Michael jordan appears to defy gravity because His motion is that of a projectile, and a projectile's motion is such that its vertical speed is minimal while at the high point of its trajectory.
What do you mean by projectile motion?
Projectile motion is a form of motion experienced by an object or particle that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. Examples of projectile motion include throwing a ball straight upward, kicking a ball and giving it a speed at an angle to the horizontal, or simply dropping an object and allowing it to free fall. In all cases, gravity is the only force acting on the object.To know more about Projectile motion here
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A baseball player pitches a 0.14-kg baseball at 30 m/s.
–Calculate the kinetic energy for the baseball.
–How much work did the player do on the ball to give it this energy?
The kinetic energy of the baseball be 63 joule.
The player had to work of 63 joule on the ball to give it this energy.
What is kinetic energy?According to the definition of kinetic energy in physics, it is the amount of work that an item may accomplish while in motion.
As a scalar quantity, kinetic energy can only be fully defined by its magnitude.
Given that:
Mass of the baseball: m = 0.14 kg.
Speed of the baseball: v = 30 m/s.
So, kinetic energy of the baseball= 1/2×0.14×30² joule = 63 joule.
Hence, the player had to work of 63 joule on the ball to give it this energy.
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use the 1st law of thermodynamics to derive a simplified equation for a turbine that explains its performance based on inlet (1) and outlet (2) conditions.
Energy can neither be created nor destroyed, but it can be transferred. First law of thermodynamics.
What is energy?This is the ability or capacity to do work. we know that the first law of thermodynamics explains energy conservation. thus, energy can neither be created nor destroyed.
Also, Zeroth's law of thermodynamics talks about the thermal equilibrium of two or more bodies. thus, if body A and Body B are in thermal equilibrium with body C. that body A, B, and C are all in thermal equilibrium with each other.
Again, the second law of thermodynamics says more about heat direction.
Therefore, the thermodynamics supports that the heat cannot be transferred from a colder to a hotter body.
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if your body has a density of 976 kg/m3, what percent of you will be submerged when floating gently in the following liquids? (a) freshwater % (b) salt water, which has a density of 1,030 kg/m3
If your body has a density of 976 kg/m3, 97% 0f the body will sink while gently floating in fresh water, and 95% will sink if it has a density of 1,030 kg/m3
The net force from buoyancy must match the weight when a body is partially submerged in fresh water. When a body is partially submerged in salt water, the net force due to buoyancy must equal the weight.
Fraction of body submerged (f sub) = density of body/density of fluid
Given that density of fresh water = 1000 kg/m3
density of salt water = 1027kg/m3
density of body = 976 kg/m3
Fraction of body submerged in fresh water = (976/1000)x100 = 97%
Fraction of body submerged in salt water = (976/1027)x100 = 95%
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a 20 kg child is on a swing that hangs from 2.2-m-long chains. for general problem-solving tips and strategies for this topic, you may want to view a video tutor solution of car rolling down a hill. part a what is her maximum speed if she swings out to a 40 ∘ angle?
The maximum speed of the swing at an angle of 45° is 4.15 m/s
Potential Energy, P. E = mgh
Kinetic Energy, K. E = 0.5mv^2
P.E = K.E
mgh = 0.5mv^2
The vertical component of the swing =
hCosθ
mghCosθ = 0.5mv^2
20 x 9.8 × 3 × cos45° = 0.5 x 20 x v²
20 x 9.8 x 0.88 = 10v²
172.48 = 10v^2
Divide both sides by 10 to isolate v²
v² = 172.48/10
v² = 17.248
V = √17.248
v = 4.15 m/s
Hence, maximum speed if she swings out to a 40 ∘ angle is 4.15 m/s
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what is the speed of the 0.100 kg sphere when it has moved 0.400 m to the right from its initial position? express your answer with the appropriate units.
The speed of the sphere is 2√2m/s when its displaces off at 0.400 m .
Mass of a spherical object is 0.100 kg displaced by 0.400m
According to Einstein's equation E=mc2, "mass" is a fundamental characteristic of all the energy that we perceive or feel. If you have any kind of energy, it must have some "mass," according to the equation. It results from the Higgs field's interactions with subatomic particles.
The Higgs interaction gave an object its intrinsic mass, which we refer to as rest mass, if it is not moving in relation to you. As you start to accelerate an object, its kinetic energy rises. In other words, if the kinetic energy is rising, then the energy must be manifesting itself in the form of mass. This is because more energy means more inertia content, which equals more mass.
[tex]V^2-u^2=2as\\\\u=0 \\\\V^2=2as\\[/tex]
[tex]V=\sqrt{2as}[/tex] -[1][tex]V=\sqrt{2s\frac{F}{m} }[/tex] -[2]Calculations-
[tex]V=\sqrt{0.8\frac{1}{0.100} }[/tex]
[tex]V=\sqrt{\frac{8000}{1000} } \\\\V=\sqrt{8} =2\sqrt{2}m/s[/tex]
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A container with volume 1.61 L is initially evacuated. Then it is filled with 0.246 g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy. of the root-mean-square speed of the gas molecules is 192 m/s, what is the pressure of the gas? Express your answer in pascals.
The pressure of the gas is 0.018 atm if the gas obeys the ideal gas law.
What is the reason for this?
We know that;
√ 3RT/M
For N2;
vrms = 192 m/s
R = 8.314 J/K.mol
T = ?
M = 28 g/mol or 0.028 Kg/mol
So;
T = vrms² M/ 3R
T = 192² * 0.028 / 3* 8.314
T = 41.3K
From PV = nRT
n = 0.246 g/28 g/mol = 0.0087 moles
P = nRT/V
P = 0.0087 moles × 0.082 atmLK-1mol-1 × 41.3K/1.61 L
P = 0.018 atm
Therefore, the pressure of gas is 0.018 atm.
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(b) at what time is the mechanical energy of the bucket-earth system at a minimum? explain your reasoning.
Plants are promoting both mechanical energy and chemical watering process but inhibit erosion of soil always of to the roots.
What is mechanical energy?
Mechanical energy (kinetic energy or potential energy) is one of the energy that is either an object in the motion or to the energy that is very stored in to the objects by their own position. Mechanical energy is also vary the driver of renewable of the energy. Many forms of the renewable energy is rely on mechanical energy to the adequately produce power or the convert energy. As we all know roots of the plant grow Deep its undergoes rock causing mechanical watering process so the mechanical watering process is the important for plants. When when plants roots undergoes the soil through The rocks mechanical watering process is must needed for growth of the plants.
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A 0. 200-kg mass attached to the end of a spring causes it to stretch 5. 0 cm. If another 0. 200-kg mass is added to the spring, the potential energy of the spring will be.
The potential energy of the spring will be 4 times as much.
What is potential energy?
Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is squeezed or extended, its potential energy increases. If a steel ball is lifted above the ground as opposed to falling to the ground, it has higher potential energy.
In the first question, we have to caculate the constant of the spring with this equation:
[tex]$$m * g=k * x$$[/tex]
Getting the k :
[tex]k=\frac{m * g}{x}=\frac{0,2[k g] * 9,81\left[\frac{m}{*^2}\right]}{0,05[\mathrm{~m}]}=39,24\left[\frac{N}{m}\right]$$[/tex]
Then we can calculate how much the spring stretch whith the another mass of [tex]$0,2 \mathrm{~kg}$[/tex] :
[tex]x=\frac{m * g}{k}=\frac{0,4[k g] * g, 81\left[\frac{m}{a^2}\right]}{39,24\left[\frac{N}{m}\right]}=0,1[m]$$[/tex]
The energy of a spring:
[tex]E=\frac{1}{2} * k * x^2$$[/tex]
For the first case:
[tex]E=\frac{1}{2} * 39,24\left[\frac{N}{m}\right] *(0,05[m])^2=0,049[J]$$[/tex]
For the second case:
[tex]E=\frac{1}{2} * 39,24\left[\frac{N}{m}\right] *(0,1[m])^2=0,0196[J]$$[/tex]
If you take the relation [tex]$\mathrm{E} 2 / \mathrm{E} 1=4$[/tex].
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what is another way to say 'the force due to gravity'? applied force air resistance normal force weight friction next
Normal force: The force that an object exerts on another object in a direction perpendicular to the surface of contact. It is the force that balances the force of gravity and prevents objects from being crushed.
What is force?
A force is an external cause that, when applied, alters or has the potential to alter a body's state. The body comes to rest when it is moving, and it moves when it is at rest. The body's direction, form, size, etc. may also change as a result. An illustration would be to push or forcefully push a door. Force has both a magnitude and a direction because it is a vector quantity. Force is described as the "product of the a body's acceleration and mass in Newton's second law. As an illustration, you should emphasise that a push or even a pull is referred as a force as the main point of your guidance at this level.
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an object is hung from a spring scale while it is immersed in water. the scale reads 5.6 n. the mass of the object is 0.75 kg. what is the density in [x103 kg/m3] of the object?
The density of object is 3.33*10³
How to calculate density of object ?The gravitational force draws any two mass-containing objects together. The gravitational force is referred to. According to the formula F=Gm1m2r2, the force will always be applied along the line connecting the two masses in the direction of the other mass. It is a force of attraction in nature.
Given,
gravitational force = 5.00N
Mass of the object = 0.5kg
reading when submerged in water = 3.5 N
The loss in weight = 5 - 3.5
= 1.5 N
This loss in water due to buoyancy in water
Loss in weight of water = weight of displaced water
So ww = 1.5 N
Weight of displaced water = w *v * g
Density of water = 10³kg/m³
Thus , 1.5=10³ * v* 10
V = 1.5/10³ * 10 m³
Let density be m/v
=0.5/1.5*10*10³
= 3.33*10³
Therefore density of object is 3.33*10³
The complete question is : The gravitational force exerted on a solid object is 5.00 N. When the object is suspended from a spring scale and submerged in water, the scale reads 3.50 N. Find the density of the object.
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g what is the magnitude of the tension ta in rope a? a. 500 n b. 3200 n c. 370 n d. 130 n e. 100 n f. 400 n value: 10 if the axis of rotation is placed on rope a, then the torques of f
To find the magnitude of the tension in rope A, we need to consider the forces and torques acting on the system.
In this problem, the forces acting on the system are the weight of the block and the tensions in ropes A and B. The torques are the forces acting on the ropes multiplied by their distances from the axis of rotation.
We can use the concept of equilibrium to solve this problem. When an object is in equilibrium, the sum of the forces and the sum of the torques must be zero. In this case, the forces on the system are balanced, so the sum of the forces is zero. We can write this as:
$$T_A + T_B - W = 0$$
where $T_A$ and $T_B$ are the tensions in ropes A and B, and $W$ is the weight of the block. We are given that $T_B = 3200 \text{ N}$ and $W = 500 \text{ N}$.
Next, we need to consider the torques on the system. If the axis of rotation is placed on rope A, the only torque acting on the system will be the torque due to the tension in rope B.
The torque due to the tension in rope B is given by the equation $\tau = rT$, where $\tau$ is the torque, $r$ is the distance from the axis of rotation to the point where the force is applied, and $T$ is the force.
In this case, the distance from the axis of rotation to the point where the force is applied is $r = 10 \text{ m}$, and the force is the tension in rope B, $T = 3200 \text{ N}$. The torque due to the tension in rope B is therefore $\tau = 10 \text{ m} \times 3200 \text{ N} = 32000 \text{ Nm}$.
Since the system is in equilibrium, the sum of the torques must be zero. We can write this as:
$$\tau = 0$$
Substituting the value of the torque due to the tension in rope B, we get:
$$32000 \text{ Nm} = 0$$
This equation is satisfied, so the system is in equilibrium.
Finally, we can use the equation for the sum of the forces to solve for
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while observing a truck with an alternator cable that is burnt and has many fuses and fusible links blown, technician a says that the battery was connected in reverse polarity. technician b says that batteries were likely deeply discharged and charged at a high current rate. who is correct?
Technician It is accurate to state that the battery was connected with the wrong polarity.
What is battery ?
A battery is a device that transforms chemical energy into electrical energy. It can include one or more electrical cells. Like many other common energy sources, batteries store energy through chemistry in the form of chemical potential.An electric circuit is used in this kind of reaction to transmit electrons from one material to another.
The heat created by the battery's reverse polarity may result in hydrogen gas (ignitable), which could blow the battery's casing up. The battery's damaged cover might allow acid to enter, melting delicate equipment and potentially inflicting serious injury. When you use a battery-powered device while it is plugged in, the entire circuit will be energised, which increases the risk of an electrical shock. Although the damage may be difficult to observe, reverse polarity can result in PCB damage and even PCB failure. Your appliances may be damaged or short-circuited by reversed polarity. Household appliances may overheat as a result of this outlet wiring error, which could also harm the wiring and internal circuitry.
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a refrigerator is an example of a . a refrigerator is an example of a . hot reservoir heat engine cold reservoir reversible process heat pump
A refrigerator is an example of a: Heat Pump
What is second law of thermodynamics?
According to Clausius' statement on the second law of thermodynamics, it is impossible to build a system that operates in a cyclical process, in which heat moves from areas of lower temperature to areas of higher temperature without working on it.
This statement applies to systems that transfer heat from a cold reservoir to a hot reservoir. Refrigerators and heat pumps do the same thing.
Refrigerators give off heat from the freezer to the atmosphere (exhaust air at the back of the refrigerator) even though the temperature inside the freezer is always lower than the temperature of the atmosphere.
Similarly, a heat pump transfers heat from a room to the outside air, cooling the room, which is cooler than the outside air.
A refrigerator is an example of a: Heat Pump
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a flatbed truck is carrying a heavy crate the coefficient of static friction between the crate and the bed of the truck 0.75 what is the maximum rate at which the driver can decelerate and still avoid having the crate slide agaainst the cab of the truck
The box must not slide, thus it is crucial for us to determine when the force of deceleration and the force of friction are equal. ma = mg, a = 0.75 * 9.8 m/s2, which is 7.35 m/s2. The driver may therefore safely decelerate at around 7.2 m/s2.
Friction is a type of force.The force produced when two surfaces glide against and touch one another is referred to as frictional force. There are a few things that impact the frictional force: The surface roughness of these forces and the amount of force pressing them together have the biggest impact.
Exactly what generates friction?Friction is believed to be created by the interactions between the microscopic bumps on surfaces when they rub against one other, however scientists are still unsure of its exact mechanism.
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hat is the period of small-angle oscillations of a simple pendulum with a mass of 0.6 kg at the end of a string of length 5 m?
4.49 sec
Given
Mass of simple pendulum = 0.6 kg
String of simple pendulum with length = 5m
Equation used:- T = 2 π (L / g)^1/2
T = period of oscillations
L = length of the pendulum
g = acceleration of gravity
T = 6.28 (5 m / 9.80 m/s^2)^1/2
T = 4.49 sec (the period is not dependent on mass)
A simple pendulum is defined to be a point mass or bob (taking up no space) that is suspended from a weightless string or rod. Such a pendulum moves in a harmonic motion
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once the person gets half way around, they decide to simply let go of the merry-go-round to exit the ride. what is the magnitude of the linear velocity of the person right as they leave the merry-go-round?
The linear velocity during leaving merry-go-round is 1.25 m/s
We define the rate of change in position over a time period as velocity. Linear velocity is simply an object's velocity in a straight line, whereas Angular Velocity is how much an object spins, rotates, or turns.
The linear velocity during leaving merry- go-round is,
v' = w' x R
v' = 0.77 x 1.63
v' = 1.25 m/s
Hence, linear velocity during leaving merry-go-round is 1.25 m/s
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Technician a says that rotary motion of the pistons is converted to reciprocating motion of the crankshaft. Technician b says that rotary motion is up and down or back and forth. Who is correct?.
Technician A says that rotary motion of the pistons is converted to reciprocating motion of the crankshaft which is correct.
Using the composite material gets converted this same reciprocating motion of such a piston to rotary motion.The connecting rod seems to be the intermediary between some of the piston and perhaps the crankshaft.Whenever the piston would be reciprocated from TDC instead to BDC, perhaps the crankshaft moves clockwise somewhere throughout the primary wheels Piston would be directly linked to the connecting rod to that same gudgeon pin as well as the crankshaft has been associated with the connecting rod to something like the crank.To know more about motion visit:
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assume that a rod-drawing operation can be carried out either in one pass or in two passes in tandem. if all die angles are the same and the total reduction is the same, will the drawing forces be different?
Unless the rod surface changes while it is between the two dies as a result of external factors like the environment or extra lubrication, the pulling forces will remain constant.
What is the physics illustration for pulling force?
In physics, tension is defined as the pulling force that is transmitted axially by a string, rope, chain, or similar object, or by each end of a rod, truss member, or other comparable three-dimensional object. Tension can also be defined as the action-reaction pair of forces acting at each end of the aforementioned elements.
The pulling force stands for what?
Every neodymium magnet has a draw force that indicates its exact strength. The draw force, which is expressed in pounds or kilograms, is the amount of force needed to remove a magnet from a steel plate that is 1/8 inch (3.175 mm) thick.
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a metal wire has a resistance of 10.0 ω at a temperature of 20oc. at 90oc, its resistance increases to 10.5 ω. what is the temperature coefficient of resistivity of this metal?
The temperature coefficient of resistivity of metal
10 = r0(1 + 20k)
10.5 = r0(1 + 90k);
10.5/10 = (1 + 90k)/(1 + 20k);
10.5 + 210k = 10 + 900k
k = 0.5/690 = 7.25·10-4 1/C
The primary unit of temperature within the worldwide gadget of units (SI) is the kelvin. It has the sign K . For normal programs, it's far often handy to use the Celsius scale, in which 0 °C corresponds very carefully to the freezing factor of water and a 100 °C is its boiling factor at sea level.
Temperature is a measure of the common kinetic energy of the debris in an object. While the temperature increases, the movement of those particles also will increase. Temperature is measured with the thermometer or calorimeter.
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calculate the moment of inertia of a thin, uniform rod of length l and mass m that rotates about a pivot at distance l/3 from one end.
The mass moment of inertia (ML²/9) is a measurement of a body's degree of inertia for rotational motion.
Explain about the moment of inertia?In physics, the term "moment of inertia" refers to the quantitative measurement of a body's inertia with respect to rotation, or the resistance that a body shows when a torque is applied to change its speed of rotation around an axis (turning force).
An engine's flywheel is a large mass that is positioned on the crankshaft. The flywheel's MOI is extremely high and aids in energy storage. In comparison to a solid shaft, a hollow shaft transmits more power (both of same mass). Because it resists rotational motion, the moment of inertia is referred to as such and not as a moment of force.
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a principle of design in which the visual weight of the forms achieves equilibrium despite being distributed unevenly throughout the picture plane is called:
Answer- Asymmetrical equilibrium Due to unequal visual weight on either side of the composition, the equilibrium is asymmetrical. There could be a dominant element on one side of the composition, which is balanced by one or more weaker focal points on the other.
Explanation: What design principle brings up equilibrium?
Balance. Visual equilibrium and our feeling of balance are related concepts in the field of balancing. Visual stability is the result of a composition's reconciling conflicting forces. The two methods that the majority of effective compositions attain balance are either symmetrically or asymmetrically.
What design tenet is characterized by the distribution of visual weight on either side of the vertical axis?
Balance. Both sides of the visual field's weight distribution are equal.
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what is the maximum speed of a 330 kg car if the spring is compressed the full amount? express your answer with the appropriate units.
The maximum speed of a completely compressed spring is 4.993m/s .
The Mass of spring is 330 kg .
As per Kinetic theory , Molecules of every system is randomly oriented. Every molecule has its own radial and angular components.
As per theory root mean square concept is introduced computing energy leakage of any system.
Zero current in electronics is such an example calculating parameters of dissipation of energy.
[tex]K.E=\frac{3RT}{2} -----[1]\\\\K.E=\frac{mv^2}{2}-----[2] \\\\eq[1]=eq[2][/tex]
comparing
[tex]3RT=mv^2\\\\v^2=3RT/m\\\\T/m=1---[Reason:-compression]\\\\v=\sqrt{3R} \\\\v=\sqrt{3* 8.31} \\=4.993m/s[/tex]
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when tuning his guitar, a music student notices that the string is not vibrating at the desired frequency of 195 hz, so he tightens the string by 16.4% to get this frequency. at what frequency was the string vibrating when he first started the tuning process?
When he started the tuning process the string vibrating frequency was 180Hz.
Frequency in a stretched string as a function of Tension(T) and linear mass density μ is given as:
f = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{\frac{T}{} }[/tex]μ
where L is the length of string
Now in first case let f be the frequency
f = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{\frac{T}{} }[/tex]μ (i)
After the string was tightened by 16.4% the tension in string will increase by 16.4% while all the other parameter will remain same. The new frequency which is equal to 195Hz is given by:
⇒ f₂ = 195 = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{1.164T[/tex] / μ
⇒ 195 = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{1.164T}[/tex]/μ (ii)
Dividing equation (i) by equation (ii), we get;
⇒[tex]\frac{f}{195}[/tex] = [tex]\sqrt{\frac{T}{1.164T} }[/tex]
⇒f = 195 [tex]\sqrt{\frac{1}{1.164} }[/tex]
⇒ f ≈ 180Hz
What is a string's natural frequency?
The length, mass, and degree of stretching a string is used to calculate its natural frequency. Giving a system a brief shock and seeing (or listening to) its reaction is the quickest technique to establish its natural frequency.
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In a typical body of fresh water there exists a diversity of aquatic animal species. Consider the following scenario. A freshwater lake, ph of the water ranging between 5. 5 and 6. 5, falls prey to acid rain. Over several decades the ph of the lake water declines to 4. 5. What are the consequences of such a change on the aquatic animal populations? choose all that apply.
In the given scenario of a fresh water lake, the pH of water ranges between 5.6 and 6.5 and falls prey to acid rain. Over several decades, the pH of the lake declined to 4.5. The answers are C and E.
The term population contain a group of organisms of a single species that can interbreed and live in the same time in the same environment. For example, a population of deer includes all individuals in a particular forest.
Thus, the option C) according to the graph of pH sensitivity, biodiversity of animal species will decrease, and option E) because pH tolerance varies, only species with a tolerance level 4.5 and below will survive are correct.
This is because the prey survive in that condition.
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A pure tone with a frequency f1 = 800 Hz is modulated by a frequency f2 = 160 Hz. The primary sidebands are______ Hz and ______Hz. The virtual pitch heard will be the related fundamental, _______Hz.
A pure tone with frequency f1 = 800 Hz is modulated by frequency f2 = 160 Hz. The primary sidebands are 960 Hz and 640 Hz. The virtual pitch heard will be the related fundamental, 800 Hz.
In physics, the term frequency refers to the number of waves passing through a fixed point in unit time. It also represents the number of cycles or oscillations an object undergoes per unit time in periodic motion.
The wave frequency (f,) is the number of waves passing through a point in one second. Frequency is measured in Hertz (Hz). One hertz equals one wave per second. Frequency is also called cycles per second or time frequency. The usual symbol for frequency is the Latin letter f or the Greek letter ν (nu).
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explain why lasers can be used to perform surgery and cut through metal while incandescent light cannot.
The phrase LASER is an acronym of mild Amplification by way of stimulated Emission of Radiation. it's miles a device to provide a sturdy, monochromatic, collimated and tremendously coherent beam of mild. it really works in the phenomenon of 'stimulated emission'.
Laser light is exceptionally monochromatic.
The laser light is a beam of monochromatic mild due to the fact all photons in the laser light have identical power, big hnu = E_2-E_1, identical frequency, large nu = frac{E_2-E_1}{h} and additionally same wavelength, big lambda = frac{hc}{E_2-E_1}.
(ii) Laser light is fairly coherent.
since the emission of all photons are in section, the laser beam is coherent.
(iii) Laser mild is relatively extreme
The depth of laser beam may be very high due to the fact all the photons within the beam are coherent.
(iv) Laser light is highly directional.
A laser beam is fantastically directional. mild from other assets can be made parallel beam by using a lens or a reflect,but the beam divergance is an awful lot more than that for laser light.
Those properties of laser mild enables it for use in surgical treatment and cut via metals.
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Suppose we replacebothhover pucks with pucks that are the same size as the originals but twice as massive. Otherwise, we keep the experiment thesame. Compared to the pucks in the video, this pair of pucks will rotateHint 1.How to approach the problemThis question asks you to relate the mass of a rotating object to the object’s angular speed(rate of rotation).You can do that using angular momentum:. In this equation, the moment of inertiais the "mass" term, equivalent toin the equation forlinear momentum.So, how does the pucks moment of inertiarelate to their mass? Is the relationship linear ()? Or is it quadratic () or inverse square()? To see the answer, try writing the general equation that defines.Now, how will doubling the mass of the pucks affect,, and?
When the mass of an object is doubled, the moment of inertia of the object is also doubled. This is because the moment of inertia of an object is proportional to the mass of the object. In the equation for angular momentum, $L = I\omega$, the moment of inertia $I$ is the "mass" term, and it is proportional to the mass of the object.
If we double the mass of the pucks in the experiment, the moment of inertia of the pucks will also be doubled. This means that the angular momentum of the pucks will be doubled, since $L = I\omega$.
However, the angular speed $\omega$ of the pucks will remain the same, since it is not directly affected by the mass of the pucks.
Therefore, the pair of pucks that are twice as massive as the original pucks will have the same angular speed but a higher angular momentum. This means that the pucks will rotate at the same rate but with more momentum, making them harder to stop or change direction.
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In Figure, a climber leans out against a vertical ice wall that has negligible friction. The distance a is 0.914 m and distance L is 2.10 m. His center of mass is distance d=0.940 m from the feet–ground contact point. If he is on the verge of sliding, what is the coefficient of static frition is?
The static friction is the frictional force applied on the opposite of the direction of body to keep it from sliding.
We know that the weight of the body will be mg.
The force F(N) from x-axis will be vertically upwards.
mgd cos θ = F.L Sinθ
F = mgd cosθ / L.sinθ = f
F(not) = 0
F(N) = mg
F = f
Then the frictional force is
f = μ.F(N)
μ = f / F(N)
μ = [ (mgd cosθ / L.sinθ ) / mg ]
= d cosθ/ L sinθ
μ = 1.85/ 2.1 = 0.88
Therefore, the coefficient of static friction is 0.88.
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A liquid of density 1330 kg/m3 flows steadily through a pipe of varying diameter and height. at location 1 along the pipe, the flow speed is 9.85 m/s and the pipe diameter ????1 is 10.1 cm. at location 2, the pipe diameter ????2 is 17.5 cm. at location 1, the pipe is δy=9.15 m higher than it is at location 2. ignoring viscosity, calculate the difference δP between the fluid pressure at location 2 and the fluid pressure at location 1.
The difference between the fluid pressure at location 2 and the fluid pressure at location 1 is 119 kPa.
What is the equation of continuity?The mass balance of a fluid moving through a stationary volume element is all that the equation of continuity is about. It says that the rate of mass inflow less outflow equals the rate of mass buildup in this volume element.
According to equation of continuity:
[tex]A_{1} v_{1} =A_{2} v_{2} \\[/tex]
A₁ = Region 1 cross-sectional area
v₁ = flow velocity of region 1
A₂ = Region 2 cross-sectional area
v₂ = flow velocity of region 2
Here, [tex]A_{1} =\frac{\pi d_{1}^{2} }{4}[/tex] , [tex]A_{2} =\frac{\pi d_{2}^{2} }{4}[/tex]
Now, putting the values in the above equation we get,
[tex]v_{2} =\frac{A_{1} }{A_{2} } v_{1} \\[/tex]
[tex]=\frac{\frac{\pi d_{1}^{2} }{4}}{\frac{\pi d_{2}^{2} }{4}} v_{1}[/tex]
[tex]v_{2} =\frac{d_{1}^{2} }{d_{2}^{2} } v_{1}[/tex]
Using Bernoulli's equation, we get,
[tex]P_{2} + \rho gz_{2} +\frac{\rho v_{2 }^{2} }{2}= P_{1} + \rho gz_{1} +\frac{\rho v_{1 }^{2} }{2}[/tex]
The difference between the location 2 fluid pressure and the location 1 fluid pressure is :
[tex]P_{2}-P_{1} =\rho g(z_{1}-z_{2} )+\frac{\rho (v_{1}^{2}-v_{2}^{2}) }{2} =\rho g(z_{1}-z_{2} )+\frac{1}{2}\rho v_{1} ^{2} (1-(\frac{d_{1} }{d_{2} } )^{4} )[/tex]
[tex]P_{2}-P_{1} = 1330*9.81*9.15+\frac{1}{2} *1330*9.85^{2} (1-(\frac{10.1}{17.5} )^{2} )[/tex]
[tex]P_{2}-P_{1} = 1.19*10^5} Pa\\P_{2}-P_{1} = 119 kPa[/tex]
Hence, the difference between the fluid pressure at location 2 and the fluid pressure at location 1 is 119 kPa.
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If gravity is the only force that plays a role in the evolution of the universe, and the mass density is less than the critical mass density, which plot correctly shows the evolution of the universe?.
Plot B correctly shows the evolution of the universe because it shows a steady/constant incline.
The correct option is B.
Evolution of the universe?
Our universe has been known to begin with an explosion of space itself called the Big Bang. Starting from extremely high density and temperature, space expanded, the universe cooled, and the simplest elements formed. Gravity gradually drew matter together to form the first stars and the first galaxies.
The nature of the universe is such that it underwent several stages of evolution, during its lifetime. These major stages include :
the radiation era, recombination eraepoch era and reionization eraOverall, a steady/constant incline will represent the various steady changes the universe has undergone in its development.
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complete question:
If gravity is the only force that plays a role in the evolution of the universe, and the mass density is less than the critical mass density, which plot correctly shows the evolution of the universe?
Plot A: a curved incline
Plot B: a steady/constant incline
Plot C: a very curved decline