Block b rests upon a smooth surface. if the coefficients of static and kinetic friction between a and b are μs = 0.4 and μk = 0.3, respectively, determine the acceleration of each block if p = 6 lb

From Newton’s law of motion, the relation for velocity, acceleration and displacement is given by v^2 = vo^2 + 2as. Where v and vo are final and initial velocity respectively, and a, s are the acceleration and displacement respectively. From Newton’s second law, F = ma. Where m is the mass.

The magnitude of the frictional fore can be calculated only before estimating the ston’s acceleration. The initial speed of stone is mentioned in the problem as 3 m/s. Also, after 40m, the stone will stop. This means that its final speed is 0 m/s and the displacement is 40m.The acceleration of rock is calculated as:

(0 m/s)^2 = (3 m/s)^2 + 2a (40m).

9 m^2/s^2 = -2a(40m)

a= -9m^2/s^2/80m = 0.1 m/s^2.

This means that deceleration will occur and this will stop the stone. Substituting to Newton’s second law of motion,

-F = 20kg * -0.1 m/s^2. Further solve,

F = 20kg * 0.1 m/s^2 = 2N. Hence, the magnitude frictional force is 2N. 

In curling, the final position of the stone depends on its initial speed and the force of friction. Team members can use brooms to adjust the stone's speed and trajectory. The force of friction opposes the stone's motion.

In the winter sport of curling, the final position of the stone depends on the initial speed at which it is launched and the force of friction between the ice and the stone. Team members can use brooms to sweep the ice, which can adjust the stone's speed and trajectory. By judicious sweeping, they can lengthen the travel of the stone by a few meters. The force of friction between the ice and the stone will oppose the motion of the stone and slow it down.

The initial speed at which the stone is launched will determine how far it travels before coming to rest. If the stone is launched with a higher initial speed, it will travel a farther distance. The force of friction between the ice and the stone will also influence the distance the stone travels. A higher frictional force will cause the stone to slow down more quickly, resulting in a shorter travel distance.

The net force on the helicopter at t=5.0s = F = 1.65.10⁴i - 3.3.10³k

Newton's 2nd law explains that the acceleration produced by the resultant force on an object is proportional and in line with the resultant force and inversely proportional to the mass of the object

[tex]\large{\boxed{\bold{a~=~\frac{F}{m} }}}[/tex]

∑F = m. a

F = force, N

m = mass = kg

a = acceleration due to gravity, m / s²

While the speed is the first derivative of distance  

[tex]\large{\boxed{\bold{V~=~\frac{dr}{dt} }}}[/tex]

While acceleration is the first derivative of the velocity function for t

[tex]\large{\boxed{\bold{a~=~\frac{dv}{dt} }}}[/tex]

It is known that the distance function (r) = (0.020 t³i + 2.2 tj-0.06t²k

Then the speed (v)

[tex]v~=~\frac{dr}{dt}[/tex]

v = 0.06t²i + 2.2j - 0.12tk

Then acceleration (a)

[tex]a~=~\frac{dv}{dt}[/tex]

a = 0.12ti - 0.12k

While :

W = m . g

[tex]m~=~\frac{W}{g}[/tex]

m = 2.75.10⁵ : 10

m = 2.75.10⁴

so  net force :

F = m . a

F = 2.75.10⁴ . ( 0.12ti - 0.12k)

for t = 5  

F = 2.75.10⁴ . ( 0.12.5i - 0.12k)

F = 2.75.10⁴ (0.6i-0.12k)

F = 1.65.10⁴i - 3.3.10³k

Newton's second law

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Keywords : Newton's Law, acceleration, net force

The net force on the helicopter at time [tex]t = 5.0\,{\text{s}}[/tex] is [tex]\fbox{\begin\\\left( {1.68 \times {{10}^4}\,\hat i - 3.36 \times {{10}^3}\,\hat j} \right)\,{\text{N}}\end{minispace}}[/tex].

Further Explanation:

The helicopter moves under the action of the force which changes the position of the helicopter with respect to time according to the following equation.

[tex]\vec{r}=(0.020\text{ m}/\text{s}^3)\text{ t}^3\hat{i}+(2.2\text{ m}/\text{s})\text{ t}^3\hat{j}-(0.060\text{ m}/\text{s}^2)\text{ t}^2\hat{k}[/tex]

The force acting on the helicopter at a particular time is given by:

[tex]\fbox{\begin\\F= m\cdot{a}\end{minispace}}[/tex]

Here, [tex]m[/tex] is the mass of the helicopter and [tex]a[/tex] is the acceleration of helicopter.

The helicopter has a weight of [tex]2.75 \times {10^5}\,{\text{N}}[/tex]. This weight of the helicopter can be converted into the mass of the helicopter.

The weight of the helicopter can be represented as.

[tex]\fbox{\begin\\W=m \cdot g\end{minispace}}[/tex]

Rearrange and simplify the expression for the mass of helicopter.

[tex]\begin{aligned}m&=\frac{W}{g}\\&=\frac{{2.75\times{{10}^5}}}{{9.8}}\,{\text{kg}}\\&=2.{\text{80}}\times{\text{1}}{{\text{0}}^4}\,{\text{kg}}\\\end{aligned}[/tex]

The velocity of the helicopter can be determined by the differentiation of the position vector of the helicopter with respect to time.

[tex]\begin{aligned}\vec{v}&=\dfrac{{d\vec{r}}}{{dt}}\\&=\dfrac{d}{{dt}}\ [(0.020\text{ m}/\text{s}^3)\text{ t}^3\hat{i}+(2.2\text{ m}/\text{s})\text{ t}^3\hat{j}-(0.060\text{ m}/\text{s}^2)\text{ t}^2\hat{k}]\\&=0.060{t^2}\hat{i}+2.2\hat{j}-0.12t\hat{k}\end{aligned}[/tex]

The acceleration of the helicopter is the derivative of the velocity with respect to the time.

[tex]\begin{aligned}\vec a&=\frac{{d\vec v}}{{dt}}\\&=\frac{d}{{dt}}\left({0.060{t^2}\hat i+2.2\hat j-0.12t\hat k}\right)\\&=0.12t\hat i-0.12\hat k\\\end{aligned}[/tex]

Substitute the value of [tex]t = 5.0\,{\text{s}}[/tex] in equation of the acceleration.

[tex]\begin{aligned}a&=0.12\left({5.0}\right)\hat i-0.12\hat k\\&=0.6\hat i-0.12\hat k\\\end{aligned}[/tex]

Substitute the values of the acceleration and the mass of the helicopter in the equation of force.

[tex]\begin{aligned}F&=\left( {2.80\times{{10}^4}\,{\text{kg}}}\right)\left({0.6\hat i-0.12\hat k}\right) \\&=\left({1.68\times{{10}^4}\,\hat i-3.36\times{{10}^3}\,\hat j}\right)\,{\text{N}}\\\end{aligned}[/tex]

Thus, the net force acting on the helicopter at time [tex]t = 5\,{\text{s}}[/tex] is [tex]\fbox{\begin\\\left( {1.68 \times {{10}^4}\,\hat i - 3.36 \times {{10}^3}\,\hat j} \right)\,{\text{N}}\end{minispace}}[/tex].

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Answer Details:

Grade: College

Subject: Physics

Chapter: Force and acceleration

Keywords:

Helicopter, force, time, 5s, position, velocity, derivative, acceleration, weight, net force, t=5s, 0.020t3 m/s3, 2.75x10^5 N, helicopter under test, gravity, mass of helicopter.

Answer:

a=5.20 m/s²

Explanation:

Given Data

Thrust = T (N)=3.0×10⁵N

Mass=m=20000kg

To find

acceleration=a=?

Solution

Newton Second law states that

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

(resultant force F)=ma

a=(resultant force F)/m

where

(resultant force F) is (Thrust-weight)  

Weight = mg = 2.0^4 kg*9.8 N/kg = 1.96^5 N

a = (resultant force F) / mass

a = (T - mg)/m = (3.0^5 N - 1.96^5 N)/ 2.0^4 kg

a=5.20 m/s²

The rocket's initial upward acceleration is 5.2m/s²

According to Newton's second law of motion

[tex]\sum F = ma[/tex]

The sum of forces is the difference between the weight and the thrust

[tex]\sum F = T -W[/tex]

[tex]T - W = ma\\a=\frac{T-W}{a}[/tex]

Given the following parameters:

T = [tex]3.0 \times 10^5 N[/tex]

W = [tex]20,000 \times 9.8 = 1.96 \times 10^5 N[/tex]

m = [tex]20,000kg[/tex]

Substitute the given parameters into the formula to have:

[tex]a=\frac{(3.0-1.96)\times 10^5}{2\times 10^4} \\a=\frac{1.04\times 10^5}{2\times 10^4} \\a = 0.52 \tmes 10\\a = 5.2m/s^2[/tex]

Hence the rocket's initial upward acceleration is 5.2m/s²

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Answer: The correct answer is constructive interference.

Explanation:

Interference is the phenomenon in which there is superposition of the two waves. Interference are of two types: Constructive interference and Destructive interference.

Constructive interference occurs when the there is a superposition of the two waves. The resulting wave has a large amplitude.

Destructive interference occurs when the there is a superposition of the two waves. The resulting wave has a low amplitude.

Therefore, Constructive interference occurs when two waves overlap and the resulting wave has a larger amplitude.

Answer:

B. Constructive

Answer:

A gliding joint means a freely moving joint in which the articulations allow only gliding motions

Explanation:

Answer: False

Explanation: The circulatory system of the body consists of the heart, blood vessels and blood. The deoxygenated blood from the body is carried to the heart.

Here, the deoxygentaed blood is converted into oxygenated by removing carbon dioxide from them and making it oxygenated.

The impure blood from the body is collected by the right ventricle and transported to the lungs for purification and then transported to the body.

The correct answer is F (False)

Explanation:

In anatomy, the heart which is the organ in charge of pumping blood to all the body is divided into different sections that include the aorta, the superior vena cava, the right/left atrium, the pulmonary valve, and the right/left ventricles. In the case of the right ventricle, this is a chamber located on the right side of the hearth and the main function of this is to pump blood that is low in oxygen or de-oxygenated blood to the lungs through the pulmonary artery. On the other hand, the left ventricle pumps oxygenated blood to all the body. This implies, it is false the right ventricle transports oxygenated blood to the lungs because it pumps de-oxygenated rather than oxygenated blood.

Answer:

electricity

Explanation:

just got the question and it was right

Answer:

the answer is false

Explanation:

your welcome

A positive entropy change (delta S) indicates that the system has become less ordered, as there is an increase in the number of possible microstates. This is aligned with the Second Law of Thermodynamics, which states that entropy increases in spontaneous processes, leading to greater disorder.

When a system undergoes a change and the entropy change (δS) is positive, this implies that the order of the system has decreased. This is because positive entropy reflects an increase in the number of microstates or possible configurations that the system can adopt, leading to a less ordered, more random state. A common example is the melting of a solid into a liquid where the rigid structure of the solid is lost, providing the particles more freedom to move in the liquid state, which translates into an increased entropy.

As per the Second Law of Thermodynamics, for all spontaneous processes in the real world, the change in entropy is positive (dδS > 0), which is consistent with the natural tendency for systems to move towards greater disorder and randomness. This concept is fundamental in predicting the spontaneous direction of chemical and physical processes. For instance, when a liquid freezes into a solid, the process is accompanied by a negative entropy change, signifying increased order in the system.

Final answer:

A positive entropy change (δS > 0) means that the order of the system has decreased, leading to a more disordered and randomized state with more microstates. This is in line with the Second Law of Thermodynamics, which predicts that the entropy of an isolated system tends to increase in spontaneous processes.

Explanation:

When the entropy change (δS) is positive, it indicates that the order of the system has decreased. This is because a positive δS suggests that the number of microstates and, therefore, the randomness of the system has increased. For example, when a solid changes into a liquid, there is an increase in entropy because the liquid state allows the particles more freedom of movement and positioning, leading to a higher number of microstates compared to the solid state. If the process were reversed and the liquid turned into a solid, δS would be negative, signifying a decrease in entropy as the system becomes more ordered.

Furthermore, the Second Law of Thermodynamics asserts that for any spontaneous process, the entropy of an isolated system will increase. This means the system will move towards a state with more microstates or higher disorder. It aligns with the observation that in irreversible processes, entropy tends to increase, indicating a spontaneous change in an isolated system.

In conclusion, a positive entropy change (δS > 0) aligns with the expectation that there are more microstates available in the final state compared to the initial one, resulting in a decrease in the orderliness of the system. The increase in entropy reflects the fundamental tendency for systems to evolve towards states of higher disorder and randomness.

Use the expression -

P²k = a³---(i)

Where P is time in years, a is in AU, k is the function of the Sun's mass and set to unity.

Further, we're looking for the mass of the new star we have slightly modified Kepler's Third Law. After all, the inverse of a constant is also a constant. The reason we do it is because we want an answer in the form of K:1, where K is the mass of the HD 10180 and the mass of the Sun is 1, so k needs to start out on the other side.

Convert 600 days in years = 600/365 = 1.64 years

Put this in the expression mentioned at (i) -

1.64²k = a³

You gave us a = 1.4 AU

1.64²k = 1.4³ ; isolating k

k = 1.4³/1.64²

k = 2.744/2.702 = 1.015

So, the requisite ratio = 1.015 : 1

The ratio of the star's mass to the sun's mass is about 1.02 : 1

[tex]\texttt{ }[/tex]

Centripetal Acceleration can be formulated as follows:

[tex]\large {\boxed {a = \frac{ v^2 } { R } }[/tex]

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

[tex]\texttt{ }[/tex]

Centripetal Force can be formulated as follows:

[tex]\large {\boxed {F = m \frac{ v^2 } { R } }[/tex]

F = Centripetal Force ( m/s² )

m = mass of Particle ( kg )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

mass of the sun = M_sun = 1.99 × 10³⁰ kg

radius of the orbit = R = 1.4 AU = 2.094 × 10¹¹ m

Orbital Period of planet = T = 600 days = 600 × 24 × 3600 = 5.184 × 10⁷ seconds

Asked:

mass of the star = M = ?

Solution:

Firstly , we will use this following formula to find the mass of the star:

[tex]F = ma[/tex]

[tex]G \frac{ Mm}{R^2}=m \omega^2 R[/tex]

[tex]G M = \omega^2 R^3[/tex]

[tex]\frac{GM}{R^3} = \omega^2[/tex]

[tex]\omega = \sqrt{ \frac{GM}{R^3}}[/tex]

[tex]\frac{2\pi}{T} = \sqrt{ \frac{GM}{R^3}}[/tex]

[tex]M = \frac{4 \pi^2 R^3}{GT^2}[/tex]

[tex]M = \frac{4 \pi^2 (2.094 \times 10^{11})^3}{6.67 \times 10^{-11} \times (5.184 \times 10^7)^2}[/tex]

[tex]\boxed {M \approx 2.0 \times 10^{30} \texttt{ kg} }[/tex]

[tex]\texttt{ }[/tex]

Next , we will calculate the ratio of the star's mass to the sun's mass as follows:

[tex]M : M_{sun} = (2.0 \times 10^{30}) : (1.99 \times 10^{30})[/tex]

[tex]\boxed{M : M_{sun} \approx 1.02 : 1}[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Circular Motion

The amount of chemical energy a substance has is determined by its molecular structure and the type of chemical bonds it contains.

1. Molecular Structure:

  - The arrangement of atoms within a molecule determines its potential energy content.

  - Different substances have varying numbers and arrangements of atoms, leading to differences in chemical energy.

2. Type of Chemical Bonds:

  - Chemical energy is stored in the bonds between atoms within molecules.

  - The strength and type of chemical bonds, such as covalent bonds, ionic bonds, and hydrogen bonds, dictate the amount of energy stored in the substance.

  - Stronger bonds require more energy to break and thus store more chemical energy.

3. Potential Energy:

  - Chemical energy represents the potential energy stored within a substance's chemical bonds.

  - When chemical bonds are broken during a chemical reaction, the stored energy is released as heat or used to perform work.

4. Examples:

  - Substances with complex molecular structures and strong chemical bonds, such as hydrocarbons in fossil fuels, tend to have high chemical energy content.

  - Conversely, simpler molecules with weaker bonds, such as gases like hydrogen and oxygen, have lower chemical energy content.

Therefore, the amount of chemical energy a substance possesses is determined by its molecular structure and the type of chemical bonds it contains, with stronger bonds and more complex structures generally correlating with higher chemical energy content.

The complete Question is given below:

What determines the amount of chemical energy a substance has?

Final answer:

The vapor pressure of cyclohexane at its normal boiling point of 81.0 ℃ is 101.3 kPa.

Explanation:

The question is asking for the vapor pressure of cyclohexane at its normal boiling point of 81.0 ℃. By definition, the normal boiling point of a liquid is the temperature at which its vapor pressure is equal to the external atmospheric pressure at sea level, which is 101.3 kPa (or 1 atmosphere). Therefore, the vapor pressure of cyclohexane at 81.0 ℃ is 101.3 kPa.

Answer:

When insulating materials rub against each other, they may become electrically charged . Electrons , which are negatively charged, may be 'rubbed off' one material and on to the other. The material that gains electrons becomes negatively charged.

Explanation:

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If a mineral with a Moh's hardness value of 7 is rubbed against the mineral with a value of 5, the mineral with value 5 get scratched with the mineral with hardness value 7.  

• A scale of relative mineral hardness invented by German scientist Mohs is known as the Mohs scale of hardness or Mohs scale.  

• It is a 10 point scale, with 10 given to mineral diamond as the most hardest mineral, which can scratch the minerals below it, that is, coming below it in the hardness scale.  

• The minerals coming in the 7 scale are Quartz, Citrine, Agate, and Amethyst, and the mineral coming in the 5 scale is apatite.  

• Thus, when one rubs the mineral with 7 hardness with a mineral with 5 hardness, than the mineral with 5 hardness will easily get scratched as it is less harder to the mineral in the 7 scale.  

Thus,  the mineral with value 5 get scratched with the mineral with hardness value 7.

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The lowest gear on a bicycle provides the greatest mechanical advantage by amplifying the force exerted on the pedals, requiring the rider to pedal more but with less effort per stroke, due to the conservation of energy.

In order to climb a steep hill on a bicycle, a rider shifts to the lowest gear. The lowest gear has the greatest mechanical advantage because it allows the rider to apply a force over a greater distance. When a gear with many teeth drives a gear with fewer teeth, the driven gear spins more times but with a smaller turning force, amplifying the force the rider exerts on the pedals.

However, this means the rider will have to spin the pedals more times to cover the same distance, which is a trade-off.

This concept of mechanical advantage applies to all machines and is governed by the conservation of energy, which states that work input is equal to work output, minus any losses due to inefficiency like friction.

The most accurate number for a population in an area is measured by adding the individuals living or born in an area and subtract those who die. So, option C.

The amount of people living in a particular area is called population density.

The majority of the time, it applies to people, but occasionally it also does to other living things. It is a significant geographic term. Population density is the total number of people residing in a certain area per square kilometer, or other units of land area.

Demography is the statistical study of populations and how they change through time.

Population size, or the total number of people, and population density, or the number of people per unit of space or volume, are the two most important measurements of a population.

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Final answer:

The most accurate way to measure population size is by adding the number of births and individuals present, while subtracting the number of deaths (which corresponds to option C). Sampling techniques like quadrats and mark-recapture are often used due to the impracticality of counting all individuals.

Explanation:

In the context of estimating population size, the most accurate measurement for a population in an area would be to add the individuals living or born in an area and subtract those who die (Option C). This method accounts for natural population changes such as births and deaths.

Although counting all individuals would provide the most precise number, this is often not feasible. Instead, scientists often use sampling techniques to estimate population size. For stationary or slow-moving organisms, a quadrat can be used, while for mobile organisms, methods like mark and recapture might be employed.

Carrying capacity is a separate concept indicating how many individuals an area can sustain based on resources. Adjustments to population estimates may be necessary when populations near their carrying capacity, as density-dependent factors might affect population growth.

The boiling point of oxygen is 90.2 K or -183.15 °C.

For an object that is under the pull of only the force of gravity, the motion is called free-fall. The equations that would allow us to calculate for the speed and distance is,

        Speed = gt

Where g is the acceleration due to gravity and the t is the time.

For the distance, it is calculated through the equation,

     Distance = vt + 1/2gt^2

Where v is the initial velocity and is equal to zero.

The graphs are attached.

The student's question pertains to the physics concept of projectile motion. The mug's trajectory is determined by its initial horizontal velocity, the counter's height, and gravity. One could compute the time it takes for the mug to hit the ground and its initial speed.

This question is about the physics concept of projectile motion. When the beer mug slides off the counter and falls to the ground, it follows a trajectory determined by the initial horizontal velocity at which it was pushed, the height of the counter, and the acceleration due to gravity.

To find out how long it takes for the mug to hit the ground, we can use the equation of motion: h = 0.5gt^2, where h is the height from which the object is dropped (1.14m in this case), g is acceleration due to gravity (approximately 9.8 m/s^2) and t is time. Solving for t gives us the time it takes for the mug to hit the floor.

Once we know the time, we can find the initial horizontal velocity using the formula v = d/t, where v is velocity, d is distance (0.60m) and t is time. This gives us the initial speed at which the mug was slid.

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