An aluminum rod is designed to break when it is under a tension of 600 N. One end of the rod is connected to a motor and a 12-kg spherical object is attached to the other end. When the motor is turned on, the object moves in a horizontal circle with a radius of 5.78 m. If the speed of the motor is continuously increased, at what speed will the rod break

Answer:

F = 1.6 N

Explanation:

Newton's Second Law of Motion states that whenever an unbalanced force is applied on a body. It produces an acceleration in the body, in its own direction. The magnitude of the force is given by the following formula:

F = ma

where,

F = Force Required to Move the Object Upward = ?

m = mass of object

a = upward acceleration = 2 m/s²

but, we know that weight of object is given as:

Weight = mg

8 N = m(9.8 m/s²)

m = 0.8 kg

using values in the equation:

F = (0.8 kg)(2 m/s²)

F = 1.6 N

Answer: -50N

Explanation:

Newton's 3rd law says that for every force applied, there is an opposite force with equal magnitude. The person pushing on the tree will experience a force of -50N

Answer:

B. period of the sound wave

Therefore, the magnitude of vector 4A is 40.

The positive x-axis of the rectangular coordinate system is the direction of the unit vector I which has a magnitude of 1. The positive y-axis of the rectangular coordinate system is the direction of the unit vector j, which has a magnitude of 1.

The magnitude (or length) of a vector can be calculated using the formula:

\(|A| = \sqrt(Ax^2 + Ay^2)\)

where Ax and Ay are the x and y components of the vector A.

Given that vector A = 6i - 8j, we can calculate its magnitude as:

\(|A| = sqrt((6)^2 + (-8)^2)\\A = \sqrt(36 + 64)\\A = \sqrt(100)\\A = 10\)

Therefore, the magnitude of vector A is 10.

To find the magnitude of 4A, we need to multiply the magnitude of A by 4:

|4A| = 4|A|

|4A| = 4(10)

|4A| = 40

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Answer:\(60^{\circ}\)

Explanation:

Given

\(\mid\Vec{A}\mid=1\)

\(\mid\Vec{B}\mid=2\)

And \(A\cdot B=1\)

We know \(\vec{A}\cdot \vec{B}=\mid\Vec{A}\mid\mid\Vec{B}\mid\cos \theta\)

Where \(\theta\) is the angle between them

Substituting the values

\(1=1\times 2\cos \theta\)

\(\cos \theta =\dfrac{1}{2}\)

\(\theta =60^{\circ}\)

Thus the angle between \(A\) and \(B\) is  \(60^{\circ}\)

The electroscope will remain charged and continue to show the presence of an electric charge if the ground is withdrawn from the knob before the charging rod is removed.

An early scientific tool used to find electrical charge on a body is called an electroscope. The movement of a test object caused by the Coulomb electrostatic force is used to detect charge. Voltage and charge on an object are inversely correlated.

There are three traditional electroscope types: the needle electroscope, the gold-leaf electroscope, and the pith-ball electroscope (third).

electroscopes are utilized to determine whether a body has an electric charge. The movement of a test object caused by the Coulomb electrostatic force is used to detect charge. Voltage and charge on an object are inversely correlated.

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The mass of the the object, given that the same force acted upon it to accelerate at 2 m/s² is 34 Kg

First, we shall determine the force. This can be obtained as follow:

Force (F) = mass (m) × acceleration (a)

Force = 4 × 17

Force = 68 N

Finally, we shall determine the mass of the object that will accelerate at 2 m/s² when the force of 68 N is applied to it. Details below:

Force = mass × acceleration

68 = mass × 2

Divide both sides by 2

Mass = 68 / 2

Mass = 34 Kg

Thus, from the above calculation, we can conclude that the mass is 34 Kg

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Explanation:

The moment of A about B is given by the formula

\(M=Fd\)

where M is the moment, F is the force acting perpandicular to the axis of rotation about B by A, and d is the horizontal distance of A from B along the axis of rotation.

Now

\(F=230 (N)\)

(a) At X,

\(M=(230)(4/2)=460 (Nm)\)

(b) At 0.5m from X,

\(M=(230)(2-0.5)=345 (Nm)\)

(c) At Y,

\(M=-(230)(2)=-460 (Nm)\)

where negative sign indicates clockwise rotation of the child about Z.

(d) At Z,

\(M=(230)(0)=0 (Nm)\)

The weight of the rover vehicle on Earth, given that it weighs 37 N on Mars is 99.5 N

We'll begin by obtaining the mass of the rover vehicle. This is shown below:

Weight (W) = mass (m) × Acceleration due to gravity (g)

W = mg

Divide both sides by g

m = W /g

m = 37 / 3.72

m = 9.95 Kg

Now, we shall determin the weight of the rover vehicle on Earth. Details below:

Weight (W) = mass (m) × Acceleration due to gravity (g)

Weight (W) = 9.95 × 10

Weight = 99.5 N

Thus, we can conclude that the weight on Erath is 99.5 N

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The difference physical properties of aluminum  ball and aluminum box is: ball is sphere and box is cubic in shape.

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The mass spectrometer separates ions of different masses by utilizing the relationship between the strength of the magnetic field, the accelerating voltage, the charge-to-mass ratio of the ions, and the resulting radius of the circular path

From the formula in the question;

B is a symbol for the magnetic field's intensity as it is applied to the mass spectrometer.

The accelerating voltage used to move the ions is called Vaccelm.

The charge of the ion, specifically its charge-to-mass ratio (q/m), is represented by the letter q.

The mass spectrometer may selectively alter the radius of the circular route for various ions by varying the magnetic field's intensity (B). This makes it possible to spatially segregate ions with various masses based on their various radii. The ions' locations and masses can then be measured using detectors placed along the journey.

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On one cookie containing 50 calories, you could potentially go approximately 298 meters

Given that one food calorie is equivalent to 4184 joules, we can calculate the total energy in joules contained in the 50 calorie cookie:

50 food calories * 4184 J/calorie = 209,200 joules

Assuming an average efficiency of around 25% (meaning 25% of the energy is effectively used for movement), and a body weight of 70 kilograms, we can use a rough estimation that it takes about 1 joule of energy to move 0.4 meters (based on the energy cost of walking).

Distance = (Energy obtained from the cookie * Efficiency) / (Energy cost per meter * Body weight)

Distance = (209,200 J * 0.25) / (1 J/m * 0.4 m/kg * 70 kg)

Distance ≈ 298 meters

Therefore, on one cookie containing 50 calories, you could potentially go approximately 298 meters

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Answer: The Boat will rise

Explanation: Because high amplitude means high in heights.

Answer: a

Explanation:

Given:

The speed of the motorcycle is,

The distance is,

The time taken by the motorcycle to travel this distance is,

Substituting the values we get,

Hence, the required time is 2.0 h.

The three missing categories of expenditure that contribute to a country's GDP are

Government spending This includes all expenditures made by the government on goods and services, such as salaries of government employees, public infrastructure, defense spending, and social welfare programs. Government spending is represented by the letter "G" in the formula for GDP GDP = C + I + G + (X-M).

Exports This refers to the value of all goods and services that a country produces and sells to other countries. Exports are represented by the letter "X" in the formula for GDP GDP = C + I + G + (X-M).

Imports This refers to the value of all goods and services that a country purchases from other countries. Imports are subtracted from the formula for GDP since they represent a leakage from the economy. Imports are represented by the letter "M" in the formula for GDP  GDP = C + I + G + (X-M).

Here is a brief description of the categories of expenditure that have already been filled in

Personal consumption expenditures (C) This category includes all spending by households on goods and services, such as food, housing, healthcare, and education.

Gross private domestic investment (I)  This category includes all investment spending by businesses, such as purchases of machinery, equipment, and structures, as well as changes in inventories.

GDP formula The formula for GDP is the sum of all final goods and services produced within a country's borders in a given time period. It can be expressed as  GDP = C + I + G + (X-M).

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Answer:

the distance x increases as the student increase the mass of the cannon.

Explanation:

a) From the question ; we get to understand that for each launch, the students use a different mass which is launch at  speed v relative to the ground.

This changes in the mass used brought about a change in the momentum at the same speed v ; perhaps an increase in momentum. However; since the conservation of the momentum is considered at each launching.

The momentum of the marble = momentum of the cannon

But since the momentum of the cannon increase ; therefore the same equivalent changes takes place in its kinetic energy . Therefore , the kinetic energy will increase and the distance will also increase in the bid to quench the amount of energy generated. Thus, the distance x increases as the student increase the mass of the cannon.

b)We all know that  conservation of the momentum will definitely  takes place after launching of the cannon.

Let assume that \(\rho\) is the momentum of the cannon with mass \(M_C\)

The kinetic energy of the canon will be:

\(\frac{\rho ^2 }{2 M_C}\)

Also the frictional force acting on the cannon is :

\(f = \mu mg\)

If the cannon move at an  additional distance x; the frictional force acting at this area quench the amount of the energy generated and consume the kinetic energy of the cannon;

So;

\(fx = K.E\)

\(fx = \frac{\rho ^2 }{2 M_C}\)

\(\mu mg x = \frac{\rho ^2 }{2 M_C}\)

\(x = \frac{\rho ^2 }{2 \mu mg M_C}\)

\(x = \frac{m_m^2 V^2 }{2 \mu mg M_C}\)

Thus; it is consistent with the answer in (a) as increase in the mass of the marble will bring about an increase in distance x

The increase in the mass of the marble increase the distance of the cannon.

Momentum:

Momentum of an object is equal to the product of the mass and the velocity of the object.

The kinetic energy of the cannon

\(K_C = \dfrac {\rho^2}{2 M_C}\)

Where,

\(\bold{\rho}\) - momentum of the cannon

Mc -  mass

The frictional force on cannon

\(\bold{F_f = \mu mg}\)

Cannon move a distance x,

Hence,

\(\bold {F_f \times x = K_C}\\\\\bold {\mu m g \times x = \dfrac {\rho^2}{2 M_C }}\\\\\bold {x = \dfrac {\rho^2}{2\mu m g M_C }} }\\\\\bold {x = \dfrac {m^2 V^2}{2\mu m g M_C } }\)

Therefore, The increase in the mass of the marble increase the distance of the cannon.

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Explanation:

a boy walks at 2m/s for 30sec and run at 5m/s for 20sec. what is his average speed

Answer:0.2 m/s^2

Explanation:

mass=18.15kg

Force=3.63N

Acceleration=force ➗ mass

Acceleration=3.63 ➗ 18.15

Acceleration=0.2 m/s^2

A girl pushes a wagon of mass 18.15 kg with a force of 3.63 N, so the acceleration of the wagon will be 0.2 m/s².

In mechanics, acceleration is the measure of how rapidly an object's velocity changes over time. Accelerations as a vector quantity. An object's acceleration depends on the direction of the net force exerted on it.

A vector quantity, acceleration, is something that has both a magnitude and a direction. As a vector quantity, velocity is also. The ratio of the velocity vector change over a time interval to that interval is the definition of acceleration.

Mass, m =18.15 kg

Force, f = 3.63 N

Force = m × a

a= f / m

a =3.63 / 18.15

a = 0.2 m/s²

Hence, the acceleration of the wagon will be 0.2 m/s².

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The driving force (df) of +15 mV propels K+ ions in an inwards directed manner.

noun Someone or anything with the ability to influence events: a motivating factor behind/for/in sth. One key factor influencing consumer spending has been the growth of stock market riches.

A stroller is put into motion when it is pulled. As long as the luggage is being pulled, the action continues. This indicates that the user's applied pull force is what propels the luggage. The force needed to draw or move the luggage is hence referred to as the driving force.

At equilibrium, the bottom of the cell ought to be negative in relation to the outside because K+ ions have an electromotive force of Ek = -78 mV.

Since Vm = -93 mV

df = Ek - Vm

= -78 mV - (-93 mV)

= +15 mV.

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Answer: 1

Explanation:

Given

Tension is the string \(T=44\ N\)

mass of object \(m=4\ kg\)

Tension is greater than the weight of the object i.e. elevator is moving upward

we can write

\(\Rightarrow T-mg=ma\\\Rightarrow T=m(g+a)\\\Rightarrow 44=4(10+a)\\\Rightarrow 11=10+a\\\Rightarrow a=1\ m/s^2\)

Based on the image provided and the location of deposition and erosion, it seems that the longshore current is moving towards the right.

Based on the image provided, it appears that the longshore current is traveling towards the right. This can be determined by looking at where deposition and erosion are occurring. Deposition is happening on the right side of the image, where sand is building up and forming a beach. Erosion, on the other hand, is happening on the left side of the image, where the waves are breaking against the cliff face and wearing it away. Longshore currents are generated by waves hitting the shore at an angle, causing the water to move parallel to the shore. In this case, the waves are coming in from the top left of the image and hitting the shore at an angle, which creates a longshore current that moves towards the right. As the water moves along the shore, it picks up sand and sediment and carries it with it. This sand is then deposited on the right side of the image, where the water slows down and loses energy. It's important to note that longshore currents can change direction depending on the direction of the incoming waves and the shape of the shoreline. But based on the image provided and the location of deposition and erosion, it seems that the longshore current is moving towards the right.

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The approximate velocity of the stuntman, once he has left the cannon, is 11 m/s.

We can use the conservation of energy, where the potential energy stored in the compressed spring is converted into the kinetic energy of the stuntman as he is launched out of the cannon.

The potential energy stored in the spring is given by:

PE = (1/2)kx²

where k is the spring constant and x is the distance the spring is compressed.

PE = (1/2)(266 N/m)(5 m)² = 3325 J

This potential energy is then converted into kinetic energy:

KE = (1/2)mv²

where m is the mass of the stuntman and v is his velocity.

3325 J = (1/2)(55 kg)v²

v² = (2*3325 J) / 55 kg

v²  = 121 m²/s²

v = √(121 m²/s²) = 11 m/s

Therefore, the approximate velocity of the stuntman, once he has left the cannon, is 11 m/s.

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The mass of a substance is not directly related to latent heat. Instead, latent heat is a parameter that describes the amount of energy required or released during a phase shift of a substance.

Latent heat can be thought of as hidden energy that is supplied or extracted to change the state of a substance without changing its temperature or pressure.

Latent heat is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process—typically a first-order phase transition.

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Answer:

4.5 OHMS

Explanation:

This is the series circuit of arrangement so we add the resistance

1 + 1.5 + 2 =4.5 OHMS

We can't see the third point of the triangle. We're assuming there's nothing else connected up there, and you want the equivalent resistance between points A and B.

The 1 and the 2 are in series, so they form a single resistor of 3 ohms.

That's in parallel with the 1.5 ohmer, for an equivalent resistance between A and B of ==> 1 ohm .

Answer:

Radius of curvature of the mirror = 250 cm

Explanation:

Given:

Object distance from mirror = 250 cm (u=-250)

Object distance appears in mirror = 250 cm (v=-250)

Find:

Radius of curvature of the mirror

Computation:

Using mirror formula

1/f = 1/v + 1/u

1/f = 1/(-250) + 1/(-250)

f = (-250/2)

f = -125 cm or 125 cm

Radius of curvature of the mirror = 2(f)

Radius of curvature of the mirror = 2(125)

Radius of curvature of the mirror = 250 cm

Answer:

Explanation:

The statue, being initially at rest, will move off at twice the velocity of the center of mass of the Skate-Statue system

The CM velocity is 1.63/2 = 0.815 m/s

so the Skates initial velocity can be found

(117 + 879)(0.815) = 879(0) + 117u

u = 6.93794...

|u| = 6.94 m/s

for elastic collisions, the relative velocity of approach will equal the relative velocity of departure.

Approach velocity 6.94 m/s

Skate's departure velocity 1.63 - 6.94 = - 5.31 m/s

|v| = 5.31 m/s

Answer:

To determine the height to which the ball rises before it reaches its peak, we need to know the initial velocity of the ball and the acceleration due to gravity. Let's assume the initial velocity of the ball is v and the acceleration due to gravity is g.

The time it takes for the ball to reach its peak is one-half the total hang-time, or 1/2 * 6.25 s = 3.125 s.

The height to which the ball rises can be calculated using the formula:

height = v * t - (1/2) * g * t^2

Substituting in the values we know, we get:

height = v * 3.125 s - (1/2) * g * (3.125 s)^2

To solve for the height, we need to know the value of v and g. Without more information, it is not possible to determine the height to which the ball rises before it reaches its peak.

Explanation:

Answer:

Approximately \(47.9\; {\rm m}\) (assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\) and that air resistance on the baseball is negligible.)

Explanation:

If the air resistance on the baseball is negligible, the baseball will reach maximum height at exactly \((1/2)\) the time it is in the air. In this example, that will be \(t = (6.25\; {\rm s}) / (2) = 3.125\; {\rm s}\).

When the baseball is at maximum height, the velocity of the baseball will be \(0\). Let \(v_{f}\) denote the velocity of the baseball after a period of \(t\). After \(t = 3.125\; {\rm s}\), the baseball would reach maximum height with a velocity of \(v_{f} = 0\; {\rm m\cdot s^{-1}}\).

Since air resistance is negligible, the acceleration on the baseball will be constantly \(a = (-g) = (-9.81\; {\rm m\cdot s^{-2}})\).

Let \(v_{i}\) denote the initial velocity of this baseball. The SUVAT equation \(v_{f} = v_{i} + a\, t\) relates these quantities. Rearrange this equation and solve for initial velocity \(v_{i}\):

\(\begin{aligned}v_{i} &= v_{f} - a\, t \\ &= (0\; {\rm m\cdot s^{-1}}) - (-9.81\; {\rm m\cdot s^{-2}})\, (3.125\; {\rm s}) \\ &\approx 30.656\; {\rm m\cdot s^{-1}}\end{aligned}\).

The displacement of an object is the change in the position. Let \(x\) denote the displacement of the baseball when its velocity changed from \(v_{i} = 0\; {\rm m\cdot s^{-1}}\) (at starting point) to \(v_{t} \approx 30.656\; {\rm m\cdot s^{-1}}\) (at max height) in \(t = 3.125\; {\rm s}\). Apply the equation \(x = (1/2)\, (v_{i} + v_{t}) \, t\) to find the displacement of this baseball:

\(\begin{aligned}x &= \frac{1}{2}\, (v_{i} + v_{t})\, t \\ &\approx \frac{1}{2}\, (0\; {\rm m\cdot s^{-1}} + 30.565\; {\rm m\cdot s^{-1}})\, (3.125\; {\rm s}) \\ &\approx 47.9\; {\rm m}\end{aligned}\).

In other words, the position of the baseball changed by approximately \(47.9\; {\rm m}\) from the starting point to the position where the baseball reached maximum height. Hence, the maximum height of this baseball would be approximately \(47.9\; {\rm m}\!\).

Given:

The mass of water is: m = 200 g

To find:

The heat necessary to vaporize 200 g of water at 100°C to form steam at 100°C.

Explanation:

The heat Q, mass m, and the latent heat L are related as:

The latent heat of the water to convert it from 100°C to form steam at 100°C is 2260 J/g. Thus,

L = 2260 J/g

Substituting the values in the above equation, we get:

Final answer:

Thus, 452 kJ of heat will be required to vaporize 200 g of water.