbon is a poor conductor of electricity and has low electrical conductivity. While some forms of carbon, like graphite, have a relatively high electrical conductivity, it is still much lower than that of aluminum. So, carbon does not allow electric current to flow through it easily.
Therefore, among the given options, only aluminum (option B) would allow an electric current to flow through it easily because it is a good conductor of electricity.
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in the vector diagram below, the magnitude of A is 15m, the magnitde of B is 18m and the magnitude of C is 6m. Find the resultant vector using component method. Angle A = 35 Angle B = 30 Angle C = 50.
Answer:
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
Explanation:
28. Batman is sitting in the Batmobile at a stoplight.
As the light turns green, Robin passes Batman in his lime-green Pinto at a constant speed of 60 km/h. If Batman gives chase. accelerating at a constant rate of 10 km/h/s. determine
a) now long 1t takes batman to attain the
same speed as Robin.
b) how far Batman travels in this time.
c) how long it takes for Batman to catch up
to Robin.
If Batman gives chase and accelerating at a constant rate of 10 km/h/s then:
a) 6 seconds
b) 360 meters
c) 12 seconds
Accelerating is a process whereby an object, or a system of objects, increases its speed or rate of change. It is a fundamental concept in physics and is used to describe the motion of objects, such as an acceleration due to a force, or the rate of change in velocity. Accelerations can also be caused by a change in direction, or due to changes in gravity, such as when accelerating towards the surface of a planet.
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Describe protons.
Location:
Charge:
Mass:
The protons location is nucleus of an atom, the Mass is 1 amu and the charge is positive.
What is protons?
Protons are subatomic particles with a positive electrical charge. They are found in the nucleus of atoms and are responsible for most of the atom’s mass. Protons are one of the three main subatomic particles, along with neutrons and electrons.
Location: Proton is located in the nucleus of an atom. The nucleus is the small, dense, positively charged center of an atom. The protons, along with the neutrons, make up the nucleus of the atom.
Mass: The mass of a proton is approximately 1.007276467 u (unified atomic mass units). It is slightly heavier than a neutron, which has a mass of approximately 1 u.
Charge: A proton has a positive charge of +1 elementary charge (e). This charge is what gives the proton its repelling force to other positively charged particles and its attractive force to negatively charged particles.
Hence, a proton is a positively charged subatomic particle with a mass of 1 amu, located in the nucleus of an atom.
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Answer:
Location:
✔ nucleus
Charge:
✔ positive
Mass:
✔ one amu
Explanation:
You perform an experiment to measure the speed of a car over time. The
results are shown in the graph below.
Speed (m/s)
30
25-
20
15
10
5
0+
O
5
10
A. 24 m/s
B. 22 m/s
15
Time (s)
What was the speed of the car after 20 seconds?
C. 20 m/s
D. 30 m/s
20
25
The speed of the car after 20 seconds are 20 m/s.
What is the speed ?The speed of an object is a measure of how quickly the object is moving in a particular direction. It is typically measured in units such as meters per second (m/s). Speed is a scalar quantity, which means it is only concerned with the magnitude of the velocity (or speed) and not the direction
The graph shows that the speed of the car was 20 m/s after 20 seconds.
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A grandfather clock pendulum reaches a maximum height of 18
cm each swing. If the mass of the pendulum bob is .85 kg,
what is the maximum potential energy for the pendulum bob?
J
The maximum potential energy for the pendulum bob is approximately 1.3817 J.
What is Potential Energy ?
Potential energy is a form of energy that an object possesses by virtue of its position, shape, or configuration. It is the energy that an object has due to the work done on it, or that it can do due to its position or state. The potential energy of an object is often associated with the force that acts on it.
The maximum potential energy for the pendulum bob can be calculated using the formula:
Potential energy = mgh
where m is the mass of the pendulum bob, g is the acceleration due to gravity, and h is the maximum height reached by the pendulum.
In this case, the mass of the pendulum bob is 0.85 kg, the maximum height reached by the pendulum is 18 cm or 0.18 m, and the acceleration due to gravity is 9.81 m/s^2. Substituting these values into the formula, we get:
Potential energy = 0.85 kg x 9.81 m/s^2 x 0.18 m
Potential energy = 1.3817 J (rounded to four decimal places)
Therefore, the maximum potential energy for the pendulum bob is approximately 1.3817 J.
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A car is stopped at a traffic light. It then travels along a straight road so that its distance from the traffic light is given by x(t)=bt^2 −ct^3 , where b=2.40ms^−2 and c=0.120ms^−3 .The instantaneous velocity of the car at t=5.0s is
The instantaneous velocity of the car at t = 5.0s is 4.5 m/s.
Take the derivative of its position function x(t) with respect to time,
[tex]v(t) = \dfrac{dx(t)}{dt}[/tex]
v(t) represents the velocity of the car at any given time t.
Given x(t) = bt^2 - ct^3,
Find the derivative as follows,
v(t) = {d/dt} (bt^2 - ct^3)
= 2bt - 3ct^2
Substitute the given values of b and c, and evaluate the velocity at t = 5.0s,
v(5.0s) = 2b(5.0s) - 3c(5.0s)^2
= 2(2.40 m/s^2)(5.0 s) - 3(0.120 m/s^3)(5.0 s)^2
= 12.0 m/s - 7.5 m/s
= 4.5 m/s
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A 24.0 kg rock, m, is on the edge of a 80.0 m cliff, h, as shown in Figure 11-20. Assume that air resistance is negligible.
(a) What potential energy does the rock possess relative to the base of the cliff?
(b) The rock falls from the cliff. What is its kinetic energy just before it strikes the ground?
(a) The potential energy of the rock relative to the base of the cliff can be calculated using the formula for gravitational potential energy:
PE = mgh
where m is the mass of the rock (24.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the cliff (80.0 m).
PE = 24.0 kg * 9.8 m/s^2 * 80.0 m = 15,360 J
(b) The kinetic energy of the rock just before it strikes the ground can be calculated using the formula for kinetic energy:
KE = 0.5 * m * v^2
where m is the mass of the rock (24.0 kg) and v is the velocity of the rock just before it strikes the ground. The velocity can be calculated using the equation of motion for a freely falling object:
v = sqrt(2gh)
v = sqrt(2 * 9.8 m/s^2 * 80.0 m) = 44.72 m/s
KE = 0.5 * 24.0 kg * 44.72 m/s^2 = 507.84 J
t: The toy car is given a push away from the origin and released. It continues to move with a constant velocity. Sketch the force g 0' after the car is released. A cart is moving toward the right and speeding up, as shown in the diagram below. Draw arrows above the cart representing the magnitudes and directions of the net (combined) forces you think are needed on the cart at t = 0 s, t = 1 s, etc., to maintain its motion with a steadily increasing velocity. Assume that the cart is already moving at t_1. Explain the reasons for your answers. If the positive direction is toward the right, what is the sign of the force at t = 2 s in Question
The car will move at a constant speed once it is unleashed, as is assumed. Hence, there is no acceleration. Newton's second law states that a straight line along zero will appear on the graph if F=ma=m(0)=0, F=0.
Acceleration is the rate at which an object changes its velocity. It is a vector quantity, which means it has both magnitude and direction. The standard unit of acceleration is meters per second squared (m/s²).
Acceleration can be caused by forces such as gravity, friction, and electromagnetism. When a force acts on an object, it causes a change in the object's motion, resulting in acceleration.
The relationship between acceleration, velocity, and time is described by the equation a = (v_f - v_i) / t, where a is acceleration, v_f is final velocity, v_i is initial velocity, and t is time.
The effects of acceleration can be seen in everyday experiences, such as feeling pushed back into your seat when a car accelerates or feeling weightless during freefall. Understanding acceleration is important in fields such as physics, engineering, and transportation.
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If the actual mass of the products from the reaction was 120 g , what was the percent yield of the reaction?.
According to the question This gives us a percent yield of 150%.
What is percent yield?Percent yield is a measure used in chemistry to calculate the efficiency of a chemical reaction. It is expressed as a percentage and is calculated by comparing the actual yield of a product obtained in a reaction to the theoretical yield, which is the maximum amount of product that could have been produced.
The percent yield of a reaction is the ratio of the actual yield of the reaction to the theoretical yield of the reaction multiplied by 100.
Therefore, to calculate the percent yield, we need to first calculate the theoretical yield of the reaction. We can do this by multiplying the given mass of reactants, in this case 80 g, by the stoichiometric coefficient of the desired product, which is 1.
This gives us a theoretical yield of 80 g.
Now, to calculate the percent yield, we divide the actual yield, which is 120 g, by the theoretical yield, which is 80 g, and multiply by 100.
This gives us a percent yield of 150%.
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1. we know that the total amount of heat that flows out of the sample and into the water at a specific time is given byLaTeX: Q\:=\:m_sc_s\left(T_{s,i}-T_s\right)Q=mscs(Ts,i−Ts), whereLaTeX: T_sTs is the temperature of the sample at a specific time and, again,LaTeX: T_{s,i}Ts,i is the initial temperature of the sample (at time 0). To simplify the math, we may neglect the heat leak term here to say that this is roughly the same amount of heat the flows into the water, soLaTeX: Q=m_wc_w\left(T_w-T_{w,i}\right)Q=mwcw(Tw−Tw,i), whereLaTeX: T_wTw is the temperature of the water at this same specific time andLaTeX: T_{w,i}Tw,i is the initial temperature of the water.
In the lab, we will measure both the sample and water temperatures as a function of time, but the important quantity is the difference between these temperatures since this is what drives the heat flow between the center of the sample and the water. Using the above equations (solving for the temperatures of the sample and the water bath at a particular time), we can find the relationship between the total amount of heat flow and the difference in the temperatures of the center of the sample and water at some moment in time. This yields _________________________________.
sample and water at some moment in time. This yields _________________________________.
Group of answer choices
Option D: the link between the total heat flow and the temperature difference between the sample's Centre and the water at a specific time.
[tex]Q\:=\:m_sc_s\left(T_{s,i}-T_s\right)[/tex]
[tex]T_s\right =(T_{s,i}-T_s\right))[/tex]
[tex]Q=m_wc_w\left(T_w-T_{w,i}\right)[/tex]
[tex]Q=m_wc_w\left(T_w-T_{w,i}\right)[/tex]
[tex]T_{diff} =(T_{s}-T_w\right))[/tex]
= [tex]T_{s,i} -\frac{Q}{m_{s}C_{s}} -(T_{w,i}\right +\frac{Q}{m_{s}C_{s}} )[/tex]
=[tex](T_{s,i} - T_{w,i} )-Q(\frac{1}{m_{s}C_{s}} +\frac{1}{m_{w}C_{w}})[/tex]
Specific time refers to a precise moment in time, often denoted by a particular time and date. It can be expressed in different ways depending on the context, such as using a 24-hour clock or the AM/PM system. Specific time is essential for scheduling events, meetings, and appointments, and for coordinating activities across different time zones. It is also crucial for time-sensitive activities such as transportation, where schedules must be coordinated down to the minute. The concept of specific time is used in many fields, including science, technology, business, and everyday life. In modern times, technologies such as smartphones and computers have made it easier than ever to track and coordinate specific times across the globe.
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The complete question is:
1. we know that the total amount of heat that flows out of the sample and into the water at a specific time is given by LaTeX: [tex]Q\:=\:m_sc_s\left(T_{s,i}-T_s\right)Q=mscs(Ts,i−Ts)[/tex], where LaTeX: [tex]T_sTs[/tex] is the temperature of the sample at a specific time and, again, LaTeX: [tex]T_{s,i}Ts,i[/tex]is the initial temperature of the sample (at time 0). To simplify the math, we may neglect the heat leak term here to say that this is roughly the same amount of heat the flows into the water, so LaTeX: [tex]Q=m_wc_w\left(T_w-T_{w,i}\right)Q=mwcw(Tw−Tw,i)[/tex], where LaTeX:[tex]T_wTw[/tex] is the temperature of the water at this same specific time and LaTeX: is the initial temperature of the water.
In the lab, we will measure both the sample and water temperatures as a function of time, but the important quantity is the difference between these temperatures since this is what drives the heat flow between the center of the sample and the water. Using the above equations (solving for the temperatures of the sample and the water bath at a particular time), we can find the relationship between the total amount of heat flow and the difference in the temperatures of the center of the sample and water at some moment in time. This yields _________________________________.
sample and water at some moment in time. This yields _________________________________.
Group of answer choices
A. [tex]T_{dif}=T_{s\:}-T_w=\left(T_{s,i}-T_{w,i}\right)-\left(\frac{1}{m_sc_s}-\frac{1}{m_wc_w}\right)Q[/tex]
B [tex]T_{dif}=T_{s\:}-T_w=\left(T_{s,i}-T_{w,i}\right)+\left(\frac{1}{m_sc_s}+\frac{1}{m_wc_w}\right)Q[/tex]
C.[tex]T_{dif}=T_{s\:}-T_w=\left(T_{s,i}-T_{w,i}\right)+\left(\frac{1}{m_sc_s}-\frac{1}{m_wc_w}\right)Q[/tex]
D. [tex]T_{dif}=T_{s\:}-T_w=\left(T_{s,i}-T_{w,i}\right)-\left(\frac{1}{m_sc_s}+\frac{1}{m_wc_w}\right)Q[/tex]
