Learning Goal: To understand that centripetal acceleration is the acceleration that causes motion in a circle. Acceleration is the time derivative of velocity. Because velocity is a vector, it can change in two ways: the length (magnitude) can change and/or the direction can change. The latter type of change has a special name, the centripetal acceleration. In this problem we consider a mass moving in a circle of radius R with angular velocity ω, r⃗ (t)=R[cos(ωt)i^+sin(ωt)j^] =Rcos(ωt)i^+Rsin(ωt)j^. The main point of the problem is to compute the acceleration using geometric arguments. (Figure 1) Part A What is the velocity of the mass at a time t? You can work this out geometrically with the help of the hints, or by differentiating the expression for r⃗ (t) given in the introduction. (Figure 2) Express this velocity in terms of R, ω, t, and the unit vectors i^ and j^. V⃗ (t) = Part Assume that the mass has been moving along its circular path for some time. You start timing its motion with a stopwatch when it crosses the positive x axis, an instant that corresponds to t=0. [Notice that when t=0, r⃗ (t=0)=Ri^. ] For the remainder of this problem, assume that the time t is measured from the moment you start timing the motion. Then the time − t refers to the moment a time t before you start your stopwatch. Part B What is the velocity of the mass at a time − t? Express this velocity in terms of R, ω, t, and the unit vectors i^ and j^. V⃗ (−t) = SubmitMy AnswersGive Up Part C What is the average acceleration of the mass during the time interval from − t to t? (Figure 3) Express this acceleration in terms of R, ω, t, and the unit vectors i^ and j^.

Answer:

Balanced forces do not result in any change in motion.

Explanation

forces applied to an object in opposite directions that are not equal in size. Unbalanced forces result in a change in motion. friction the force that opposes the motion or tendency toward motion of two objects that are in contact.

Answer:

balanced forces are equal in size and opposite in direction

Answer:

&3?.&.)/&282/8//8338/.)9

Explanation:

Uranus continues to generate internal heat through gravitational contraction: True.

Uranus is generating internal heat through gravitational contraction. This process occurs as the planet's gravity causes it to gradually shrink, which generates heat as potential energy is converted into kinetic energy. Although Uranus is not as active as Jupiter or Saturn, it is still generating internal heat, primarily due to the energy released by its continued contraction. Additionally, the decay of radioactive isotopes in Uranus' core may also contribute to its internal heat. Evidence of internal heat sources in Uranus' atmosphere supports the idea that the planet is still generating heat through gravitational contraction.

Gravitational contraction is the process by which an astronomical body, such as a planet or star, generates heat due to the gradual shrinking of its size under the influence of gravity. In the case of Uranus, it is indeed generating internal heat through this process.

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The statement "Uranus continues to generate internal heat through gravitational contraction" is false because The internal heat of Uranus is thought to be a combination of leftover heat from its formation and ongoing processes within its interior, such as the slow cooling of its core and the release of heat from the decay of radioactive elements.

Uranus consists mainly of hydrogen and helium, with minor quantities of methane and other substances. Unlike certain celestial bodies like Jupiter or Saturn, Uranus does not produce internal heat through gravitational contraction.The internal heat of Uranus is believed to arise from various factors, including residual heat from its formation and ongoing processes taking place within its interior. These processes encompass the gradual cooling of its core and the emission of heat resulting from the decay of radioactive elements. Nevertheless, the precise mechanisms and sources responsible for Uranus' internal heat are not yet fully comprehended.

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The approximate angle of repose for average soils when using the sloping method for the prevention of cave-ins is option c.) 1.5:1.0. This means that for every 1.5 feet horizontally, the soil should slope down 1 foot vertically.

The angle of repose is the maximum angle at which a soil can remain stable without collapsing. Sloping the soil at this angle helps to prevent cave-ins by providing stability and support to the walls of the excavation.

It is important to note that the angle of repose may vary depending on the type and condition of the soil, so it is always best to consult with a qualified engineer or geotechnical expert for specific recommendations.

However, as a general rule of thumb, the slope angle is typically in the range of 1.5:1.0 to 2.0:1.0, which means for every foot of vertical depth, the slope should extend 1.5 to 2 feet horizontally.

This angle allows the soil to maintain its stability and prevent it from collapsing or sliding, providing a safe working environment. Therefore, the correct option would be (c) 1.5:1.0 to (d) 2.0:1.0.

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The availability of suitable nesting sites is one of the most important limiting factors for the purple martin bird population.  Building more birdhouses can help address this limiting factor and increase the size of the purple martin population in the area.

There are several limiting factors that can decrease purple martin populations, but one of the most important is the availability of suitable nesting sites. Purple martins are cavity-nesting birds, which means they require hollow spaces, such as tree cavities or specially designed birdhouses, to build their nests and raise their young. In areas where suitable nesting sites are scarce, the population of purple martins may be limited by the number of available nesting sites.

Therefore, by building more birdhouses, Latrice is addressing this limiting factor and helping to increase the size of the purple martin population in her area. Other limiting factors for purple martins may include the availability of food, the quality of habitat, and the presence of predators.

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Answer:

An inelastic collision is a collision in which there is a loss of kinetic energy. While momentum of the system is conserved in an inelastic collision, kinetic energy is not.

The specific heat of a substance of a container affect the quantity of substances that can be accommodated in the container at a given temperature.

The specific heat capacity of a substance is the quantity of heat required to raise the temperature of a unit mass of the substance.

Mathematically, the formula relating specific heat capacity and heat capacity of a substance is given as;

Q = m x  c  x Δθ

where;

From the formula above we can make mass " m " the subject of the formula;

m = ( Q ) / (  c  x Δθ )

As the specific heat of a substance increases, the smaller the mass of the substance that can be held in a container at equal heat gain and temperature and vice versa.

Thus, the specific heat of a substance affects the performance of a container as it depends the mass or volume of the substance that can be held in a container at a constant heat capacity and temperature.

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Answer:

bad

Explanation:

Answer:

The net external force on the apple is 9.18 N and the direction of net force is 82.6°.

Explanation:

Given that,

Force of gravity = 9.11 N

Force of wind = 1.18 N

We need to calculate the net external force on the apple

Using formula of net force

\(F'=\sqrt{(9.11)^2+(1.18)^2+2\times1.18\times9.11\cos90}\)

\(F'=9.18\ N\)

We need to calculate the direction of net force

Using formula of direction

\(\theta=\tan^{-1}(\dfrac{9.11}{1.18})\)

\(\theta=82.6^{\circ}\)

Hence, The net external force on the apple is 9.18 N and the direction of net force is 82.6°.

The magnitude of the net external force on the apple is 9.19 N and the direction of the net external force is 82.6⁰.

The given parameters;

The magnitude of the net external force on the apple is calculated as follows;

\(F= \sqrt{F_y^2 + F_x^2} \\\\F= \sqrt{9.11^2 + 1.18^2} \\\\F = 9.19 \ N\)

The direction of the net external force on the apple is calculated as follows;

\(\theta = tan^{-1}(\frac{F_y}{F_x} )\\\\\theta = tan^{-1}(\frac{9.11}{1.18} )\\\\\theta = 82.6 \ ^0\)

Thus, the magnitude of the net external force on the apple is 9.19 N and the direction of the net external force is 82.6⁰.

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Answer:

Sorry

Explanation:

I really don't know what to say about this question I am not sure what to say about this

option (B) ←  is the direction of the average velocity of the particle during this time interval. The displacement is directly to the left. The average velocity is proportional to the displacement.

Velocity=displacement/time

Displacement=velocity X time

For constant time,

Displacement ∝velocity

If we increase the velocity of the object, then it covers the more distance for same time.

Directly to the left is where the displacement is. The displacement is inversely proportional to the average velocity.

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Complete Question is :

a particle continuously moves in a circular path at a constant speed in a counterclockwise direction, as shown. consider the time interval during which the particle moves along this circular path from point p to point q. point q is exactly halfway around the circle from point p. what is the direction of the average velocity of the particle during this time interval?

(A) →  

(B) ←  

(C) ↑  

(D) ↓  

(E) The average velocity is zero.

Magnitude of the gravitational force of the earth on the student is  635.05 N

Mass of the Earth M = \(6 * 10^{24} kg\).

Mass of the Object m = 65 kg

Radius of the earth R = \(6.4*10^6 m\)

Force of gravitation between them, F = \(\frac{GMm}{R^2}\).

F = \(\frac{6.67 * 10^{-11} * 6*10^{24}* 65}{(6.4* 10^6)^2}\) = 635.05 N

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Okay, let's think this through step-by-step:

* The rate of energy transfer is 50 J/s

* We need to calculate the energy transferred in 4 seconds

* So we would calculate:

Energy in 4 seconds = Rate x Time

= 50 J/s x 4 s

= 200 J

So the heat energy produced within 4 seconds with an energy transfer rate of 50 J/s is 200 J.

Let me know if you have any other questions!

The total work done on the crate of bananas is 4800 J (the work done to move it horizontally).

Work done is defined as the product of displacement and force, w = FS.

Here,

There are two parts to the work done on the crate of bananas: the work done to move it horizontally and the work done to lift it vertically.

First, let's calculate the work done to move the crate horizontally. The formula for work is,

Work = Force x Distance x cos(Ф)

where theta is the angle between the force and the displacement. In this case, the force is the tension in the rope, and it is pulling horizontally. So, theta is 0 degrees, and cos(Ф) is 1.

The distance the crate is moved horizontally is 5 meters, and the force applied by the motor is,

Force = Power / Velocity = 40 W / (5 m / 120 s) = 960 N

So, the work done to move the crate horizontally is:

Work = 960 N x 5 m x cos(0) = 4800 J

The distance the crate is lifted vertically is not given in the problem, so we cannot calculate the work done to lift the crate without this information.

Therefore, the total work done on the crate of bananas is 4800 J (the work done to move it horizontally).

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The end velocity of an object is equal to its initial velocity plus its acceleration multiplied by the period of travel, according to the formula used in this velocity calculator.

As long as three of the variables are known, this calculator can be used to determine initial velocity, ultimate velocity, acceleration, or time.

Initial velocity (u) squared plus two times the acceleration (a) times the displacement equals final velocity (v) squared.

When the body has achieved the maximum acceleration over a period of time, final velocity enters the picture. The acceleration is the difference between the object's initial and final velocities over time.

The end velocity of an object is equal to its initial velocity plus its acceleration multiplied by the period of travel, according to the formula used in this velocity calculator.

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The answer is C) more. When a bathroom scale is placed on an incline, the weight will be greater than when placed on a level surface due to the increased force of gravity.

This can be explained mathematically using the equation\(F = mg\), where F is the force, m is the mass, and g is the acceleration due to gravity. If the scale is on an incline, the force of gravity on the object will be greater than if it were on a level surface, resulting in a higher weight reading on the scale.Gravity is a force of attraction between two objects that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

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complete question:When you weigh yourself on a bathroom scale on a slight incline instead of a level surface, your weight reading on the scale will be

A) less.

B) no different.

C) more.

If the velocity-time graph is horizontal, the acceleration is zero because the slope will be zero.

Answer:

The value is \(v_t = 172 \ km/h\)

Explanation:

From the question we are told that

    The average speed for the first 12 hours is \(u = 185 km/h\)

    The average speed for the next 13 hours is  \(v = 160 \ km/h\)

Generally the total time taken is mathematically represented as

     \(t_t = 12 + 13\)

=> \(t_t = 25 \ h\)

The distance covered in the first movement is

          \(D = u * 12\)

         \(D = 185 * 12\)

        \(D = 2220 \ km\)

The distance covered in the first movement is

          \(d= v * 13\)

         \(d = 160 * 13\)

        \(d = 2080 \ km\)

The total distance traveled is  

       \(D_t = D + d\)

       \(D_t = 2220 +2080\)

      \(D_t = 4300 \ km\)

The average  of the whole journey is

      \(v_t = \frac{D_t}{t_t}\)

     \(v_t = \frac{4300}{25}\)

     \(v_t = \frac{4300}{25}\)

    \(v_t = 172 \ km/h\)

The accelaration is 15 ms.

Acceleration (a) is the reason that  change in velocity (Δv) over to the change in time (Δt).

represented by the equation to  a = Δv/Δt. This allows you to measure how fast velocity by the  changes in meters per second squared (m/s^2).

1 . Here the change in to the  velocity is (50-20) or 30 m/s

And the time interval by to  the 5

So acceleration is 30/5 or 6 ms^-2

2. Here the change is the  (40-10) or 30 m/s in time is the  interval is 2 second

So acceleration is 30/2 or 15 ms^-2.

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Answer:

by increasing the force applied to the objects

Answer:

measures of central tendency are numbers that describe what an average or typical within a distribution of data there are three main measures of central tendency mean medium and mold well they are all measuring essential tendency each is calculated differently and measures something different from others

The magnitude of the resultant displacement of the caterpillar is 1.4m. Therefore, option B is correct.

The change in the position of an object is called displacement, it is the distance between starting and endpoints. It has both magnitude and direction, it is a vector quantity.

If a caterpillar climbs 1.3 m up a tree, then 0.72 m right, the magnitude of resultant displacement is given by:

H² = P² + B²

H² = (1.3)² + (0.72)²

H² = 1.69 + 0.51

H = \(\sqrt2.2\)

H = 1.4m

Thus, the magnitude of the resultant displacement of the caterpillar is 1.4m. Therefore, option B is correct.

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Explanation:

Scientists define these charges as “+1” and “−1.” In an uncharged, neutral atom, the number of electrons orbiting the nucleus is equal to the number of protons inside the nucleus. In these atoms, the positive and negative charges cancel each other out, leading to an atom with no net charge.

Among the given options, natural gas is considered a nonrenewable energy source. Nonrenewable energy sources are those that cannot be replenished or regenerated at a rate that matches their consumption.

Natural gas is formed from the remains of ancient plants and animals that were buried and subjected to heat and pressure over millions of years. Once extracted and used, natural gas is depleted and cannot be easily replaced within a human lifetime.

On the other hand, solar power, wind power, and geothermal energy are considered renewable energy sources. Solar power harnesses the energy from the sun using photovoltaic panels, while wind power utilizes the kinetic energy of wind to generate electricity. Geothermal energy taps into the heat from the Earth's core. These renewable sources are considered sustainable as they are continuously available and do not deplete with usage. They offer a cleaner and more environmentally friendly alternative to nonrenewable energy sources like natural gas, which contribute to carbon emissions and climate change.

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Answer:

please let me know when you find it

Explanation:

i have the same question and cant find it

Answer:

It’s 5m/s^2

Explanation:

The relationship between the angles of incidence and refraction when a light ray passes across the boundary between two media with differing refractive indices is described by Snell-Descartes law.

Snell's law

n₁sinθ₁ = n₂sinθ₂

In the following equation, n1 and n2 stand for the refractive indices of the two media. θ₁ for angle of incidence (the angle between the incident ray and the normal to the boundary), and θ₂ for angle of refraction (the angle between the refracted ray and the normal to the boundary). Sometimes referred to as Snell-Descartes law, in its mathematical form.

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Answer:

Yes, greater power is necessary to lift a car with your own body in a dire emergency situation than it would be to lift the same car using a jack.

Explanation:

This is because lifting the car with your body requires a combination of strength, power, and speed, all of which must be generated by your muscles. In contrast, a jack is a tool that uses hydraulic pressure to lift the car, which requires much less effort on your part.

When lifting a car with your body, you are essentially performing a squat or deadlift with an extremely heavy weight. This requires your muscles to produce a tremendous amount of force to overcome the weight of the car and gravity, as well as to generate the speed and power necessary to lift the car quickly and effectively.

In addition, lifting a car with your body requires you to use multiple muscle groups simultaneously, including your legs, back, arms, and core. This makes it a very taxing exercise that can quickly fatigue your muscles and potentially lead to injury if not performed correctly.

In contrast, using a jack to lift a car requires minimal effort on your part, as the hydraulic pressure does the majority of the work. This means that you do not need to generate as much force, speed, or power with your muscles, and can avoid the risk of injury or fatigue associated with lifting the car with your body.

Overall, lifting a car with your body is a remarkable feat that requires a tremendous amount of strength, power, and speed. While it can be done in dire emergency situations, it should not be attempted unless absolutely necessary, and only by individuals who are properly trained and physically capable of performing the lift safely.