Answer:
Yvette has just proposed a hypothesis. A hypothesis is a proposed explanation for a phenomenon or observation. In this case, Yvette has observed that her plant is not growing and has proposed that increasing the amount of water it receives will cause it to grow. To test this hypothesis, Yvette could try increasing the amount of water the plant receives and observe whether it starts to grow. If the plant does start to grow, this would provide support for Yvette's hypothesis. However, if the plant does not start to grow, this would suggest that the hypothesis is incorrect and Yvette would need to come up with a new explanation for why the plant is not growing.
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?
a string and allowed to revolve in a circle
of radius 1.7 m on a frictionless horizontal
surface. The other end of the string passes
through a hole in the center of the surface,
and a mass of 1.5 kg is tied to it, as shown.
The suspended mass remains in equilibrium
while the puck revolves on the surface.
0.029 kg
1.7 m
1.5 kg
What is the magnitude of the force that
maintains circular motion acting on the puck?
The acceleration due to gravity is 9.81 m/s?.
Answer in units of N.
part 2 of 2
What is the linear speed of the puck?
Answer in units of m/s.
The magnitude of the force that maintains circular motion while acting on the puck is 14.7 N
F=ma
F=1.5 kg×9.8 m/s^2
F=14.7 N
When an object interacts with another object, it feels a push or a pull. Each object that two objects make contact with experiences a force. Once the encounter is over, the force between the two objects is gone. Forces are merely interactions; they do not exist independently. When two objects interact and appear to be in physical contact with one another, contact forces are generated. Several types of contact forces include frictional forces, tensional forces, normal forces, air resistance forces, and applied forces. Even when two interacting objects are far apart from one another, action-at-a-distance forces are still present.
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as an automobile approaches an observer at rest, the driver sounds her 450 hz horn. if the car moves at 45 mi/hr, find the frequency heard by the stationary observer.
The frequency heard by the stationary observer is 468.44 Hz. Frequency is a measure of the number of cycles of a periodic phenomenon that occurs in a unit of time.
Frequency is an important concept in many areas of physics and engineering, including acoustics, electronics, and telecommunications. It is also used in other fields, such as biology and medicine, to describe the periodic phenomena that occur in those fields. It is typically measured in Hertz (Hz), which is the number of cycles per second.
The frequency of the horn as heard by the stationary observer is given by the Doppler shift formula:
frequency_heard = frequency_emitted * (speed of sound + speed of observer) / (speed of sound - speed of car)
Plugging in the values given in the problem, we get:
frequency_heard = 450 hz * (331.5 m/s + 0 m/s) / (331.5 m/s - (45 mi/hr * 1609 m/hr / 3600 s))
Converting the speed of the car to meters per second, we get:
frequency_heard = 450 hz * (331.5 m/s + 0 m/s) / (331.5 m/s - 12.5375 m/s)
Simplifying the expression and converting the result to hertz, we get:
frequency_heard = 450 hz * (331.5 m/s) / (319 m/s)
frequency_heard = (450 hz * 331.5 m/s) / 319 m/s
frequency_heard = 450 hz * 1.0398936170212766
frequency_heard = 468.4414893617021 hz
So the frequency heard by the stationary observer is approximately 468.44 Hz.
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Consider the photoelectric effect when one decreases only the frequency of the incoming light onto the emitter, one measures an increased current. either a. or c. You cannot determine which from the information given. no change in either current or stopping voltage. a decrease in the necessary stopping voltage. an increase in the necessary stopping voltage.
An increase in the required stopping voltage if the photoelectric effect simply affects the frequency of a incident sunlight onto to the emitter.
What is the way Einstein described the photoelectric effect?Since photons are the units of light, according to Einstein's theory, an electron receives the entire photon's energy when it collides with a metal surface. The ejected electron receives the remaining energy as kinetic energy after using some of this energy to free it from the metal atom's hold.
What are the main points of the photoelectric effect?Three key properties of the photoelectric effect that are not consistent with classical physics include: (1) the lack of a lag, (2) the independence of photoelectrons' kinetic energy from the strength the incident radiation, and (3) the existence of a cut-off frequency.
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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 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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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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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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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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. describe the physical appearance (color)of each complex (formula of complex) substance produced of cu
A complex will appear to be the colours that is right opposite it on the colour wheel if it absorbs a specific colour. Colors are produced by the partially filled d orbitals of the stable ions Cr3+(aq), Fe3+(aq), and Co2+ (located to the left, centre, and right, respectively).
Because the [Cu(NH3)4]2+ ion absorbs the orange and red light, leaving the complementary colours of blue and green, it has a blue colour. Some of the light's wavelengths are absorbed by [Cu(NH3)4]SO4 solution when white light, such as common sunshine, travels through it. Red light in the spectrum is absorbed by the [Cu(NH3)4]2+ ions in solution. All the colours, with the exception of red, will be present in the light that exits the solution. This combination of wavelengths appears light blue to us (cyan). The diagram illustrates what happens when white light is sent through a [Cu(NH3)4]SO4 solution.
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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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At the surface of Mars, Gravity is [tex]3.8m/s^2[/tex]. A robot weights 150N on the surface of Mars.
(a) Find it's mass on Mars.
(b) State it's mass on Earth.
(c) Calculate it's weight on Earth.
The mass of the robot on mars will be 39.4 Kg. The mass of an object is constant hence, the mass of the robot in earth also be 39.4 Kg. But it weight in earth changes to 386 N.
What is gravitational force?Gravitational force is the force by which an object attracts other objects into its centre of mass. Earth exerts a gravitational force to every objects on its surface and that's why everything stay on the ground and experience a weight.
The weight of a body in a gravitational field is the product of its mass and acceleration due to gravity g. The g value in mars is 3.8 m/s². The weight of the robot in mars is 150 N
mass of robot = 150 N/3.8 m/s² = 39.4 Kg.
Mass of an object is constant everywhere and the mass of robot in earth be 39.4 Kg.
The g value of earth is 9.8 m/s². Thus, weight of the robot in earth = 34.9 × 9.8 m/s² = 386 N.
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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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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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Unpolarized red light is incident on two identical, narrow vertical slits. The photograph at right shows the interference pattern that appears on a distant screen. a. Specify the quantity or quantities that are adding to zero at the interference minima. light waves from the two slits are adding to zero is not a sufficient answer.)b. A polarizer is placed directly in front of both slits, so that the light is vertically polarized before passing through the slits. It is observed that the intensity at each point on the screen decreases by a factor of two. How can your account for the decrease in intensity at the interference maxima?c. The polarizer is slowly rotated through 360 degree . As the polarizer is rotated, it is observed that the interference pattern does not change. What is the flaw in the reasoning? Explaind. Now imagine that one polarizer is placed in front of each slit: one polarizer with its direction of polarization vertical; the other, horizontal.Would there still be locations on the screen at which the intensity is zero? Explain why or why not.
Electromagnetic waves make up light. Electric fields can be in any direction perpendicular to the propagation of unpolarized light rays. At each point, the intensity is halved.
a). Light is an electromagnetic wave. It consists of minimally intense, pulsing electric and magnetic fields that are directed in all directions perpendicular to the propagation diffraction pattern. Electric fields of light from two slits add up to zero, therefore they likewise sum to zero in terms of light intensity.
b). In light waves (unpolarized), the electric field can be in any direction perpendicular to its propagation. Polarization entails facing the electric field in all directions except one toward zero. While polarisation, for example, in the vertical direction, additional electric field components from other directions are added to the necessary (remaining) direction.
c). Electric fields at angle θ to vertical adds Ecosθ to vertical field
before polarisation: same E in all directions
I∝E²
∝[tex]\int\limits^\pi _0[/tex]E² dθ =E² π
After polarisation;
I∝ [tex]\int\limits^\pi _0[/tex] (E cosθ )²dθ =E² π/2
Hence, Intensity is halved at every point
d). Electric field cannot be stopped by slits since it is not a mechanical thing that can be.
e). The horizontal and vertical electric field vector addition cannot be zero. Therefore, there won't be any places with 0 intensity.
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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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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 heat engine takes in 330 J of energy from a hot reservoir and performs 22.0 J of work in each cycle. Find (a) the efficiency of the engine and (b) the energy expelled to the cold reservoir in each cycle.
a) The efficiency of the engine is 67% b) The energy expelled to the cold reservoir in each cycle is 307.89 J
Qh=330 J , W= 22.0 J
a) n= W/Qh = 22 J/330 J = 0.06675 = 0.067
b) n= W/Qh = (Qh-QL)/Qh = 1 - QL/Qh
Plugging values,
0.067 = 1 - QL/330 => QL = 307.89 J
As a ratio of useful work completed to heat produced, an engine efficiency is determined. completed the task. The power delivered at the clutch or the driveshaft is referred to as the "work done" in this context. As a result, the work produced by thermodynamic expansion is reduced by losses such as friction and other losses. Today's gasoline engines are only about 30 to 35 percent efficient, meaning that about 65 cents of every dollar you spend on gas is wasted even with routine auto maintenance like a tune-up or an oil change. According to the Second rule of thermodynamics, it is impossible for heat engines to achieve 100% thermal efficiency.
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A given net force propels an object along a straight-line path. If the mass were doubled, its acceleration would O quadruple be half double stay the same
A given net force propels an object along a straight-line path. If the mass were doubled, its acceleration would be half.
What is the relationship between force and acceleration mass?Force is mass times acceleration, or F = m * a. This means an object with a larger mass requires a stronger force to be moved along at the same acceleration as an object with a small mass. This is Newton's Second Law of Motion.
Newton's Second Law of Motion defines the relationship between force and acceleration. They are directly proportional. If you raise the force applied to an object, the acceleration of that object raises by the same factor. In short, force equals mass times acceleration.
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a quantum oscillator in the wall of a black body cabity has frequency of 5.0*10(14) Hz. calculate the energy of the first two quantum states.
The energy of the first two quantum states, given that the black body cabity has frequency of 5.0×10¹⁴ Hz is 3.313×10⁻¹⁹ J
How do I determine the energy?Energy is defined as the capacity to do work. However, energy and frequency are related according to the formula given below:
E = hf
Where
E is the energyh is the Planck's constant f is the frequencyWe can obtain the energy of the two quantum states as shown below:
Frequency (f) = 5.0×10¹⁴ HzPlanck's constant (h) = 6.626×10⁻³⁴ JsEnergy (E) =? 6.23×10⁻¹⁹ JEnergy (E) = Planck's constant (h) × frequency (f)
E = hf
E = 6.626×10⁻³⁴ × 5.0×10¹⁴
E = 3.313×10⁻¹⁹ J
Thus, we can conclude from the above calculation that the energy is 3.313×10⁻¹⁹ J
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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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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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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 thin circular wooden hoop of mass m and radius Rrests on a horizontal frictionless plane. A bullet, also of mass m, moving with horizontal velocity v, strikes the hoop and becomes embedded in it as shown in the figure. (a) (2) Calculate the center of mass velocity (b) (2) Calculate the angular momentum of the system about the CM. (c) (32) Calculate the angular velocity w of the hoop. (d) (4) Calculate the kinetic energy of the system, before and after collision (e) (48) Find a point of the hoop which remains at rest after collision
The velocity of the center of mass of the system is the same as the velocity of the bullet, which is v. The total angular momentum of the system about the center of mass is Lhoop + Lbullet. he kinetic energy of the system, before and after collision Khoop + Kbullet and Khoop_after + Kbullet_after respectively. The axis of rotation, which is the center of the hoop, will remain at rest after the collision.
The center of mass of the system is at point Q, which is a distance d from point O, where:d = (mP + mO)/(2*m).The velocity of the center of mass is the derivative of the position with respect to time. Since the bullet is moving with constant velocity, the position of its center of mass is also moving with constant velocity. The position of the center of mass of the hoop is not changing, so its velocity is zero. Therefore, the velocity of the center of mass of the system is the same as the velocity of the bullet, which is v.
The angular momentum of the bullet about the center of mass is:Lbullet = Ibulletw + md*v where Ibullet is the moment of inertia of the bullet about its center of mass, and d is the distance from the center of mass to the point of contact between the bullet and the hoop. The total angular momentum of the system about the center of mass is the sum of the angular momenta of the hoop and the bullet: Ltotal = Lhoop + Lbullet
Since angular momentum is conserved, this change in angular momentum must be due to the change in the angular momentum of the hoop. Therefore, we can set the change in angular momentum of the hoop equal to Ltotal and solve for the angular velocity w:
Ltotal = Lhoop + Lbullet
Ltotal = Ihoopw + mRv + Ibulletw + mdv
Ltotal = (Ihoop + Ibullet)w + (mR + md)v
w = Ltotal/(Ihoop + Ibullet) - (mR + md)*v/(Ihoop + Ibullet).
kinetic energy is conserved, this means that the change in kinetic energy of the hoop must be equal to the change in kinetic energy of the bullet. Therefore, we can set the change in kinetic energy of the hoop equal to the change in kinetic energy of the bullet and solve for the kinetic energy of the hoop after the collision:
Khoop_after - Khoop = Kbullet - Kbullet_after
Khoop_after = Khoop + Kbullet - Kbullet_after
The kinetic energy of the system after the collision is the sum of the kinetic energies of the hoop and the bullet after the collision:
Ktotal_after = Khoop_after + Kbullet_after
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Mark pushes his broken car 190 m down the block to his friend's house. He has to exert a 160 N horizontal force to push the car at a constant speed. How much thermal energy is created in the tires and road during this short trip? Express your answer to two significant figures and include the appropriate units. Delta E_Ts =
The thermal energy is created in the tires and road during this short trip is 30400 J.
Thermal energy is a type of energy that occurs when the temperature rises. Thermal energy is directly proportional to the temperature change of an object. Heat is a form of thermal energy. The hotter the substance, the greater its thermal energy. The increase in thermal energy caused by raising the temperature is due to the faster movement of atoms and molecules in matter.
Calculation :
Here,
distance ,d = 190 m
force exerting , F = 160 N
for the thermal energy created
thermal energy created in tires = work done by the pushing force
thermal energy created in tires = 190 * 160
thermal energy created in tires = 30400 J
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Plaskett's binary system consists of two stars that revolve In a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is |v | = 240 km/s and the orbital period of each is 12.5 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 times 1030 kg Your answer cannot be understood or graded. More Information solar masses
Each star has a mass M of 1.43 × 10³²kg.
The simplest types of orbits in celestial mechanics are circular orbits, in which an orbiting body moves around a gravitational mass while maintaining a constant radius.
Calculation:We learn from the question that the stars'masses are m1 = m2 = M.
Each star orbits at a speed of Vs = 240 km/s or 240000 m/s.
T = 12.5 days, often known as 12.5246060, or 1080000sec, is the orbital period.
The mathematical formula for the centripetal force exerted on these stars isFc = Mv²/r
The mathematical formula for the gravitational force exerted on these stars is
Fg = GM²/d²
so Fc = Fg
Mv²/r = Gm₁ₓm₂/d²
v²/r = GM/(2r)²
v²/r = GM/4r²
M = v² × 4r /G
Each sun travels a certain distance during one cycle, which is mathematically expressed asD = V × T
D = 240000 × 1080000
D = 2.592×10¹¹ m
Now this can also be represented asD = 2πr
Therefore
2πr = 2.592×10¹¹ m
r = 2.592×10¹¹ / 2π
r = 4.124 × 10¹⁰ m
So,
M = v² × 4r/ G
M = (240000)² × 4 × 4.124 × 10¹⁰/ 6.67 × 10 ⁻¹¹
M = 1.43 × 10³²kg.
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Which of the following color combinations will produce white light?
a. blue light + red light
b. blue light + magenta light
c. blue light + cyan light
d. blue light + yellow light
Answer:
d) blue light + yellow light
Explanation:
The color combination that will produce white light is blue light + yellow light. White light is the combination of all colors of the visible spectrum. When blue and yellow light are mixed together, they create a white light because blue and yellow are complementary colors. Complementary colors are pairs of colors that are opposite each other on the color wheel, and when they are mixed together, they create a neutral color (in this case, white). Therefore, the correct answer is d) blue light + yellow light.
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
Hope this helps!
Where does the maximum acceleration occur in SHM?
A. At equilibrium
B. At the amplitude
C. Not enough info
D. Somewhere in the middle
Answer:
A: at equilibrium
Explanation:
In simple harmonic motion (SHM), the maximum acceleration occurs at the points where the displacement of the object is zero, which is also known as the equilibrium position. Therefore, the correct answer is option A: at equilibrium.
Maximum acceleration is max at the amplitudes in simple harmonic motion. Velocity is maximum at equilibrium. Refer to the photo.
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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