a 12 kg runaway grocery cart runs into a spring, attached to a wall, with spring constant 290 n/m and compresses it by 80 cm . part a what was the speed of the cart just before it hit the spring? neglect any friction.

We can determine the magnetic field at two different distances from a system made up of two conductors using Ampere's law:

a) The system's magnetic field is:

b) The magnetic field for the system's exterior is b = 0.

Ampere's Rule.

According to Ampere's law, the magnetic field's dot product times a closed path is proportional to the current flowing through the path.

∫ B. ds = μ₀ I

Here, B is the magnetic field, S is the closed path, μ₀ is the vacuum permittivity, and I is the current where bold indicates vectors.

Ask about the magnetic fields within the two conductors (optional).

Fixing the associated circular path will cause I, the current that stops inside the path, to flow through the system.

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The maximum number of 23 pieces a person could eat without exceeding 150 calories.

A calorie can be described as unit of energy. The large calorie, food calorie was originally described as the amount of heat required to raise the temperature of 1 Kg of water by one degree Celsius.

The small calorie was defined as the amount of heat required to cause the same increase in one gram of water.  In physics and chemistry, the calorie usually refers to a small unit of energy. One calorie is equal to exactly 4.184 Joules.

Given, the  234 calories contained in pieces of candy = 36

Then 150 calories contain by pieces of candy = (36/234) ×150 = 23

Therefore, a maximum number of 23 pieces someone could eat without exceeding 150 calories.

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The magnitude of the induced EMF in the coil is 5.56V.

The number of turn in the coil is 1300 and the diameter of the coil is 2.0 cm. The magnetic flux changes from 0.15T to 0 T in 11ms.

The induced EMF in the coil can be found as,

E = nAΔB/t

Where,

n is the number of turn in the coil,

A is the area,

B is the magnetic field and t is the time,

Putting values,

E = 1300 x π(0.01)² x 0.15/11 x 10⁻³

Solving further,

E = 5.56 V.

So, the EMF induced in the coil is 5.56 V.

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The metal has a resistance of 5.0x10-8 ohm x m.

Given: radius=1cm , resistance=3.2x10¬⁵ω .

Using ohms () as the unit, resistance acts as a gauge to quantify how easily current will flow through a circuit. When resistance falls, current rises, and when resistance rises, current falls. In order to make sure that current is flowing in circuits at the proper rate, resistors are crucial.

When electricity flows through with a conducting, such a metal wire, an electric current occurs. The electrons in the metal may clash with the travelling electrons. Resistance is created as a result, making it harder for current to flow.

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The gravitational acceleration at the surface of the planet, times a function of r is g = mG/r².

Gravitational acceleration is described as an object receiving acceleration due to the gravitational force acting on it.

From Newton's second law of motion we can write

F=ma

Here, F is the force acting on the object.

m is its mass and

"a" is the acceleration.

Also according to Newton's law of gravity we can write,

Fg = GmM / (r+h)²

Also a = Fg/M

a = g = {GmM / (r+h)²} / M

g = Gm/r²

The gravitational acceleration at the surface of the planet, times a function of r is g = mG/r².

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Since the bird is traveling at a constant horizontal velocity, the coconut hits the beach below, the bird will be in a position that is directly above the coconut in relation to the coconut.

The free fall of an object refers to the motion of an object that is released from a certain height above the ground and allowed to fall freely under acceleration by the force of gravity alone.

Objects that are experiencing free fall, are accelerated by a constant value that is equal to the value of acceleration due to gravity.

Examples of objects experiencing free fall include:

For the coconut dropped by a bird flying at a constant horizontal velocity, the initial horizontal velocity of the coconut is the velocity of the bird in the horizontal direction.

When the bird drops the object, the object will fall with a vertical velocity that is accelerated by g. The object will fall at a distance equal to the horizontal distance traveled by the bird.

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As wave energy concentrates at headlands and tends to disperse in coves and bays through a process known as wave refraction, wave activity helps to straighten a coastline.

A disruption or fluctuation that causes energy to be transferred gradually from one place to another in a medium. It might be in the form of an elastic deformation or a change in pressure, electrical or magnetic intensity, electric potential, or temperature.

Waves are the organized movement of disturbance from one location to another. There are two types of waves: mechanical and non-mechanical. Like sound waves, mechanical waves need a medium to travel.

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Transient-flow are processes that involve changes within a control volume with time.

Explain  transient flow and its effects?

Unsteady flow is a flow in which velocity and pressure vary with time. A transient flow condition is when a change occurs in the fluid system, such as starting or stopping a pump, opening or closing a valve, or changing the tank level. Otherwise, the system is in steady state. In many cases, transient flow conditions exist as oscillating pressure and velocity waves for some time after the original event that caused them.

Transient flow is commonly referred to as surge or water hammer, and the terms are often interchanged. Strictly speaking, however, surge is when the fluid's mass vibration is the dominant force and the fluid's compressibility is not important. For example, two connected reservoirs vibrate up and down. Water hammer on the other hand is where the compressibility of the fluid has the dominant effect such as the sudden closure of a valve. Transient flow can result in significant transient pressures that may exceed the design limit of the pipes and fittings. Or it may be important to maintain a steady flow for example in the process industry. Therefore a detailed understanding of transient flow can be very important.

Thus, Transient-flow are processes that involve changes within a control volume with time.

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Similar to a head-on shot with the cue ball on a pool table, the projectile will come to rest and the target will move off with an equal velocity for a head-on impact with a stationary object of equal mass.

A collision is considered elastic if it does not result in a net loss of kinetic energy for the system. Momentum and kinetic energy are both conserved in elastic collisions.

Elastic collisions occur when there is no net loss of kinetic energy in the system as a result of the collision. Accidental crashes. Inelastic collisions are the kind of collisions when there is a loss of kinetic energy.

Elastic collisions preserve both kinetic and momentum energy. The total kinetic energy of the system prior to the collision is equal to the total kinetic energy of the system following the collision.

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A 1,800 kg car is parked on a road that has an elevation angle of 7°. Suppose the coefficient of static friction of the kinds of rubber and asphalt involved is 0.65.The force of static friction between the tires and the road is 2149.8 N

To find the force, the given data can be,

m = mass of the car = 1800 kg

g = acceleration due to gravity

  = 9.8 m/s²

Fg = force of gravity on the car

When an object is static these irregularities get more time to be interlocked as compared to when an object is in motion thus the coefficient of static friction is more than the coefficient of sliding friction.

Force of gravity on the car is given as

Fg= mg

Substituting the values,

Fg= (1800) (9.8)

   = 17640 N

Fs= static frictional force acting on the car

From the force diagram of the car, the static frictional force is opposite to the parallel component of force of gravity on the car . hence static frictional force must balance the component of force of gravity parallel to inclined surface.

Fs =  Sin7°

    = (17640) Sin7°

    = 2149.8 N

Hence, the force of static friction between the tires and the road is 2149.8 N.

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A spiral galaxy with a very small central bulge and clumpy spiral arms would be classified as Sc/SBc.

According to the closeness of their spiral, the clumpy of their spiral arms, and the size of their central bulge. These contrasts can be tracked back to the comparitive amounts of gas and dust contained within the galaxies.

A spiral galaxy has a rotating circular disc with spiral arms that curve out from a thick central region. The Milky Way is a spiral galaxy. Four categories which  are used to analyze galaxies are

A galaxy's bulge is a central, spherical structure composes of numerous amounts of stars, gas and dust particles. The dark material surrounding the center of the galaxy is gas and dust that is being thrown into the central region by the bar. The blue regions are the clusters of young stars.

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Answer:

by collecting the sun's heat. Solar thermal power plants use heat from the sun to create steam, which can then be used to make electricity. On a smaller scale, solar panels that harness thermal energy can be used for heating water in homes, other buildings, and swimming pools.

Explanation:

If a spinning star gets larger in diameter its rotation rate is decreases.

As the radius of a spinning star decreases, some of its rotational inertia is lost, which results in a rise in rotational speed owing to the conservation of angular momentum. Because stars gradually slow down over time, much like a top spinning on a table, a star's spin rate depends on its age. The mass of a star also influences its spin; astronomers have discovered that larger, heavier stars have a tendency to spin more quickly than smaller, lighter ones. As the radius of a rotating star decreases, some of its rotational inertia is lost, which results in a rise in rotational speed due to the conservation of angular momentum.

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Two vectors are said to be parallel if and best if the perspective between them is zero tiers. Parallel vectors also are known as collinear vectors. The two parallel unit vectors are 0, 3/√10i, -1/√10 j.

Consider the points p(,,) and q(,,):

P (-4,1,0)

Q (-4,-5,2)

A. find and state your answer in two forms

PQ = (-4+4, -5-1, 2-0)

= (0,-6,2)

B. find the magnitude

 |PQ|= √(0)2+ (-6)2 + (2)2

= √36+4

= √40

= 2√10

C. find two unit vectors

Unit vector parallel to PQ

= < 0, -3/√10, 1/√10 >

= < 0, 3/√10, -1/√10 >

In physics, magnitude is defined as the maximum size and orientation of an object. Size is used as a common factor for vector size and scalar size. By definition, we know that a scalar quantity is one that has only one quantity.

Force Magnitude is a numerical value that expresses the strength of a force. Example: Suppose the force is = 10 N towards the east. "East" is the direction, and "10" is the strength.

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The maximum friction pressure that can act at the block is given with the aid of fax = muS*N, in which muS is the coefficient of static friction.

In physics, pressure is a power that could alternate the movement of an object. A force can motivate an item with mass to alternate its velocity, i.e, to boost up pressure also can be defined intuitively as a push or a pull. A pressure has both significance and path, making it a vector quantity.

Exceptional kinds of pressure are contact forces and non-forces. a few examples of pressure are Nuclear force, gravitational force, Frictional pressure, magnetic pressure, electrostatic force, spring pressure, and so on.

In physics, a force is a push or pull between gadgets. it is called an interplay because if one object acts on another, its action is matched by using a response from the alternative item. This idea is called Newton's 0.33 regulation, wherein movement and reaction are identical and opposite.

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Let us assume θ = 45⁰, so sin(2θ) = 1

R = v² x sin(2θ) / g = v² / g

v² = R x g

a) To find the kinetic energy,

E = 0.5 x mv² = 0.5 x R x g

E(javelin) = 0.5 x 0.8 x 9.8 = 384 J

E(discuss) = 0.5 x 2 x 74 x 9.8 = 725.2 J

E(shot) = 0.5 x 7.2 x 23 x 9.8 = 811.4 J

b) To find the average force exerted,

F = W / Δx = Δk / Δx

F(javelin) = 384 / 2 = 192 N

F(discuss) = 725.2 / 2 = 363 N

F(shot) = 811.4 / 2 = 406 N

c) Yes, air resistance is an important factor.

Therefore, air resistance must affect each of them very differently because the average force the person could throw with, should be same.

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Momentum is conserved for any collision in an isolated system. Before and after the collision, the collection of items in the system had an equal amount of total momentum.

What does physics define as momentum?

Momentum is characterized as the intensity of a body's motion.

As momentum relies on both velocity and the direction of the body's motion, it is quantified by "mass velocity".

What is the connection between collision and momentum?

During collisions between objects, momentum is a relevant concept. The total momentum before a collision between two objects equals the total momentum after the impact (in the absence of external forces). The law of conservation of momentum is this. It holds true in every collision.

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The temperature of the junction point = [tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]

Temperature is a unit used to describe hotness or coldness. It can be stated in terms of any number of arbitrary scales and shows the direction in which heat energy will naturally flow, i.e., from a hotter body to a colder body (one at a lower temperature). Temperature does not equal the energy of a thermodynamic system; for instance, an iceberg has a far larger total thermal energy than a match, despite the fact that a match is burning at a much higher temperature.

According to the given information

[tex]T_{1} - T_{j} = 2 ( T_{j} - T_{0})[/tex]

Q/t = K × A ×([tex]T_{1} - T_{j}[/tex] )/L

However you have the Y shape so that half the heat transfer goes into each part of the Y. So you need a factor of 2 when you add in the Y parts.

(Q/t)bottom = 2x(Q/t)top

[tex]T_{1} - T_{j} = 2 ( T_{j} - T_{0})[/tex]

[tex]T_{1} + 2T_{0} = 3T_{j}[/tex]

[tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]

The temperature of the junction point = [tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]

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A passenger weighing 500N is inside an elevator weighing 24500 N that rises 30 m every minute is 12500 W (12.5 kW).

What is Power?

Power is the amount of work that is done per unit of time. It can be associated with the speed of a change of energy within a system, or the time it takes to perform a job.

There are different types of power,

Mechanical power: is that work performed by an individual or a machine in a certain period of time.

Electric power: which is the result of the multiplication of the potential difference between the ends of a load and the current flowing there.

P= W/t

Where, P- Power,

W- Work

T- Time

The total weight of the passenger + elevator is

Fg = 500+24500

    = 25000

The total work done to rise the elevator + passenger is equal to the product between the total weight and the distance covered during the trip (d = 30 m):

W = Fgd

   = 25000×30

   =7,50,000 J.

The power needed for the trip is equal to the ratio between the work done (W) and the time taken (t):

P = W/t

Since the time taken is t = 1 min = 60 s, the power needed is

P = 750000 / 60

   = 12,500 W

P = 12.5 kW

Thus, Power was calculated as P = 12.5 kW.

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The angular velocity of the pendulum at the bottom is 2.82 rad/s.

The length of the pendulum rod is 1.5ma nd the radius of the pendulum is 0.8m. The mass of the pendulum bob is 14kg and the mass of the rod is 3 kg.

When the pendulum is dropped,

Rotational kinetic energy = Potential energy

Iw²/2 = Mg(L+R) + mgL

Where,

L is the length of the rod and the R is the radius of the bob and I is the moment of inertia of the system while W is the angular speed,

[mL²/3 + MR² + M(L+R)²]W²/2 = Mg(L+R) + mgL

Now, solving the above complex equation,

W = 2.82 rad/s.

So, the angular speed of the pendulum is 2.82 rad/s.

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Complete question- The pendulum consists of a 14 kg uniform disk and a 3 kg uniform slender rod. It is released from rest in the position shown. Suppose that L = 1.5 m. Determine the angular velocity, measured clockwise, when it rotates clockwise 90 degrees.

A 600-kg satellite is in a circular orbit about earth at a height above earth equal to earth’s mean radius. find (a) the satellite’s orbital speed.  

T = 39.8hr

mass of the satellite = 600 Kg

mass of earth = 5.98 x 10²⁴ Kg

height of the satellite

  r = 2 R_e

R_e is radius of earth = 6.38 x 10⁶ m

Assuming orbital velocity of the satellite

       v = 5.59 x 10³ m/s

      time period = 2 pi r/v

      time period = 2pi*2*6.38*10^6/5.59*10^3

       T = 14342.3 s

     T = 14342.3/60*60 Hr

     T = 3.98 Hr

An orbit is a regular, repeating course that one object in area takes around any other one. An item in an orbit is called a satellite tv for pc. A satellite can be herbal, like Earth or the moon. Many planets have moons that orbit them. A satellite tv for pc can also be guy-made, just like the global space Station.

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If acceleration is present, both the system's and the individual objects' accelerations are the same. Usually, a system analysis is done to figure out the system's acceleration.

An individual object analysis is combined with the system analysis. Any one of the two items is isolated and treated as a distinct, independent entity in the individual object analysis. The forces operating on the item individually are recognized and computed using a free-body diagram. It is customary to analyze each object separately in order to calculate the magnitude of any force acting between the two. One of the two methods that is frequently used to evaluate two-body problems is the dual combination of a system analysis and an individual object analysis.

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It picks one of the three edges that meet at each vertex, each of which has an equal chance of being chosen, and crawls along that edge to the vertex at its opposite end is p=182/729 and n is 182.

Let[tex]$V_k$[/tex] crawl exactly [tex]$k$[/tex] meters starting from vertex [tex]$V$[/tex] and ending at vertex A, where [tex]$V\in\{A,B,C,D\}$[/tex] and k is a positive integer. We wish to find [tex]$A_7.$[/tex]

Since the bug must crawl to vertex [tex]$B,C,$ or $D$[/tex]

on the first move, we have

[tex]where $S_k=A_k+B_k+C_k+D_k.$[/tex]

More generally, we get

[tex]\[A_{k+2}=A_k+2S_k. \qquad\qquad (\spadesuit)\]\[/tex]

The requested probability is

[tex]\[p=\frac{A_7}{3^7}=\frac{2(3)+2\left(3^3\right)+2\left(3^5\right)}[/tex]

[tex]{3^7}=\frac{2(1)+2\left(3^2\right)+2\left(3^4\right)}{3^6}=\frac{182}{729},\]from which $n=\boxed{182}.$[/tex]

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A uniform solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal. fast is it moving after it has rolled 2.2 m down the plane =O 2.6 m/s

Definition: This type of uniform is defined as the movement of an item in which the object travels in a direct line, and its velocity stays steady along that line because it covers identical distances in the same intervals of time, irrespective of the period of time.

If the velocity of an object transferring alongside an instant line maintains changing, its movement is referred to as non–uniform. An item shifting alongside an immediate line with a steady speed is stated to be in uniform motion.

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According to the principle of continuity, the velocity of a fluid multiplied by the cross-section through which it flows at one point will equal the product of velocity and cross-section at another point.

The principle of continuity, also known as the continuity equation, is the fluid mechanic's principle. Simply put, what flows into a defined volume over a specified period of time minus what flows out of that volume over that specified period of time must accumulate in that volume. The substance in that volume is depleted if the accumulation's sign is negative.

This is so that our eyes, once they start to follow anything, will keep moving in that direction until they come across another thing or object. A line with an arrow at the end of it, for instance, is a great illustration of the continuity concept.

Note that three conditions must be met for a function to be continuous at a point: At that time, the limit must exist.

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It will be a more stable moving platform than the empty barrel when the barrel is full because it has significantly more moment of inertia and resistance to variations in rotation.

The moment of inertia of a rigid body—also referred to as the mass moment of inertia, angular mass, second moment of mass, or—most precisely—rotational inertia—determines the torque required for a desired angular acceleration about a rotational axis, much like mass determines the force required for a desired acceleration. The term "rotation" refers to an object moving in a circle around its centre. A rotation around the centre point is conceivable for various shapes. A rotation in mathematics corresponds to a map.

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The Capacitive reactance of the circuit is 221 ohms. The capacitor draws a charging current from the supply and charges up to a value equal to the applied voltage.

From the question, we have

Capacitors connected in parallel

Cequ = 4 + 4 + 4 = 12 muF

Xc = 1 / 2 pi f C = 1 / (2 pi * 60 * 12 * 10-6)

Capacitive reactance = 221 ohms

Capacitive reactance :

When a DC voltage is supplied to a capacitor, as we saw in the RC Network tutorial, the capacitor draws a charging current from the supply and charges up to a value equal to the applied voltage. The charge stored in the capacitor also decreases and discharges as the supply voltage is lowered. The internal impedance of the capacitor limits the current that can travel through it when it charges or discharges. This internal impedance is frequently referred to as capacitive reactance and is represented by the Ohms symbol XC.

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if the moon rises around 3 a.m., its phase must be  Waning crescent .

The moon will look as a half moon, or third quarter moon, when the light level drops. The shadow cast by a third quarter moon will increase until it resembles a crescent form, which is known as a fading crescent.

A fading crescent moon has an illuminated area of less than 50% but is still growing.

You'll notice that the energy is waning as the moon begins to move back into the new phase, allowing you to calm down and devote more attention to your inner thoughts.

When the moon is transitioning from a full moon to a new moon, it is said to be in its declining phase. The declining moon, keep in mind sympathetic magick, is wonderful for banishing work, or cutting ,

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Answer: 0.025 J or 25 mJ

Explanation:

Elastic potential energy = 1/2 * k * x^2

Where k is the spring constant (N/m) and x is the springs stretch from the point of equilibrium.

=1/2*125N/m * (0.02m)^2 = 0.025 J or 25mJ

The absolute maximum shear stress in the shaft are Tmax = 129.4 MPa  for the shaft that has an outer diameter of 100 mm and an inner diameter of 80 mm.

The shaft constitutes an important aspect of the hole shaft motor, that's utilized in electrically powered vehicles, along with trains. Hollow shafts also are appropriate for the development of jigs and furnishings in addition to computerized machines.

Here we have diameter of 80 mm and outer diameter of 100 mm .

[tex]T = π / 16 × T × (D^4 -d^4)/D\\15×1000 = π/16 × T × 0.1^4 - 0.08^4 /0.1\\Tmax = 129.4 × 10 ^6 N/m^2\\Tmax = 129.4 MPa.[/tex]

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