Q8 The figure 3 below shows a metallic ball passing through a ring before being heated.
(a) Describe how the particles inside the ball are moving at the start of experiment.
(b) When the ball is heated using a Bunsen burner, it no more passes through the ring. Explain, in terms of particles, why the ball does not pass through the ring after being heated.
(c) Define radiation.
Answers
The particles inside the ball are vibrating about a fixed position at the start of the experiment.
When the ball is heated using a Bunsen burner, it no more passes through the ring because the particles have increased kinetic energy, hence, they are able to vibrate across a larger space and more frequently, resulting in an increase in volume of the ball.
Radiation is a process of heat transfer that occurs through space and thus does not require an intervening material medium for heat transfer.
What are some of the effects of heat on a substance?When heat energy is added to a substance, some of the observable effects include:
an increase in temperaturean increase in volumea change of state.Heat is transferred through two main processes; conduction, convection, and radiation.
When an object is heated, the particles acquire kinetic energy and collide faster resulting in an increase in temperature as well as volume of the object.
Thisbis observed in the ball and ring experiment.
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Related Questions
PLEASE HELP ME ANSWER THE PHYSICS QUESTIONS ON MY PROFILE!!! i will give brainliest to the first to answer!!! this one and the other ones
A 2500 kg train car moving at 20 m/s, east collides with a different train car at rest. The cars stick together after the collision and move together at 13 m/s, east. Find the second car’s mass.
options :
A) 245 kg
B) 50000 kg
C) 9.62 kg
D) 1346 kg
Answers
In Fig. 30-46, a stiff wire bent into a semicircle of radius a = 1.4 cm is rotated at constant angular speed 30 rev/s in a uniform 20 mT magnetic field. What are the (a) frequency and (b) amplitude of the emf induced in the loop?
Answers
A stiff wire bent into a semicircle of radius a = 1.4 cm. The frequency is 30 Hertz and the amplitude of the emf induced in the loop is 1.16 x 10⁻³ V
Formula for the angular frequency is:
ω = 2πf
Where:
ω = angular frequency (rad/s)
f = frequency (Hertz)
In the given problem,
ω = 30 rev/sec = 30 x 2π rad/s
a) f = ω / 2π
f = 30 x 2π / 2π = 30 Hertz
b) The induced emf is:
ε = Bπ²a²f sin(ωt)
Where:
B = magnetic field
a = radius
In the given problem,
B = 20 x 10⁻³ T
a = 1.4 x 10⁻² m
Hence, the amplitude or the maximum emf is:
ε_max = Bπ²a²f
= (20 x 10⁻³) π² (1.4 x 10⁻²)² (30) = 1.16 x 10⁻³ Volt
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the vertical and horizontal distance of the projectile will be equal if the angel of the progectile is
Answers
Answer: The vertical and horizontal distance of a projectile will be equal if the angle of projection is 45 degrees.
Explanation:
This is because at an angle of 45 degrees, the projectile will be equally influenced by the horizontal and vertical components of its motion. As a result, the projectile will travel the same distance horizontally as it does vertically.
For other angles of projection, the projectile will be more influenced by either the horizontal or the vertical component of its motion, depending on the angle. At an angle of 90 degrees (straight up), the projectile will be primarily influenced by the vertical component of its motion, while at an angle of 0 degrees (horizontal), the projectile will be primarily influenced by the horizontal component of its motion.
In machines with low efficiency, most of the lost energy is turned into?
a. Light
b. Sound
c. Power
d. Heat
Answers
Answer:
Option (C)
Explanation:
All electric machines are not ideal, therefore they have some losses due to which efficiency being less than 100%.
Suppose the driver in this example now slams on the brakes, stopping the car in 4.00 s. Find (a) the acceleration and
(b) the distance the car travels while braking, assuming the acceleration is constant.
Answers
The initial velocity of the car is 39.6 m/s and the final velocity is zero. Then, the acceleration of the car is - 9.9 m/s². The average distance covered is 158.4 m.
What is acceleration?The acceleration of a moving body is the rate of change in its velocity. Acceleration is a vector quantity and is characterized with a magnitude and direction.
Acceleration is the ratio of change in velocity to the change in time. Here, the initial velocity is 39.6 m/s. The car is stopping , therefore the final velocity is zero.
The time taken to stop is 4 seconds. Hence, the acceleration is :
a = 0 - 39.6 m/s / 4 s
= - 9.9 m/s²
The distance covered within this time is the product of its velocity and time.
Distance = velocity × time = 4 s × 39.6 m/s = 158.4 m
Therefore, the car travels up to a distance of 158.4 m before stops.
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Your question is incomplete. But your complete question probably was:
Suppose a driver is moving with speed 39.6 m/s, and slams on the brakes, stopping the car in 4. s.
the acceleration and
(b) the distance the car travels while braking, assuming the acceleration is constant.
which of the following free-body diagrams could be used to analyze the forces exerted on the moon when it is at the position indicated in the figure?
Answers
Option F, with the GRAVITY arrow pointing to the right, is the appropriate diagram. By means of gravity, a planet and other body pulls items toward its core.
Describe the moon's orbit around a planet.Moons are subject to the gravitational pull of planets. So because near side of the moon is subjected to a stronger pull compared to the far side, it is drawn into a slightly expanded shape. The moon seems to have a comparable differential pull to the Earth that causes ocean tides.
The Moon's and Earth's gravitational pull caused this particular case of tidal locking (called synchronous rotation).
One orbit of Sun is completed by the Earth in 365 and one-quarter days, or one year. The Earth rotates around the Moon just like the Moon does around the Sun. The Moon's orbit will last 27 1/2 days.
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In an amusement park water slide, people slide down an essentially frictionless tube. The top of the slide is 3.1 m above the bottom where they exit the slide, moving horizontally, 1.4 m above a swimming pool.
What horizontal distance do they travel from the exit point before hitting the water?
Answers
They travel a horizontal distance of 4.17 m from the exit point before hitting the water.
What is the law of conservation of energy?Energy cannot be created or destroyed, according to the law of conservation of energy. However, it is capable of change from one form to another.
height of the slid: h = 3.1 m
horizontal movement above swimming pool: s = 1.4 m
Let the horizonal speed of the people at the end of the water slide= v
Using energy conservation
mgh = 1/2 mv²
v = √(2gh)
Again time taken for falling s = 1.4 m under gravitation:
t = √(2s/g)
Hence, the horizontal distance travelled = speed × time
= √(2gh)×√(2s/g)
= √(4hs)
= √(4 × 3.1 × 1.4)
= 4.17 m.
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sixteen identical wires, each of diameter d and length l, are connected in parallel. the combination has the same resistance as a single similar wire of length l but whose diameter is:
Answers
Compared to a single comparable wire of length l but diameter 3d, the combination is the same resistance.
What results in opposition?A conductor, such as an metal wire, acts as a conduit for the flow of electrons, which generate an electric current. With the atoms in the metal, the traveling electrons may collide. Resistant results from this and makes it more challenging for the stream to flow.
Exactly how is resistance measured?Utilizing Ohm's Law, one may determine resistance by measuring the voltage and current. Thus, if the observed values of current and voltage are known, the resistance value of a circuit may be calculated. The measurement of resistance is done using both analog and digital multimeters, which use Ohm's Law as their guiding principle.
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Referring to question 1, what is C1 in uf, omit units.
Answers
Enthalpy Changes the overall energy change in the substance portrayed in the graph at 48°C.
What are the data that were obtained from the question?Mass (m) = 0.3 Kg
Initial temperature (T1) = 20°C
Heat (Q) added = 35 KJ
Specific heat capacity (C) = 4.18 KJ/Kg°C
Final temperature (T2)
The final temperature of water can be obtained as follow:
Q = MC(T2 – T1)
35 = 0.3 x 4.18 (T2 – 20)
35 = 1.254 (T2 – 20)
Clear the bracket
35 = 1.254T2 – 25.08
Collect like terms
1254T2 = 35 + 25.08
1.254T2 = 60.08
Divide both side by the coefficient of T2 i.e 1.254
T2 = 60.08/1.254
T2 = 47.9 ≈ 48°C
Therefore, the final temperature of the water is 48°C.
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An object with a mass of 9.0kg has an acceleration of 3m/s the force acting on it is 3n
True or false?
Answers
Answer:
False
Explanation:
This can be proved through the simple force formula, [tex]\displaystyle{\sum \vec F = m\vec a }[/tex]. [tex]\displaystyle{\sum \vec F}[/tex] stands for net force, m is mass and [tex]\displaystyle{\vec a}[/tex] is acceleration.
As you see, force is equal to mass times acceleration. If we substitute mass = 9.0 kg and acceleration = 3 m/s² then we will have:
[tex]\displaystyle{\sum \vec F = 9.0 \, \text{kg} \, \times \, 3 \, \text{m/s}^2}[/tex]
This will result:
[tex]\displaystyle{\sum \vec F = 27 \, \text{kg}\cdot \text{m/s}^2}\\\\\displaystyle{\sum \vec F = 27\, N}[/tex]
Therefore, the force acting on the object should equal 27 N, not 3 N.
In Chapter 9 we will define the center of mass of an object and prove that its motion is described by the particle under constant acceleration model when constant forces act on the object. A gymnast jumps straight up, with her center of mass moving at 2.80 m/s as she leaves the ground. How high above this point is her center of mass (a) 0.100 s , (b) 0.200 s (c) 0.300 s, and (d) 0.500 s thereafter?
Answers
A position established in relation to an object or set of objects is the center of mass. It represents the system's average location as weighted by each component's mass.
The center of mass for straightforward stiff objects with homogeneous density is found at the centroid. The location where the distribution of mass is constant in all directions called the center of mass.
speed of the gymnast = 2.80 m/s
using the second equation of motion,
s = u t + 1/2 a t ^2
the position at time, t = 0.100 sec
s = (2.80) (0.100) + 1/2 (-9.8 m/s^2) (0.100)^2
s = 0.231 m.
the position at time, t = 0.200 sec
s = 0.364 m.
the position at time, t = 0.300 sec
s = 0.399 m.
the position at time, t = 0.500 sec
s = 0.175 m.
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according to the diagram, which shows the earth during the northern hemisphere winter solstice, how many hours of sunlight will the north pole receive on this day?
Answers
The north pole will receive 0 hours of sunshine on this day, which is the northern hemisphere solstice.
Where does the Northern Hemisphere take place?Northern Earth is inclined toward the Sun for a portion of our orbit. In the northern hemisphere, it is summer right now, which means there are longer daylight hours, a higher Sun, and more direct Sun rays hitting the ground, which results in warmer temperatures. Light is always present at the north pole!
What nation is at the planet's center?Based on a 2003 estimate, Skilip, Turkey, was determined to be the geographic center of all surface waters on Earth. It is the place here on surface of the Earth where the total distances to all places on land are least, to put it another way.
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6. The work done in pushing a 40 kg chair from the kitchen table to 10 meters down the
hall would be about_
,neglecting friction.
A. 40J
B. 4000J
C. OJ
D. 0.25J
Answers
Answer:
B
Explanation:
W = f * d
= mg * d
= 40(9.81)(10) =~4000 J
a person attempts to lift a heavy object using several pulleys and a 0.5 inch diameter rope. the first attempt to lift the object is unsuccessful. which of the following will make lifting of the object more likely?
Answers
The pulleys can be attached in such a way that the force required to lift the object will be less, and the direction of the pulley can be shifted systematically.
What is force?In the body, force is the result of either a push or a pull. The three main categories of forces are friction, nuclear, and gravitational. For instance, when a hand strikes a wall, the hand puts force on the wall and the wall also exerts a force on the hand. Newton was given a variety of laws to help him understand force.
We can move objects much more easily because of simple machinery called pulleys that can shift the direction of the force. When we employ many pulleys together, they also boost mechanical advantage. By using this method, less force is needed to raise an object.
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Read each question carefully. Show all your work for each part of the question. The parts within the question may not have equal weight. A satellite of mass mis orbiting Earth in a stable circular orbit of radius R. The mass and radius of Earth are Mg and Rg , respectively. Express your answers to parts (a), (b), and (c) the following in terms of m, R, ME, Rg , and physical constants, as appropriate.
(a) Derive an expression for the speed of the satellite in its orbit.
(b) Derive an expression for the total mechanical energy of the satellite-Earth system in its orbit.
(c) Derive an expression for the period of the satelliteâs orbit.
(d) The satellite is replaced with a similar satellite that has twice the mass. The new satellite is placed into the same orbit as the original satellite. Is the new satelliteâs orbital speed greater than, less than, or equal to the original satelliteâs orbital speed?
Answers
A satellite of mass mis orbiting Earth in a stable circular orbit of radius R, (a) Speed of satellite is v = sqrt(G x Mg/R). (b) total mechanical energy is E = KE + PE. (c) the period of the satellite as orbit is T = 2 x pi x sqrt(R^3 / (G x Mg)).
(a) The speed of the satellite in its orbit can be derived using Kepler's second law of planetary motion, which states that a planet or satellite's orbital speed is inversely proportional to the square root of the distance from the center of the planet or satellite to the center of the primary body. This can be expressed mathematically as:
v = sqrt(G x Mg / R)
where v is the orbital speed of the satellite, G is the gravitational constant, Mg is the mass of Earth, and R is the radius of the satellite's orbit.
(b) The total mechanical energy of the satellite-Earth system in its orbit can be calculated using the formula for kinetic energy and the formula for gravitational potential energy. The kinetic energy of the satellite is given by:-
= KE
= 1/2 x m x v^2
The satellite's gravitational P.E. determined by:
= PE
= -G x Mg x m / R
The total mechanical energy of the satellite-Earth system is the sum of the kinetic energy and gravitational potential energy, so:
= E
= KE + PE
= 1/2 x m x v^2 - G x Mg x m / R
(c) The period of the satellite's orbit is the time it takes for the satellite to complete one full orbit around Earth. This can be calculated using the formula:-
= T
= 2 x pi x sqrt (R^3 / (G x Mg))
where T is the period of the orbit, G is the gravitational constant, Mg is the mass of Earth, and R is the radius of the satellite's orbit.
(d) If the new satellite has twice the mass of the original satellite, then its kinetic energy will be four times greater, since KE is proportional to m. However, the gravitational potential energy of the new satellite will also be four times greater, since PE is proportional to m. Since the total mechanical energy of the satellite-Earth system is the sum of the kinetic and gravitational potential energy, the total mechanical energy of the new satellite-Earth system will be the same as the total mechanical energy of the original satellite-Earth system. Therefore, the new satellite's orbital speed will be the same as the original satellite's orbital speed.
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If the average hang time of a professional football kick is 4.60 s, then determine the average maximum height.
The average maximum height is what?
Answers
The average maximum height will be 103.7m.
What is a Projectile?A projectile is defined as an object that has an initial velocity and follows a path that dependent on the gravitational acceleration.
The gravitational force initially will act on the opposite direction until it reach the maximum height, and right after that, the gravitational force will accelerate the speed of the projectile.
The formular used will be;
[tex]H = \frac{1}{2} gt^{2}[/tex]
In this case, the initial velocity u = 0;
where g = 9.8m/s2
t = 4.6s
[tex]H = \frac{1}{2} (9.8)(4.6)^{2}[/tex]
H = 4.9 x 21.16
H = 103.7m.
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An experimental power plant at the Natural Energy Laboratory of Hawaii generates electricity from the temperature gradient of the ocean. The surface and deep-water temperatures are 28 ∘C and 5 ∘C, respectively.
Answers
The maximum theoretical efficiency of this power plant is 7.9
What is a power plant?A power plant , also referred to as a generating station or generating plant, is described as an industrial facility for the generation of electric power. Power plants are generally connected to an electrical grid.
The cold temperature =
5°C = 278K
Hot temperature =
28 ° = 273 + 28 K
28° = 303 K
n(efficiency) = 1- Tc/ Th
n(efficiency) = 1- 278/301
n(efficiency) = 1- 0.9175
(efficiency) = 0.082 x 100
n(efficiency) = 8.2 %
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Complete question =
An experimental power plant at the Natural Energy Laboratory of Hawaii generates electricity from the temperature gradient of the ocean. The surface and deep-water temperatures are 28 ∘C and 5 ∘C, respectively. What is the maximum theoretical efficiency of this power plant?
The answer to my English subject
Answers
A particular transition of the rubidium atom emits light whose frequency is 3.84 Ã 10^14 Hz. Is this light in the visible spectrum? If so, what is the color of the light?
Answers
The frequency of 3.84 x 10^14 Hz corresponds to a color in the blue-violet range of the visible spectrum. So, the color of the light emitted by the rubidium atom is blue-violet.
The frequency of light determines its position in the electromagnetic spectrum, which includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. The frequency of light that is visible to the human eye is in the range of approximately 400-700 nanometers (nm). This corresponds to a frequency range of approximately 7.5 x 10^14 Hz to 4.3 x 10^14 Hz.
The frequency of light emitted by the rubidium atom, 3.84 x 10^14 Hz, is within this range, so it is in the visible spectrum. To determine the color of the light, you can use the relationship between the frequency of light and its corresponding color. The colors of the visible spectrum, from lowest frequency to highest, are red, orange, yellow, green, blue, indigo, and violet.
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the purpose of high voltage direct current transmission lines to decrease the number of conductors needed for transmission of power in a grid system.
Answers
Capacitance is a direct issue with alternating current. The amount of power that may be sent across a line and the minimum distance between lines are both constrained by capacitance between parallel lines.
What does voltage mean, exactly?When charged electrons (current) are forced through a conducting loop by the pressure of an electrical circuit's power source, they may perform tasks like lighting a lamp. In a nutshell, voltage equals pressure and is expressed in volts (V).
What does voltage mean in kid-friendly terms?The difference in electrical energy between two circuit components is known as voltage. It is measured in volts and is measurable with a voltmeter. The current increases as the voltage grows. Higher electrical voltage and current are required for large electrical appliances.
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A square meter of the axon membrane has a resistance of 0.2 ohms. The membrane is 7.5 x 10‐⁹ m thick. What is the resistivity of the membrane?
Answers
Answer:
R = p_a d/A therefore RA/d = p_a = 2.67 x 10^-7 ohm m
Explanation:
If a football quarterback runs into and tackles another player by grabbing onto them, what type of collision would this technically be?
a. Elastic
b. Inelastic
Which of the following would be an example of a closed system?
a. A person pushing a refrigerator box across a rough floor
b. A water bucket being pulled up by rope from a well
c. A rolling oil drum across a smooth, frictionless marble floor
d. A large moving rock slowing down while ploughing through loose sand
Answers
''If a football quarterback runs into and tackles another player by grabbing onto them'' is Elastic collision. A closed system is a rolling oil drum across a smooth, frictionless marble floor.
What is meant by Elastic collision?A collision between two bodies in physics is referred to as an elastic collision if their combined kinetic energy stays constant. There is no net conversion of kinetic energy into other forms, such as heat, noise, or potential energy, in an ideal, fully elastic collision.When two small objects collide, the kinetic energy of the collision is first transformed into the potential energy of an attractive or repulsive force between the particles. (when the particles move against this force, that is, when the angle between the force and the relative velocity is acute), and then this potential energy is transformed back into the kinetic energy of the collision (when the particles move with this force, i.e. the angle between the force and the relative velocity is acute).Learn more about Elastic collision refer to :
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Starting from long-run equilibrium at A with output equal to and the price level equal to P1, if there is an unexpected monetary contraction that shifts aggregate demand from AD1 to AD3, then the short-run nonneutrality of money is represented by the movement from:
Answers
If there is an unexpected monetary contraction that shifts aggregate demand from AD1 to AD3, starting from long-run equilibrium at A with output equal to and the price level equal to P1, then the short-run non neutrality of money is represented by the movement from option A: point A to point B.
What is the long-run equilibrium about?At point A, the economy is in long-run equilibrium, with output equal to and the price level equal to P1. The unexpected monetary contraction shifts aggregate demand from AD1 to AD3, which reduces the demand for goods and services in the economy.
This reduction in demand causes a decrease in the price level and a decrease in output. As a result, the economy moves from point A to point B on the AD-AS curve, where output is lower and the price level is lower.
Therefore, This movement represents the short-run non neutrality of money, as the unexpected monetary contraction has caused a change in both output and the price level in the short run.
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See full question below
3. (Exhibit: AD–AS Shifts) Starting from long-run equilibrium at A with output equal to Y
and the price level equal to P1, if there is an unexpected monetary contraction that shifts
aggregate demand from AD1 to AD3, then the long-run neutrality of money is
represented by the movement from:
A) A to B.
B) A to G.
C) A to C.
D) A to D.
You should place 2kg mass onto a 0.2 kg block. What is the total weight in newtons ?
Answers
The total weight in Newtown is 21.56 N.
What is weight?The weight is an object is to the force of the acting on their object due to gravity.
Weight is a force described by the physics which is due to the gravitation pull of earth mercury is the
It's magnitude can be the calculated by multiplying the mass with the by the acceleration due to gravity but to the
And direction is always to the the centre of earth has
the weight of an object is to the force acting on their object by the due to gravity. Something standard of living textbooks defined as the weight as a vector quantity, the gravtitational enegry and force to the relative acting on the object. Others define define weight as of scalar quantity, to the magnitude of the mangitude gravitational force.
Here earth acceleration due to gravity is g= 9.8 ms^-2
And mass is 2+0.2 = 2.2 kg
So weight is 2.2(9.8)
= 21.56 N
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a motor is most powerful, when the: group of answer choices the workload is longer the workload is shorter time interval for the work is shorter.
Answers
The key idea is that time and power are inversely related to each other for a given quantity of work. A more powerful engine should be able to complete the same amount of work faster, according to the power equation.
Which of the following best describes how quickly work is completed?
The rate of doing work is known as power. It is the same as the amount of energy used up in a given amount of time. The joule per second (J/s), or SI system, is the unit of power.
Is negative work even possible?Work may be positive or negative; if it has a component in the same direction as the object's displacement, it is positive work.
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The city of London in the United Kingdom is found approximately at the same latitude as the city of Calgary in Canada. Calgary has an average high temperature in December of -4 degrees Celsius, while London has an average high temperature of 8.6 degrees Celsius.What best explains why the average temperature of London is warmer than that of Calgary in December?
Answers
The average temperature of London is warmer than that of Calgary in December as the oceanic currents warm the atmosphere in London.
Gravity, wind, and water density are what cause ocean currents, which are the continuous, predictable, directed movement of seawater. There are two directions in which ocean water can move: horizontally and vertically. Vertical shifts are referred to as upwellings or downwellings, while horizontal motions are known as currents.
Long-distance ocean currents combine to form the global conveyor belt, which is a major factor in determining the climate in many parts of the world. Ocean currents specifically affect the temperature of the areas they pass through.
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A 5.1 g experimental dart is fired into a block
of wood with a mass of 27.5 g. The wood
block is initially at rest on a 2.4 m tall post.
After the collision, the wood block and dart
land 2.1 m from the base of the post.
Find the initial speed of the dart.
Answer in units of m/s.
PLSSSS NEED URGENT
Answers
We can find the momentum of the dart by using the formula p = mv, where p is the momentum, m is the mass, and v is the velocity. Before the collision, the dart has a mass of 5.1 g and is at rest, so its momentum is 0. After the collision, the dart has a velocity of 2.1 m/s and a mass of 5.1 g, so its momentum is 10.7 kg*m/s.
We can also find the momentum of the wood block by using the same formula. Before the collision, the wood block has a mass of 27.5 g and is at rest, so its momentum is 0. After the collision, the wood block has a velocity of 2.1 m/s and a mass of 27.5 g, so its momentum is 57.9 kg*m/s.
Since the total momentum of the system must remain constant, the momentum of the dart and the wood block after the collision must add up to 0. We can set up the following equation to solve for the initial velocity of the dart:
10.7 kgm/s + 57.9 kgm/s = 0
Solving for v, we find that the initial velocity of the dart is -5.37 m/s. This is the negative of the final velocity of the wood block, indicating that the dart and the wood block moved in opposite directions after the collision.
The final answer is 5.37 m/s.
what is the wavelength of the longest wavelength standing wave pattern that can fit on this guitar string? express your answer in centimeters. view available hint(s)
Answers
Therefore, only half of the wave fits since it is evenly divided and a whole crest fits on the string; the longest wavelength standing-wave pattern which can fit on this guitar has a wavelength of 1 = 120 cm.
What do wavelengths and frequencies refer to?The distance of two wave crests is known as the wavelength, and it also applies to troughs. The amount of vibrations that travel across a certain area in one second is measured in cycles each second, or frequency.
How is wavelength determined?The wavelength is calculated by calculating the distance between two identical positions on adjacent waves. The distance of one compressive to the next or from one conformational to the subsequent is measured in order to calculate the wavelength of such a longitudinal wave.
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A plumb bob (a mass m hanging on a string) is deflected from the vertical by an angle θdue to a massive mountain.A) Make an estimate of the mass of Mt. Everest, assuming it has the shape of a cone 3910m high and base of diameter 3910m Assume its mass per unit volume is3000kg/m3.B)Estimate the angle of the plumb bob if it is 5.20km rom the center of Mt. Everest.
Answers
a)An estimate of the mass of Mt. Everest is 4.7 × [tex]10^{13}[/tex] kg.
b) The angle of the plumb bob is - 6.83 ×[tex]10^{-4}[/tex] degree.
Given data
h = the height of the cone = 3910m
[tex]d_{1}[/tex]= the base diameter = 3910m
ρ = the mass per unit volume = 3000kg
d=the distance of the plumb bob from the center of Mt. Everest
= 5.2km = 5200m
[tex]R_{earth}[/tex] = earth's radius = 6400000m
[tex]M_{earth}[/tex] = earth's mass = 5.97 ×[tex]10^{24}[/tex] kg
A) Mass = Volume × Density
M = [tex]\frac{1}{3} \frac{\pi }{4} d_{1} ^{2} h[/tex] × ρ
M = [tex]\frac{1}{3} \frac{\pi }{4} * (3910)^{2} * 3910 * 3000[/tex]
M = 4.7 × [tex]10^{13}[/tex] kg
Therefore, an estimate of the mass of Mt. Everest is 4.7 × [tex]10^{13}[/tex] kg.
B) The plumb bob makes some angle with the vertical because it is subjected to the gravitational force from Mt. Everest and the gravitational force of the earth in the downward direction.
calculating the sideway force from Mt. Everest:
[tex]F_{x} = \frac{GM_{bob} * M }{d^{2} }[/tex]
calculating the downward force from the center of the earth:
[tex]F_{y} = \frac{GM_{bob} * M_{earth} }{R_{earth} ^{2} }[/tex]
then,
tanθ = [tex]\frac{{GM_{bob} * M }/{d^{2} }}{{GM_{bob} * M_{earth} }/{R_{earth} ^{2} }}[/tex]
tanθ= [tex]\frac{M * R_{earth} ^{2} }{M_{earth} * d }[/tex]
tanθ = [tex]\frac{4.7 * 10^{13} * 6400000 }{5.97 * 10^{24} * 5200^{2} }[/tex]
= 1.193 × [tex]10^{-5}[/tex]
θ = 6.83 × [tex]10^{-4}[/tex] degree
So, the angle of the plumb bob is - 6.83 ×[tex]10^{-4}[/tex] degree.
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During the launch from a board, a diver's angular speed about her center of mass changes from zero to 6.60 rad/s in 250 ms. Her rotational inertia about her center of mass is 12.0 kg·m2.
(a) During the launch, what was the magnitude of her average angular acceleration?
rad/s2
(b) During the launch, what was the magnitude of the average external torque on her from the board?
N·m
Answers
Her average rotational acceleration is equal to the board's average external torque over her, which is Nm234.16 Nm, or 28.18 rad/s.
Simple definition of angular acceleration.An object rotating experiences a change of angular velocity per unit of time, which is quantified as angular acceleration (also known as rotational acceleration). It is a vector quantity that has two strongly outlined directions or senses and a magnitude component.
Given: Initial angular speed w, = 0 rad; Initial and final angular speeds cf, = 6–20 rad/s lime
Rotational inerlia I (= 12 leg m° at time t = 220 x163 5 Rotational angulas acceleration wU = wo tat 6.20 = 0 + xx 220 x103 6.20 = = 0.02918 x10 220 x103 a = 28.18 rad/s -> Quality varies torque N= IX 12x28.18 234.16 Nm
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