Two carts, a and b, are connected by a rope 39 ft long that passes over a pulley p. the point q is on the floor h = 12 ft directly beneath p and between the carts. cart a is being pulled away from q at a speed of 3 ft/s. how fast is cart b moving toward q at the instant when cart a is 5 ft from q? (round your answer to two decimal places.)

Answer:

Force, F = 9800 N

Explanation:

It is given that,

The spring constant for the industrial scale at the junkyard is, k = 39,200 N/m

The compression in the spring, x = 25 cm = 0.25 m

To find,

The force applied to the scale by the car.

Solution,

The Hooke's law gives the relation between the force and the compression in the spring. Its expression is given by :

[tex]F=-kx[/tex]

[tex]F=39200\times 0.25[/tex]

F = 9800 N

So, the force applied to the scale by the car is 9800 N.

Final answer:

To calculate the acceleration of the elevator when a woman's weight reads 0.75 of her regular weight, we use Newton's second law, resulting in an acceleration of -2.45 m/s². This indicates that the elevator is accelerating downwards or decelerating while moving upwards.

Explanation:

If a woman standing on a bathroom scale in an elevator observes that the scale reads only 0.75 of her regular weight, it means that the net force acting on her is reduced because the elevator is accelerating.

To calculate the acceleration of the elevator, we can use Newton's second law of motion and some assumptions about gravitational acceleration (g = 9.8 m/s2).

Let's denote the woman's mass as m, her regular weight as W = mg (where g is the acceleration due to gravity), and the scale reading when the elevator accelerates as 0.75W. When the elevator is accelerating, the apparent weight (scale reading) is W' = 0.75mg.

The net force (Fnet) acting on the woman in the elevator is her apparent weight, W', minus her actual weight, W, leading to Fnet = ma. Therefore:

Fnet = W' - W

ma = 0.75mg - mg

a = 0.75g - g = -0.25g

This gives us a = -0.25(9.8 m/s2) = -2.45 m/s2. The negative sign indicates that the acceleration is directed downwards - meaning that the elevator is accelerating downward or decelerating while going up.

Answer:

a vector.

Explanation:

The arrow labeled '3.5 m/s' in the given scenario, which denotes both the speed and direction of a croquet ball, is called a vector. A vector, in physics, represents a quantity showcasing both magnitude (in this case, velocity measured as '3.5 m/s') and direction.

In the context of the question, the arrow labeled '3.5 m/s' that is indicating both the speed and the direction of the croquet ball is known as a vector. In physics, a vector is a quantity that possesses both magnitude (size or quantity) and direction. In this case, the '3.5 m/s' is the magnitude of the vector (the speed of the ball), and the direction the arrow is pointing indicates the direction the ball is moving. This is as opposed to a scalar quantity, which only has magnitude.

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To calculate the force needed to budge the stubborn pig, we need to consider the frictional forces acting on it. Given the given values of μs and the weight of the pig, the force required to budge the pig can be found by subtracting the force of friction from the maximum force the farmer can exert.

To calculate the force needed to budge the stubborn pig, we need to consider the frictional forces acting on it. The friction force can be calculated using the formula F_friction = μs ×F_normal, where F_normal is the normal force acting on the pig. The normal force is equal to the weight of the pig, which is given by F_weight = m × g, where m is the mass of the pig and g is the acceleration due to gravity.

Using the given values of μs and the weight of the pig, we can calculate the force of friction. Given that the maximum force the farmer can exert is 800 N, the force required to budge the pig can be found by subtracting the force of friction from the maximum force.

Let's calculate the force:

The force required to budge the pig is approximately 520 N.

Explanation:

It is given that,

Initial position of the Apple, [tex]h_o=1.4\ m[/tex]

Initial velocity, u = 3.1 m/s

Position of friend, Y = 4.2 m

Using second equation of motion as :

[tex]Y=ut-\dfrac{1}{2}gt^2+h_o[/tex]

[tex]4.2=3.1t-\dfrac{1}{2}\times 9.8t^2+1.4[/tex]    

[tex]3.1t-4.9t^2-2.8=0[/tex]..............(1)

On solving the above quadratic equation we get t = 2.02 seconds

Since, the value of t is real. So, the apple will reach a friend in a tree house. Hence, this is the required solution.                                    

An endothermic reaction is the one that makes use of chemical energy.

An endothermic reaction is defined as a chemical reaction which is a thermodynamic process  accompanied by an increase in enthalpy  of the system.In this process, a system absorbs energy from the surroundings  which is mainly thermal energy.

Thus an endothermic reaction leads to an increase in the temperature of the system with a decrease in the temperature of the surroundings.Endothermic reactions usually involve the formation of bonds which requires input of energy.In endothermic reactions, entropy of the surrounding decreases.

Many endothermic processes involve the physical changes rather the chemical changes.In an endothermic reaction ,the potential energy of products is greater than that of reactants.

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An occluded front involves three air masses of different temperatures: two cold air separated by a warm air .

Due to different densities, when big amounts of warm and cold air collide, they do not mix. They instead create a front that is typically hundreds of miles long. When a warm air mass is sandwiched between two cold air masses, an occluded front forms. As the cool air masses collide in the centre, the warm air mass rises. As the warm air mass is "cut off" from the earth and forced upward, the temperature decreases. Such fronts have the potential to produce violent winds and copious rain.

Typically, mature low pressure zones are where occluded fronts form.

Early occlusion of an extratropical cyclone in the Northern Hemisphere

Occlusion comes in two flavours, warm and cold:

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The answer is D

Children who watch more television may have parents who are home less often to help them with schoolwork

The maximum height achieved by the ball thrown vertically upwards is 243.9 ft.

A time varying function is a function whose final value varies with time.

Example - f(t) = 2t + 5

Given is a ball which is thrown vertically upward from the ground with a velocity of 96 ft/s, then its height after [t] seconds is S = 96t − 16t².

We can write -

S = 96t − 16t²

Differentiating with respect to 't', we get -

dS/dt = 96 - 2 x 16 x t

dS/dt = 96 - 32t

Now, for maximum height -

dS/dt = 0

96 - 32t = 0

32t = 96

t = 96/32

t = 3 seconds

At t = 3 seconds, the height will be maximum. Now, it is given that -

[u] = 96 ft/sec

[v] = 0  (at maximum height)

[g] = - 9.8 m/s²

Using the second equation of motion, we get -

S = ut + 1/2 gt²

S [max] = 96 x 3 - 0.5 x 9.8 x 3 x 3

S [max] = 288 - 44.1

S [max] = 243.9 ft

Therefore, the maximum height achieved by the ball thrown vertically upwards is 243.9 ft.

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According to law of conservation of energy, energy of motion is described by kinetic energy as the kinetic energy is displayed only when the object is in motion as per how much energy is stored in the object which are equal.

According to law of conservation of energy, it is evident that energy is neither created nor destroyed rather it is restored at the end of a chemical reaction .

Law of conservation of mass and energy are related as mass and energy are directly proportional which is indicated by the equation E=mc².Concept of conservation of energy is widely used in field of chemistry, fluid dynamics.

Law needs to be modified in accordance with laws of quantum mechanics under the principle of mass and energy equivalence.This law was proposed by Julius Robert Mayer in the year 1842.

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Answer:

[tex]v = 68.7 m/s[/tex]

angle made with the vertical

[tex]\theta = 21.3 degree[/tex]

Explanation:

Velocity of rain with respect to the car with vertical direction makes 38 degree angle

so let say rain velocity is

[tex]v_r = v_x\hat i + v_y \hat j[/tex]

[tex]v_{rc} = v_r - v_c[/tex]

[tex]v_{rc} = (v_x + 25)\hat i + v_y[/tex]

now we have

[tex]tan38 = \frac{v_x + 25}{v_y}[/tex]

while return to home

[tex]v_{rc} = (v_x - 25)\hat i + v_y[/tex]

now the angle with vertical is zero

so we have

[tex]v_x = 25[/tex]

now we have

[tex]tan38 = \frac{50}{v_y}[/tex]

[tex]v_y = 64 m/s[/tex]

so we have

[tex]v_r = 25 \hat i + 64 \hat j[/tex]

now magnitude of the speed is

[tex]v = \sqrt{25^2 + 64^2}[/tex]

[tex]v = 68.7 m/s[/tex]

angle made with the vertical

[tex]\theta = tan^{-1}\frac{25}{64}[/tex]

[tex]\theta = 21.3 degree[/tex]

Final answer:

Bernoulli's principle describes the relationship between pressure and velocity in fluids and is applicable in various fluid flow situations.

Explanation:

Bernoulli's principle describes the property of a fluid where there is an inverse relationship between the pressure and velocity of the fluid. According to Bernoulli's equation, for an incompressible, frictionless fluid, the sum of pressure, kinetic energy, and potential energy per unit volume is constant. This principle is applicable in various situations involving fluid flow, such as in the analysis of fluid devices and systems.

Bernoulli's principle serves as a fundamental concept in fluid dynamics, providing insights into the interplay between pressure and velocity within a flowing fluid. Its application extends to understanding phenomena like lift in aviation, the operation of carburetors, and the behavior of blood flow in arteries. By recognizing the conservation of energy in fluid motion, Bernoulli's principle contributes to the analysis and design of fluid-based systems across diverse fields.

The earth has many elements heavier than iron due to the hypothesis that the explosions of sun have become more massive to man kind over a period of time, thus creating heavier elements found on Earth.

Heavy elements such iron are formed by nuclear fusion reaction. Example include the heavy element of iron.

Source of these heavy elements are:

Many elements that are heavier than iron has been formed over the years due to the sun explosions.

The formation of these heavy elements occurs due to the process called neutron capture, where neutrons penetrate an atomic nucleus in explosions of the sun.

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A skater moves with an initial velocity of 2 m/s, and a final velocity of 7 m/s by which he covers 12 meters, so the acceleration will be 1.875 m/s².

A vector measurement of the direction and speed of the motion is what is meant by the term "velocity" in physics. In more detail, the rate of change in an object's position relative to a frame of reference and time can also be described as the object's velocity.

Velocity, which is defined as the rate of motion of an object in a specific direction, tells us how quickly an object is traveling. The speed at which anything is traveling is determined by this.

Given information according to the question,

Initial velocity, u = 2 m/s

Final velocity, v= 7 m/s

Distance, d = 12 m

Use the equation of motion to find the acceleration of the skater,

v² - u² = 2as

7² - 2² = 24a

a = 45/24

a = 1.875 m/s².

Therefore, the acceleration of the skater is 1.875 m/s².

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The final speed is approximately 17.79 m/s. The final speed of the block is determined by calculating the net force and resulting acceleration, then using kinematic equations.

Final Speed of the Block

To determine the final speed of the block, we first need to calculate the net force acting on the block. Given:

The force of kinetic friction (Ffriction) is calculated as:

[tex]F_{friction} = \mu_k \times N[/tex]

Where N is the normal force, and on a level floor N = mg:

[tex]N = m \times g = 2.5 kg \times 9.8 m/s^2 = 24.5 N[/tex]

Thus, the force of friction:

[tex]F_{friction} = 0.25 \times 24.5 N = 6.125 N[/tex]

The net force (F_{net}) acting on the block is:

[tex]F_{net} = F - F_{friction} = 30 N - 6.125 N = 23.875 N[/tex]

Using Newton's second law (F = ma) to find acceleration (a):

[tex]a = F_{net} / m = 23.875 N / 2.5 kg = 9.55 m/s^2[/tex]

We use the kinematic equation to find the final speed (v):

[tex]v^2 = v_0^2 + 2ad\\v = \sqrt{((7.0 m/s)^2 + 2 \times 9.55 m/s^2 \times 14 m)} = \sqrt{(49 + 267.4)} = \sqrt{(316.4)} = 17.79 m/s[/tex]

Therefore, the final speed of the block is approximately 17.79 m/s.