Lagrange's equations of motion for the system is d(ml³Ф2 + ml²Ф1 cos (Ф1-Ф2)) − (−ml³Ф1Ф2 sin (Ф1-Ф2)-mgl sinФ2 )/dt = 0.
Newton’s method of developing equations of motion requires taking elements apart. When forces at interconnections are not of primary interest, more advantageous to derive equations of motion by considering energies in the system
Lagrange’s equations is Indirect approach that can be applied for other types of systems (other than mechanical) Based on calculus of variations.
A plane pendulum (length l and mass m), restrained by a linear spring of spring constant k and a linear dashpot of dashpot constant c. The upper end of the rigid massless link is supported by a frictionless joint.
A mass spring dashpot subsystem in a falling container of mass m1. The system is subject to constraints that confine its motion to the vertical direction only. The mass m2 linear spring of undeformed length l0 and spring constant k, and the linear dashpot of dashpot constant c of the internal subsystem.
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the a string on a cello vibrates in its first normal mode with a frequency of 220 hz. the vibrating segment is 66.0 cm long and has a mass of 1.80 g.(a) Find the tension in the string.N(b) Determine the frequency of vibration when the string vibrates in three segments.Hz
The string vibrates in three segments at a frequency of 660 Hz while exerting a force of 166.27 N. The first normal mode of a cello string vibrates at a frequency of 220 Hz.
The frequency of an event is its repetitions per unit of time. As a contrast to spatial frequency, it is also sometimes referred to as temporal frequency, and as a contrast to angular frequency, it is sometimes referred to as ordinary frequency. The hertz unit is used to measure frequency (Hz). f = 220Hz
L = 66cm = 0.6m for the wire's length
Wire mass = 1.8*10-3 kg, m/L = 1.8*10-3/0.66, and kg/m = 2.7*10-3
F = 4*2.7 *10^-3 *(0.6^2)*(220)^2 = 166.2N
The frequency at which n segments appear in a string is known:
fn = nf1
For, n = 3
f3 = 3f1
f3 = 3*220
f3 = 660Hz
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an air capacitor is made by using two flat plates, each with area a, separated by a distance d. then a metal slab having thickness a (less than d) and the same shape and size as the plates is inserted between them, parallel to the plates and not touching either plate (figure 1).
An air capacitor is made by using two flat plates, each with area a, separated by a distance d, then a metal slab having thickness a (less than d) and the same shape and size as the plates is inserted between them, a capacitor has dielectric material between two plates.
A capacitor is a device that stores electrical energy in an electric field by using the buildup of electric charges on two neighboring surfaces that are electrically insulated from one another. It is a passive electrical component with two terminals. A capacitor's effect is referred to as capacitance. A capacitor is an electrical component designed to increase capacitance, even though there is some capacitance between any two neighboring electrical wires in a circuit. In its early days, the capacitor was referred to as a "condenser," and you may still see it in a few compound names, such "condenser microphone." There are several sorts of practical capacitors that are often used, and they are available in a wide range of physical shapes and constructions. The majority of capacitors include two or more electrical conductors separated by an insulating substance, typically in the form of metallic plates or surfaces. An electrolyte, thin sheet, sintered metal bead, or foil can all function as conductors. The nonconducting dielectric increases the charge capacity of the capacitor.
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a hippo's body is 4.0 m long with front and rear feet located as in (figure 1). the hippo carries 60% of its weight on its front feet.
The distance at which the center of gravity of hippo is located from the tail of hippo is equal to 1.58 m.
Center of gravity is referred to the point in any object at which the weight of the object is distributed evenly in all the directions. We need to find the position of Center of Gravity of the Hippo from the tail. We are given that Hippo carries 60% weight on its front feet that is
M(front) = 0.60 W
M(rear) = 0.40 W
Let d be the distance of center of gravity from tail and we write the equation as
0.60(1.8 + 0.5 - d) - 0.4(d - 0.5) = 0
=> 1.08 + 0.3 - 0.60d - 0.4d + 0.2 = 0
=> d = 1.58 m
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Complete Question:
A hippo's body is 4.0 m long with front and rear feet located as in (Figure 1). The hippo carries 60% of its weight on its front feet. How far from its tail is the hippo's center of gravity?
The speedometer of a car reads 85 mph. It passes a truck in the next lane traveling at 75 mph. Which of the following statements is true?
Both measurements are scalar quantities.
Both measurements are vector quantities.
The car's measurement is a scalar, and the truck's measurement is a vector.
The car's measurement is a vector, and the truck's measurement is a scalar.
The statements that is true about the car and the truck is "The car's measurement is a scalar, and the truck's measurement is a vector"
third option is the correct answer.
What is scalar quantity?Scalar quantities are those quantities that can be described by magnitude only.
These type of quantity has no direction, but can be effectively described by direction only.
Examples of scalar quantities include the following;
temperaturemassenergydistancespeeddensityVector quantities are those type of quantity which can be described by both quantity and direction.
Examples of vector quantities include the following:
velocityaccelerationdisplacementforcepositionmomentum, etcSpeedometer is a device used in measuring the speed of a car, hence the measurement of the car is scalar. The speed of the truck has direction (next lane), so it can be effectively regarded as vector quantity.
Thus, the speed of the truck has both magnitude and direction and can be called vector measurement.
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type 1a supernovae are caused when a_____accretes enough mass to overcome the chandresekhar limit.
When a white dwarf gains enough mass to surpass the Chandra-Sekhar limit, type 1a supernovae are produced.
The importance of the Chandrasekhar limit in Type-1a supernovae has been recognised in astrophysics. The Chandrasekhar limit is thought to be crossed by a white dwarf, causing a catastrophic collapse, which is assumed to be the cause of these supernovae. It is believed that Type Ia supernovae (SNIa) are produced when a carbon-oxygen white dwarf in a binary system reaches the Chandrasehkar limit, either as a result of accretion from a donor or mergers. One of the two stars must be a white dwarf in order to cause a type Ia supernova.
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what are the 5 major gyres
Answer:
The North Atlantic Gyre, the South Atlantic Gyre, the North Pacific Gyre, the South Pacific Gyre, and the Indian Ocean Gyre.
Explanation:
The 5 major gyres are:
1. the North Atlantic Gyre
2. the South Atlantic Gyre
3. the North Pacific Gyre
4. the South Pacific Gyre
5. the Indian Ocean Gyre
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Blocks A and B have a mass of 7kg and 10kg, respectively. Using the coefficients of static friction indicated, determine the largest vertical force P which can be applied to the cord without causing motion.
The largest vertical force applied to the cord without causing motion is
P ≤ 16.68 N.
From the free body diagrams shown in the attachment, we can write
∑ Fy = 0; -98.1 + Nab = 0
Nab = 98.1 N
-98.1 - 68.67 + Na = 0
Na = 166.77 N
∑ Fx = 0; P - Fab = 0, P = Fab = Fa
Fab - Fa = 0
Fab = Fa
1st assumption: Block B slides alone
Fab = μab Nab = 0.3* 98.1 = 29.43 N
Fa = 29.43 is not less than μa Na = 0.1 * 166.7 = 16.68 N
Fa = 29.43 > μa Na = 16.68 N
P = 29.43 N
2nd assumption: Block A and B moves together
Fa = μa Na = 0.1 * 166.7 = 16.68 N
Fab = 16.68 < μab Nab = 29.43 N
P = 16.68 N
Thus, we can conclude that, P ≤ 16.68 N.
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we will model the spine and upper body as a horizontal rigid rod of uniform density with a length of 50.0 cm and a mass of 40.0 kg. assume that the person attempts to lift an object with their arms, which we will model as attached at the far end of the rod. support of the back in this position is provided primarily by the erector spinalis muscle which we will model as being attached at one end to the spine at a point 33.0 cm from the hip at an angle of 10
Tension in the back muscle for this scenario is 3095.4 N and the compressive reaction force is 3048 N, and the ratio is 5.53.
Two forces are acting on the compartment, Gravity acting downward, Tension T in cable acting upward.
Force is an influence which could change the movement of an object. A pressure can reason an object with mass to change its pace (e.g. moving from a kingdom of relaxation), i.e., to boost up. pressure can also be described intuitively as a push or a pull. A pressure has both importance and course, making it a vector quantity. it's far measured within the SI unit of newton (N). it's far a wellknown mechanical quantity. pressure is represented with the aid of the symbol F (previously P).
A) In equilibrium net torque about the hip = 0
T*sintheta*x - Fgup*L/2 - Fgob*L = 0
T*sin10*0.33 - 40*9.8*0.5/2 - 16.2*9.8*0.5 = 0
Tension(T) = 3095.4 N
B) Fv = FRx = T*costheta
Fv = 3095.4*cos10
= 3048 N
C) Fv/(wub + wobj) = 3048/((40+16.2)*9.8) = 5.53
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A. 101/ B. 20Hz If 25) is taken away by heat from a sys in internal energy of the system? A. SA B..SJ SJ The amount of damping force that allow shortest possible time is called
The amount of damping force that allow shortest possible time is called critical damping of the system.
What is critical damping?Critical damping is the threshold between overdamping and underdamping at which the oscillator returns to the position of equilibrium quickly as possible.
Critical damping is frequently desired because such a system returns to and maintains equilibrium quickly. Furthermore, a constant force applied to a critically damped system moves the system to a new equilibrium position as quickly as possible without overshooting or oscillating around the new position.
Critical damping thus provides the rapid approach to zero amplitude for a damped oscillator.
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17. A skateboarder is going 10 m/s the instant it is launched vertically off a ramp. If the mass of the skateboarder is 50 kg, how high above the ramp can he possibly go? If the mass of the skateboarder is 100 kg, how high above the ramp can he possibly go? If the speed of the skateboard is 20 m/s when it is launched how high above the ramp can he possibly go? (5.1m, 5.1m, 20.4m)
Answer: To solve this problem, we can use the principle of conservation of energy. Energy is a property of an object or system that is related to its ability to do work, and can take many different forms. In the case of a skateboarder being launched off a ramp, the energy of the system is made up of two forms: kinetic energy and potential energy.
Kinetic energy is the energy of motion, and is equal to one half of an object's mass times its velocity squared. In this case, the skateboarder has a kinetic energy of 0.5 * 50 kg * (10 m/s)^2 = 2500 J when it is launched off the ramp.
Potential energy is the energy of position, and is equal to an object's mass times the acceleration due to gravity times its height. In this case, the skateboarder has a potential energy of 50 kg * 9.8 m/s^2 * h, where h is the height above the ramp.
Since energy is conserved, the sum of the kinetic and potential energy of the system must be constant. Therefore, at the peak of the skateboarder's motion, his kinetic energy must be 0, and all of the energy of the system must be in the form of potential energy. This means that the maximum height that the skateboarder can reach is equal to the kinetic energy of the system divided by the acceleration due to gravity times the mass.
For a skateboarder with a mass of 50 kg, the maximum height that he can reach is 2500 J / (9.8 m/s^2 * 50 kg) = 5.1 m. For a skateboarder with a mass of 100 kg, the maximum height that he can reach is also 5.1 m. This is because the maximum height that an object can reach is only dependent on its initial kinetic energy, not its mass. However, if the skateboarder is moving at a higher initial velocity, such as 20 m/s, then the maximum height that he can reach will be higher. In this case, the maximum height will be 0.5 * 50 kg * (
Explanation:
A3,242 kg truck moving with a velocity of 11 m/s hits a 1,413 kg parked car. The impact causes the 1,413 kg
car to be set in motion at 15 m/s. What is the velocity of the truck immediately after the collision?
The velocity of the truck after the collision is 4.47 m/s.
What is the velocity of the truck?We know that we can be able to use the principle of the conservation of momentum to be able to obtain the velocity of the truck. We know that from this principle, the momentum after collision would be the same as the momentum before collision.
Using this approach we can say that;
Momentum before collision = Momentum after collision
Then;
(3,242 * 11) + (1,413 * 0) = (3,242 * v) + ( 1,413 * 15)
35662 = 3242v + 21195
v = 35662 - 21195/3242
v = 4.47 m/s
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The velocity of the truck immediately after collision is 4.46m/s
What is conservation of linear momentum?
Conservation of linear momentum states that in a closed system, if two bodies collides ,the momentum is always conserved. Or we can say conservation of linear momentum states that the momentum before collision is equal to the momentum after collision.
Momentum is expressed as : momentum = mass × velocity
The momentum before collision =
3242× 11 + 1413×0
= 35662+0 = 35662kgm/s
The momentum after collision
3242v + 1413× 15
= 3242v + 21195
from conservation of momentum
35662= 3242v+ 21195
3242v = 35662-21195
3242v = 14467
v = 14467/3242
v = 4.46m/s
therefore the velocity of the truck after collision is 4.46m/s
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virtual particles are the hypothesized particles that combine to form quarks and other fermions. the graviton, and other particles predicted but not yet observed. particles that temporarily materialize out of the vacuum of space. a mathematical tool used to solve the equations describing the motion of real particles in quantum mechanics.
In quantum mechanics, virtual particles are the hypothesized particles that combine to form quarks, graviton etc is a correct statement.
Quantum mechanics is the branch of science that examines the atomic and subatomic behavior of matter and light. It tries to explain and characterize the properties of molecules, atoms, and their constituent protons, neutrons, electrons, and other less well-known particles like quarks and gluons. These characteristics include electromagnetic radiation and how the particles interact with one another (i.e., light, X-rays, and gamma rays). It can be difficult to understand and accept the implications of the quantum theory because the behavior of matter and radiation at the atomic level frequently appears peculiar. Its theories frequently contradict intuitions derived from observations of the real world.
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a student throws a ball straight up into the air. which of the following statements concerning the velocity and acceleration of the ball when it is at its maximum height is most accurate?
Velocity is zero, acceleration is non-zero is correct statement.
It is given that a ball is thrown upwards so a ball. So when ball is at maximum height, the condition will be that it's velocity will be zero.
So at maximum height velocity will become zero. No acceleration acting on it, acting on eight will be -G,
then G=-9.8 m/[tex]s^2[/tex]
So this extra acceleration due to gravity will always be same on the ball whether it is moving or it is at maximum height.
When the velocity will be zero only while our city is zero needed and the expiration is not equal to zero.
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A newly discovered planet has twice the mass of the Earth, but the acceleration due to gravity on the new planet's surface is exactly the same as the acceleration due to gravity on the Earth's surface. The radius of the new planet in terms of the radius R of Earth is (A) 1/2R (B) √2/2R (C) √2R (D) 2R (E) 4R
In relation to the radius R of the Earth, the new planet's radius is √2R.
Calculation:The value, represented by r earth, equates to roughly 6,371,000 meters (6.371 x 106 m). This equates to 3,960 statute miles or around 6,371 kilometers (km). The formula r = (A/) can be used to determine the radius of a circle using area.
What is the formula for Kepler's third law?The period of a planet's orbit (P) squared is equal to the size of the semi-major axis of the orbit (a) cubed when it is stated in astronomical units because P2 = a3 according to Kepler's Third Law. If the mass of the planet is known, Kepler's Third Law can be applied to determine the planet's orbital radius.
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Eventually, the suit vents so much air that all of the nitrogen is gone. It now must add oxygen just to keep the atmospheric pressure normal, at about 1 atm. Which of the following are true about breathing too much oxygen?
a. generally a partial pressure of oxygen of 0.45 atm is considered toxic, but the duration of the exposure is also important
b. short exposures to oxygen of 0.6 atm are survivable, but there will be symptoms of hyperoxia
c. breathing 100% oxygen for a full day will result in death.
d. all of these are true statements
Generally, a partial pressure of oxygen of 0.45 atm is considered toxic but the duration of the exposure is also important. Option A.
High air pressure pushes our bodies harder and limits how much our tissues can expand. Low atmospheric pressure, on the other hand, causes the tissues of the body to swell more, putting more pressure on nerves and other parts of the body.
During the rainy season, most surface waters are enriched with oxygen because rains saturate them with oxygen. As mentioned earlier, higher partial pressure of oxygen in the alveoli causes the pulmonary arterioles to dilate, thereby increasing blood flow.
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a golf ball stays on the tee until the golf club hits it. which of the following principles best describes why this occurs?
Newton's law of inertia best describes why a golf ball stays on the tee until the golf club hits it.
Newton's law of inertia states that an object at rest will remain at rest unless acted upon by an external force. In the case of a golf ball on a tee, the golf ball is not moving because there is no external force acting upon it. Therefore, the golf ball will remain on the tee until the golf club is used to hit it, applying an external force and causing the golf ball to move.
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces.
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a child throws a rock with a velocity of 25 m/s at angle of 65 degrees above the horizontal. the rock hits the side of the building at a height of 12 meters. (a) How far above the release point does the ball hit the wall? What are the (b) horizontal and (c) vertical components of its velocity as it hits the wall? (d) When it hits, has it passed the highest point on its trajectory?
(a) The ball hits the wall 5.3 meters above the release point.
(b) The horizontal component of its velocity is 17.5 m/s. (c) The vertical component of its velocity is 17.1 m/s.
(d) Yes, it has passed the highest point on its trajectory.
(a) Using the equation for range, we can solve for time:
R = V*t*cosθ =>25*t*cos65 = 12 t = 0.75 s
We can then solve for the height using the equation for vertical displacement:
h = V*t*sinθ - 0.5*g*t^2
h = 25*0.75*sin65 - 0.5*9.8*0.75^2 h
= 5.3 m
(b) We can solve for the horizontal component of the velocity using the equation for range:
R = V*t*cosθ 17.5
= 25*t*cos65 t
= 0.7 s V = 17.5 m/s
(c) We can solve for the vertical component of the velocity using the equation for vertical displacement:
h = V*t*sinθ - 0.5*g*t^2 17.1
= 25*0.75*sin65 - 0.5*9.8*0.75^2 V = 17.1 m/s
(d) Yes, the ball has passed the highest point on its trajectory because the ball is traveling downwards when it hits the wall.
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An irregularly shaped flat object of mass 2.40 kg is suspended from a point at a distance d from its center of mass and allowed to undergo simple harmonic motion in the vertical plane. The object has moment of inertia I = 1.24 kg · m2 about an axis passing through the point of suspension and perpendicular to the plane of the object. The frequency of this oscillatory motion is 0.640 Hz. What is the distance d of the pivot point from the center of mass of the object?
_____m
The distance of the pivot point from the center of mass of the object = 0.85 m
Oscillatory motionOscillatory motion is any motion that is repeated at the same time interval and through the same trajectory in its motion.
The simplest oscillatory motion is harmonic motion or simple harmonic motion (SHM).
The simple harmonic motion is a periodic motion that occurs at the same time interval.
We have,
Mass of point = 2.40 kg ⇒ m
Moment of inertia = 1.24 kgm² ⇒ I
Frequency = 0.640 Hz ⇒ f
Acceleration due to gravity = 9.8 m/s² ⇒ g
Now, find the angular velocity first,
ω = 2[tex]\pi[/tex]f
= 2[tex]\pi[/tex] (0.640)
= 4.0192 rad/s
So, the distance of the pivot point from the center of mass of the object is:
ω = [tex]\sqrt{\frac{mgd}{I} }[/tex]
4.0192 = [tex]\sqrt{\frac{(2.40)(9.8)(d)}{1.24} }[/tex]
d = (4.0192)² (1.24) / (2.40)(9.8)
= 20.0309211/23.52
= 0.85 m
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A heat pump has a coefficient of performance equal to 4.20 and requires a power of 1.75 kW to operate. (a) How much energy does the heat pump add to a home in one hour? (b) If the heat pump is reversed so that it acts as an air conditioner in the summer, what would be its coefficient of performance?
a) Energy added = 3.113 × 107 J b) coefficient of performance 3.70
A) COPhp= QH/Win
Hence QH = (COPhp)Win = 4.70×1.84 = 8.648 kW
Energy added = QH(60×60) = (8.648×103)(3600)
Energy added = 3.113 × 107 J
B) coefficient of performance = (COP)hp - 1 = 4.70 - 1 = 3.70
Various efficiencies can be used to convert energy between different forms. Transducers are objects that change between these states. Examples of transducers include a battery, which converts chemical energy into electric energy, a dam, which transforms gravitational potential energy into the kinetic energy of moving water (and the turbine blades), and finally into electric energy via an electric generator (from heat to work)
Energy transformation examples include creating electric power from heat energy using a steam turbine or lifting something against gravity while using electrical energy to power a crane motor. When an object is lifted against gravity, mechanical work is done on it and gravitational potential energy is stored inside it. Gravity performs mechanical work on the thing if it falls to the ground.
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an energy storage system based on a flywheel (a rotating disk) can store a maximum of 3.6 mj when the flywheel is rotating at 12000 revolutions per minute.
I = 1.82 kg/m2 is the flywheel's moment of inertia. The highest amount of energy that can be stored by a flywheel-based energy storage system (a revolving disc) is 3.6 mj.
The torque required to achieve a desired angular acceleration is determined by the rigid body's moment of inertia, also referred to as the mass moment of inertia, angular mass, second moment of mass, or, more precisely, rotational inertia.
Given that, E = 3.6 MJ = 3.6*106J is the maximum energy that can be stored in the flywheel.
Flywheel angular velocity is w = 12000 revs per second, or 12094.39 rads per second.
the flywheel's moment of inertia must be determined. In rotational kinematics, the energy of a flywheel is given by I = 2E/W2.
I = 1.82 kg - m^2
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a friend in a spaceship moves away from you at 0.05c, and then fires a rocket also away from you at 0.5c relative to the spaceship. from your frame of reference, the speed of the fired rocket is
The speed of the rocket is 3.6 * 10⁸ m/s.
The rocket's speed relative to spaceship is
Speed of spaceship = v(s) = 0.05c
Speed of rocket = v(r) = 0.5c
We have to find the speed of rocket measured by friend in the space if the spaceship is fired away from the rocket.
We need to calculate the rocket's speed relative to Earth
Using formula of relative speed
v = v(s) - v(r) / 1 - {v(r) - v(s) / c²}
Put the value into the formula
v = 0.05 - 0.5 / 1 - { 0.5 - 0.05 / c²}
v = c * 1.2
v = 3.6 * 10⁸ m/s
Therefore, the speed of the rocket is 3.6 * 10⁸ m/s.
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A wire of negligible mass is wrapped around the outer surface of the disk of mass M. If the disk is released from rest, determine its angular velocity at time t. Given: M = 2 kg , t = 3 s , r = 80 mm
If the disk is released from rest, Angular velocity (ω) of the disk is [tex]245\frac{rad}{s}[/tex]
In physics, the angular velocity or rotational velocity (ω or Ω) is also known as the angular frequency vector, is the rate at which an object's angular position or orientation changes over time (i.e., the object's rotation speed is a pseudo-vector representation. or spin relative to a point or axis).
The magnitude of the pseudovector represents the angular velocity, i.e. the speed at which the object rotates or rotates, and its direction is perpendicular to the current plane of rotation or angular displacement. Angular velocity direction is conventionally given by the right-hand rule.
Calculation :
Given : M = 2kg, t = 3s, r = 80mm
solution :
[tex]0 + Mgrt = \frac{3}{2} Mr^{2}[/tex]ω
ω = [tex]\frac{2}{3} (\frac{g}{r} ) t[/tex]
ω = [tex]245\frac{rad}{s}[/tex]
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A copper wire loop is initially at rest in a uniform magnetic field. Between times i=t, and t=tv+delta t the loop is rotated about a vertical axis as shown. Will current flow through the wire of the loop during this time interval? If so, indicate the direction of the induced current and explain your reasoning. If not, explain why not.
The force acting on the coil must also act parallel to the magnetic field if it is being accelerated parallel to the field.
A fundamental requirement that must be satisfied for current to be induced in a coil is that the magnetic field and force (acceleration) directions must be perpendicular to one another. As a result, current is induced in a path that is perpendicular to the directions in which the force acting on the coil and the magnetic field are moving. The coil would conduct this current either in a clockwise or anticlockwise direction. We may recast the change in fux as shown above because B is constant due to the constant magnetic Feld. Since A is a positive number, there will be a.
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assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, the figure. the ball is accelerated uniformly from rest to 8.1 m/s in 0.38 s , at which point it is released. assume that the forearm has a mass of 3.7 kg and rotates like a uniform rod about an axis at its end. neglect gravity.
The angular acceleration of the arm is 68.76 rad/s².
We know the formula for angular acceleration as,
α = (ω - ω₀)/t
It is given that the ball is accelerated from rest, so ω₀ = 0.
We know the formula for velocity as, v = r* ω
ω = v/r
Given that, Velocity v = 8.1 m/s
Time t = 0.38 s
Radius r = 31 cm = 0.31 m
So, α = 8.1/0.31 * 1/0.38 = 26.13 /0.38 = 68.76 rad/s²
Angular acceleration is calculated to be 68.76 rad/s².
The question is incomplete. We should find out the angular acceleration of the arm. The figure is attached in the attachment below.
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In the photoelectric effect, suppose that the intensity of the light is increased, while the frequency is kept constant. The frequency is greater than the minimum frequency fo. State whether each of the following will increase, decrease, or remain constant, and explain your choice: (a) the current in the phototube, (b) the number of electrons emitted per second from the metal surface, (c) the maximum kinetic energy that an electron could have, (d) the maximum momentum that an electron could have, and (e) the minimum de Broglie wavelength that an electron could have.
(a) According to the photoelectric effect, the intensity of light corresponds to the density of photons; if you have a more intense beam of light, you have more photons. Since the frequency is higher than the minimum frequency required to overcome the work function of the metal, more photons imply that more electrons will be ejected from the metal. Therefore, the current in the phototube will be higher.
(b) Current is defined as charge per unit of time. Electrons are charged, and we said in part (a) that the current would increase, so the number of electrons emitted from the metal surface will increase as well.
(c) The maximum kinetic energy will not change because the energy of the incident photons is constant at E = hf and the work function (the energy taken away by the metal) is a constant depending on the particular metal.
(d) Momentum and kinetic energy, you will note, are basically the same thing since
KE = [tex]mv^{2} \frac{1}{2m} = p^{2} /2m[/tex]
So we get the same answer as in part (c); namely, the maximum momentum will remain the same independent of the intensity.
(e) The definition of the de Broglie wavelength is
λ = h/p
so, since the maximum momentum Pₘₐₓ is constant, and h is Planck's constant, the minimum de Broglie wavelength is constant.
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You are at a furniture store and notice that a Grandfather clock has its time regulated by a physical pendulum that consists of a rod with a movable weight on it. When the weight is moved downward, the pendulum slows down; when it is moved upward, the pendulum swings faster. If the rod has a mass of 1.23 kg and a length of 1.25 m and the weight has a mass of 1.99 kg, where should the mass be placed to give the pendulum a period of 2.00 seconds? Measure the distance in meters from the top of the pendulum.
I think the equation for this problem is T= 2pi * sqrt ( I / mgd), where I = md^2
The reason why I think that is because it is no a simple pendulum, it is a physical pendulum which means that a hanging object hangs about a fixed axis that does not pass through its center of mass.
The distance from the top of the pendulum is 2.98 m.
Given,
Mass of the pendulum rod, M = 1.23 kg
Length of the pendulum rod, L = 1.25 m
Mass of the weight, m = 1.99 kg
Time period, T = 2 s
Let,
The distance is d.
We know that the formula of the time period is given by
[tex]T =[/tex] [tex]2\pi \sqrt{\frac{1}{(M+m)g} \frac{1}{3}ML^{2}+\frac{1}{(M+m)g}md^{2}}[/tex]
4 = 4π² {1/3(1.23)(1.25)(1.25) + (1.99)d²}/{(1.23 + 1.99)9.8}
94.668 = 6.034 + 10d²
d = 2.98 m
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Suppose you use three different scales to weigh a bag of oranges. One scale
says the bag weighs 2.1 lb, a second says it weighs 2.2 lb, and a third says it
weighs 2.1 lb. The actual weight of the bag of oranges is 2.153 lb. Which of
the following best describes these results?
O A. Precise but not accurate
OB. Accurate but not precise
C. Both accurate and precise
OD. Neither accurate nor precise
The statement that describes the results of the different weighing scales is as follows: Both accurate and precise (option C).
What is accuracy and precision?Accuracy is the exact conformity to truth, or to a rule or model i.e. degree of conformity of a measure to a true or standard value while precision is the ability of a measurement to be reproduced consistently.
Accuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements are to their true value, while precision is how close the measurements are to each other.
According to this question, three different scales were used to weigh a bag of oranges. One scale says the bag weighs 2.1 lb, a second says it weighs 2.2 lb, and a third says it weighs 2.1 lb. The actual weight of the bag of oranges is 2.153 lb.
Based on the above observation, it can be said that the results are both accurate and precise because the measurements are both close to one another and to the true or standard value.
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g 5. the decomposition of br2 is followed as a function of time in two different plots. determine the order of the reaction and the rate constant
To determine the order of a chemical reaction, you can plot the concentration of one of the reactants or products versus time and monitor the slope of the line. The slope of the line will be proportional to the rate of the reaction, and the exponent of concentration term in the rate law will be the order of the reaction.
If you have two plots of the decomposition of Br₂ as a function of time, you can choose order of the reaction by comparing the slopes of the lines. If slopes of lines are the same, then the reaction is first order. If slopes of lines are proportional to the concentrations of Br₂ to the power of 2, then the reaction is second order. If slopes of lines are proportional to the concentrations of Br₂ to the power of 3, then the reaction is third order.
To calculate rate constant, you will require to employ the rate law for the reaction. The general form of rate law is: rate = k[A]^m[B]^n...
To determine the rate constant, you will require to estimate the concentrations of the reactants and the rate of the reaction at different times and utilize the rate law to solve for "k". The rate of the reaction can be calculated by estimating the change in concentration of a reactant or product over a particular time interval.
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The G string on a guitar is a 0.46 mm diameter steel string with a linear density of 1.3 g/m. When the string is properly tuned to 196 Hz, the wave speed on the string is 250 m/s. Tuning is done by turning the tuning screw, which slowly tightens - and stretchs - the string. By how many mm does a 75 cm long G string stretch when it's first tuned?
When the string is properly tuned to 196 Hz, the wave speed on the string is 250 m/s then 75 cm long G string stretched when it's first tuned is 1.833 mm.
Simple harmonic motion (SHM) occurs when the restoring force (the force directed toward a stable equilibrium point) is proportional to the displacement from equilibrium.
Repetitive motion through a central equilibrium point, Symmetry of maximum displacement, Period of each cycle is constant, Force causing the motion is directed toward the equilibrium point (minus sign).
At the equilibrium point x = 0 so, a = 0 also. When the stretch is a maximum, a will be a maximum too. The velocity at the end points will be zero, and it is a maximum at the equilibrium point.
As we know,
v = sqrt(T/mu)
250 = sqrt(T/(1.3*10^-3))
So T = 81.25 N
Young's modulus for steel = 200 x 10^9 Pa
Y = (T/A)/(deltal/l) = T*l/(deltal*A)
So delta l = (T*l)/(Y*A) = 81.25*0.75/(200*10^9*pi*(0.23*10^-3)^2)
= 1.833*10^-3 m
= 1.833 mm
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A 4.0 ohm resistor is connected in parallel with a 12 ohm resistor and both of these are connected to a DC power supply with voltage V. If the total current in this circuit is 2.0 A, what is the current through the 4.0 ohm resistor?
What is resistance?
Resistance refers to the quantity that AN object impedes or resists in an electrical current. current refers to the flow of electrons. a better thanks to make a case for resistance is to think about an example of an individual in a very jam-pawncked market troubled to travel from one look to another.
Resistance may be a live of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω). Ohms are named once Georg Simon Ohm a German man of science who studied the connection between voltage, current and resistance.
Equivalent resistance
R= 4 * 12 / 4+12
Req = 3 ohm
From ohm's law
V = IR
V = 2 * 3 = 6V
I4ohm = V/R4
= 6/4 = 1.5 ampere
Hence, final answer is current through 4ohm is 1.5 ampere
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