Use the equation GPE = mx 9.8 m/sxh to calculate the gravitational potential of a 10-kg
sack of groceries on a shelf 1 m above the floor?

Answer: 14.41*10^2 m/s

Explanation:

let, V be the escape velocity of the moon.

M be the mass of the earth.

r be the distance between the moon and the earth.

G be the universal gravitational constant.

And G = 6.67428*10^-11 m^3kg^-1 s^-2

here, given in the question that

The earth has a mass of 5.98*10^24 kg.

so, M = 5.98*10^24 kg.

And the distance from the earth to the moon is 3.84*10^8 m.

so, r = 3.84*10^8 m.

now, we know,

V = √2GM/r

V = √(2 * 6.67428*10^-11* 5.98 * 10^24 )/ 3.84*10^8

V = √79.82*10^13/3.84*10^8

V = √20.78*10^5

V = 14.41*10^2 m/s

Option D) 200 kg object at 2 m/s has the highest momentum.

What is momentum?

Momentum formula,                P = mv

p = momentum

m = mass \ velocity

The newton-second is a unit of measurement for momentum in the International System of Units (SI), and the kilogram metre per second (kg m/s) is its SI counterpart.

A) 50 kg object at 5 m/s

m = 50 kg

v = 5 m/s

Momentum, p = m x v

                       = 50 x 5

                       = 250 kg m/s

B) 100 kg object at 10 m/s

m = 100 kg

v = 10 m/s

Momentum, p = m x v

                       = 100 x 10

                       = 1000 kg m/s

C) 150 g object at 5 m/s

m = 150 g

    = 0.15 kg

v = 5 m/s

Momentum, p = m x v

                       = 0.15 x 5

                       = 0.75 kg m/s

D) 200 kg object at 2 m/s

m = 200 kg

v = 2 m/s

Momentum, p = m x v

                       = 200 x 2

                       = 400 kg m/s

Hence, Option B has the highest momentum.

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The acceleration of the SUV during crash as the crumple zone is collapsing is 0.0063 m/s².

Acceleration is the ratio of the force on a body to the mass of the body.

To calculate the acceleration of the  SUV, we use the formula below.

Formula:

Where:

Make a the susbject of the equation

From the question,

Given:

Substitute these values into equation 2

Hence, the acceleration of the SUV is 0.0063 m/s².

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The exact centripetal acceleration experienced by passenger  ∝ₙ and  driver ∝ⁿ is 80m/s²  & 66.67m/s² respectively.

Mathematically , Centripetal acceleration ∝= v²/r

In the given question velocity will be same for passengers and driver because of common frame.

But the radius is different since distance from each points of frame to the Centre of road will vary. so their centripetal acceleration will differ.

∝= v²/r using this we can find out the exact centripetal acceleration experienced by passenger  ∝ₙ and  driver ∝ⁿ

∝ₙ= 20²/5= 80m/s²

∝ⁿ=20²/6= 66.67m/s²

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When a car is at rest, it begins to accelerate at a pace of 8 Sec at 5 m/s It then continues moving at same speed for another lap after coming to rest in 4 seconds.

The maximum velocity attained by the car, the velocity would be 8m/s.

Initial velocity, u= 0m/s

Distance travelled in 8 sec would be

s= u ×t+ 1/2at²

= 1/2 ×5 ×(8)²

= 160m

Velocity after t= 4sec

= 2×4= 8m/s

Average velocity is defined as the change in position or displacement (x) divided by the time intervals (t) during which the change occurs. Based on the direction of the displacement, the average velocity might either be positive or negative. The unit of measure for average velocity in the SI is meters per second (m/s or ms-1).

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The correction options indicating a decomposition reaction are:

This a reaction in which a compound breaks down into smaller elements or compound by the application of heat. Example is given below:

AB₂ -> A + B₂

We can see that AB₂ decomposed to produce A and B₂

With the above information in mind, we can easily determine which reaction is decomposition reaction from the given options.

The options from the question are:

Observing the given options with the knowledge of decomposition reaction, we can conclude that the correct options are:

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The Maximum tangential speed the ball can have would be = 5.3m/s.

A tangential speed is defined as the speed of an object that has an angular velocity with respect to an instantaneous velocity.

The formula used to calculate the maximum tension;

T = mv²/r

Where T = Maximum tension = 132.3N

M = mass= 4kg

r = radius = 0.86m

V= tangential speed = x

Make v the subject of formula;

V = √Tr/m

V = √ 132.3 × 0.86/4

V = √113.778/4

V= √28.4445

V = 5.3 m/s.

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Complete question:

An athlete swings a 4.00 kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.860 m at an angular speed of 0.660 rev/s. If the maximum tension the rope can withstand before breaking is 132.3 N, what is the maximum tangential speed the ball can have?

The work done by a 20-newton force applied at an angle of 45.0° is 565.69 J.

Calculation:-

Force = 20 N

distance = 40 meters

angle = cos 45°

Work done = F.d cosθ

                 = 20×40 × 1/√2

                 = 800 / √2

                =  565.69 J

Force is a push or pulls upon an item because of the object's interaction with some other object. pressure is a power that can exchange the motion of an object. A force can reason an object with mass to alternate its speed, i.e., to boost up. pressure also can be described intuitively as a push or a pull. A force has each significance and course, making it a vector amount.

The phrase 'Force' has a unique meaning. At this degree, it is absolutely appropriate to describe a force as a push or a pull. A force is not something that an object consists of or 'has in it. A force is exerted on one object through another. The concept of a force isn't always restricted to living matters or non-living matters.

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Answer:

the gravitational attraction of each ball, so technically the others too lol

The speed ball when it reaches the bottom of the homemade ramp is 1.68 m/s.

The speed of the ball at the bottom of the ramp is determined by applying the principle of conservation of energy as follows;

total kinetic energy = total potential energy

rotational kinetic energy + translational kinetic energy = total potential energy

¹/₂Iω²  +  ¹/₂mv²   =  mgh

where;

¹/₂I(v/r)²  +  ¹/₂mv²   =  mgh

¹/₂Iv²/r²  +  ¹/₂mv²   =  mgh

I = ¹/₂mr²

¹/₂(¹/₂mr²)v²/r²  +  ¹/₂mv²   =  mgh

¹/₄mv² + ¹/₂mv² = mgh

¹/₄v² + ¹/₂v² = gh

v² + 2v² = 4gh

3v² = 4gh

v² = 4gh/3

v = √(4gh/3)

where;

v = √(4 x 9.8 x 0.215/3)

v = 1.68 m/s

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The maximum height reached by the cylinder at the given initial velocity is 0.2 m.

The maximum height travelled by the cylinder is calculated by applying the following kinematic equation as shown below.

v² = u² - 2gh

where;

At maximum height, the final velocity of the cylinder = 0

v² = u² - 2gh

0 = u² - 2gh

2gh = u²

h = u²/2g

h = (2²) / (2 x 9.8)

h = 0.2 m

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The simple conclusion I can make from the task given above is that all the objects in the universe possess constant acceleration under the influence of a free fall is actually due to gravity.

It has been practically proven that all objects or bodies; regardless of their masses have the same acceleration as long as they are under a free fall as a result of the Earth's gravitational force.

So therefore, it can now be deduced with understanding that all free falling objects have the same acceleration due to gravity.

Complete question:

What conclusion can you make on acceleration and free falling objects grade?

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Potential energy is lost as the skier starts to descend the hill, while kinetic energy, or the energy of motion, is gained. The skier increases her speed as she decreases height (and thereby potential energy) (and thus gains kinetic energy).

Mass and speed are the two main determinants of kinetic energy. Because an object's motion is influenced by its velocity as well as its mass, though mass is the more crucial factor.

You are working against inertia when you accelerate an object. The change in the object's kinetic energy is equal to that work. Starting with the common equation for work against inertia, it is possible to prove that the relationship exists.

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(a) To generate a 1 T magnetic field inside the solenoid, we need 7.96 x 10⁶ turns.

(b) If we had an iron core inside the solenoid with relative permeability of 64,000, the number of  turns would be 124 turns.

The number of turns of the solenoid is determined by applying the following equation for magnetic field strength at the center of the solenoid.

B = μnI

where;

n = B/ μI

N/L = B/μI

N = (BL)/μI

where;

n = (1 x 0.01) / (4π x 10⁻⁷  x 0.001)

n = 7.96 x 10⁶ turns

If we had an iron core inside the solenoid with relative permeability of 64,000, the number of turns would be calculated as;

N = (BL)/(μI x μr)

where;

N = (1 x 0.01) / (4π x 10⁻⁷  x 0.001 x 64,000)

N = 124 turns

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The energy needed by a stove to transfer heat completely to 1 g of liquid water fro 1 °C to 25 °C is 100.37 J.

Energy is the ability or the capacity to do work.

To calculate the  amount of energy, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The energy required is 100.37 J.

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Taking into account the definition of calorimetry, the energy that a stove must transfer to completely heat 1 g of liquid water from 1 °C to 25 °C is 100.416 J.

Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.

When heat added or removed from a substance causes a temperature change in it without affecting its molecular structure, it is called sensible heat.

So, the expression that allows to calculate heat exchanges is:

Q = c× m× ΔT

where:

In this case, you know:

Replacing in the definition of calorimetry:

Q = 4.184 J/gC× 1 g× 24 C

Solving:

Q= 100.416 J

Finally, the energy needed is 100.416 J.

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The net force on the electron is F = 1X10-13 N.

The mass of the electron is m = 1X10-30 kg.

The distance covered by an electron is S = 10 cm.

The acceleration of an electron can be calculated as:

F = ma

a = F/m

Substitute the values in the above expression.

[tex]a = (\frac{1 * 10^{-13}N }{1* 10^{-30kg} } ) \\[/tex]

a = [tex]1*[/tex][tex]10^{-17} m/s^{2}[/tex]

Thus. the acceleration of the electron is. [tex]a = 1*10^{-17} m/s^{2}[/tex]

The expression of time taken by the electron is given by,

S = ut + [tex]\frac{1}{2} at^{2}[/tex]

Here, u is the electron's initial velocity, whose value is zero because the electron is initially at rest.

Substitute the values in the above expression.

(10cm x 1m/100cm) = 0 x t + 1/2 x (1 x [tex]10^{17}[/tex] m/s²) x t²

(0.1m) x 2 = (1 x [tex]10^{17}[/tex] m/s²)x t²

[tex]t = \sqrt{\frac{0.2m}{(1*10^{17} m/s^{2} )} }[/tex]

t = 1.414 x [tex]10^{-9}[/tex]s

Thus, the time taken by the electrons to be accelerated from rest is t = 1.414 x [tex]10^{-9}[/tex]s

Electrons are accelerated from rest by a potential difference of V volts. The speed of individual electrons in metal wires is typically millions of kilometers per hour. In contrast, drift velocities are typically only a few meters per hour, while signal velocities are 100 million to 1 billion kilometers per hour.

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The approximate centripetal force on an astronaut of mass 80Kg if the centrifuge rotates once every 2s is 3.94 KN

ac = v² / r

v = 2 π r / T

ac = Centripetal acceleration

v = Linear / Tangential velocity

T = Time period

r = Radius

r = 5 m

T = 2 s

v = 2 * 3.14 * 5 / 2

v = 15.7 m / s

ac = 15.7 * 15.7 / 5

ac = 49.298 m / s²

Fc = m ac

m = Mass

m = 80 kg

Fc = 80 * 49.298

Fc = 3943.8 N

Fc = 3.94 KN

Therefore, the approximate centripetal force on the astronaut is 3.94 KN

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It is important for the measurements that the track is level for rolling motion in physics because the rolling objects only move on the tract that is leveled correctly.

The rolling motion is a fusion of translational motion and rotational motion. For a body, the motion of the center of mass is the adaptation motion of the body. During the rolling motion of a body, the exterior contact gets disfigured a little temporarily. A combination of translational and rotational motions happens during the rolling motion of an object. To define rolling motion, we must recognize the forces like angular momentum and torque. It is a merger of two types of motion i.e. translational and rotational motion. The translational motion of a body is the movement of the whole body from one place to another.

So we can conclude that Rolling motion is that usual combination of encircling and translational motion that we see everywhere and every day.

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Explanation:

There two types of transformers which are mainly stepup and step down transformers

the former is used for increasing voltage while the latter is used for reducing voltage

The distance of this star in kilometers is equal to 5.64 × 10¹⁸ kilometers. Also, the distance of this star in light-years is equal to 626.67 light-years.

Mathematically, the inverse square law for light can be used for calculating its luminosity at a distance by using this mathematical expression:

d = √(L/4πF)

Where:

Substituting the given parameters into the formula, we have;

Distance in kilometers, d = √(6.0 × 10²⁶/4 × 3.142 × 1.5 × 10⁻¹²)

Distance in kilometers, d = √(6.0 × 10²⁶/1.885 × 10⁻¹¹)

Distance in kilometers, d = √3.183 × 10³⁷

Distance in kilometers, d = 5.64 × 10¹⁸ kilometers.

For the distance in light-years, we would divide the distance in kilometers by 9.0 × 10⁻¹⁵:

Distance in light-years = 5.64 × 10¹⁸/9.0 × 10¹⁵

Distance in light-years = 626.67 light-years.

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Fgrav = 4.90 N; Fnorm = 4.90 N; Fnet = 1.73 N, then the acceleration of the cart is (a) = 3.46 m/s/s,

Acceleration is defined as a vector quantity, the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. It can be either positive, negative, or zero depending upon the velocity and its direction. Three types of acceleration are Uniform acceleration, non-uniform acceleration, and average acceleration.

Formula

{a} = v - v0/t =Δv/Δ t

{a} = average acceleration

v = final velocity

v_0 = starting velocity

t = elapsed time

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Answer:

b. 49.8

Explanation:

θc = sin^-1(1/1.309) = 49.81

The Force exerted by the physicist as she steps on a piece of gum is 18 Newtons and the right option is B) 18 Newtons.

Force can be defined as the product of mass and acceleration. The S.I unit of force is Newton (N) or kilogram- meter-per-seconds (kgm/s).

To calculate the amount of force she would exert, we use the formula below.

Formula:

Where:

From the question

Given:

Substitute these values into equation 1

Hence, the force exerted by the physicist is 18 N.

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Metals are great conductors because the electrons are able to move freely between the different energy levels within the atom.

What are conductors?

A substance or material that has the capability of conducting electricity or allows the passage of electricity to flow through it is known as conductor or electric conductor. The electrical charge carriers i.e., electrons or ions move easily from one atom to another when a voltage is applied on it.

The outer bound electrons of the metals are loosely bound  as the nucleus gets very less attracted on the electrons present on the outermost shell and because of this the charge carriers in them can move the current applied easily when there is a potential difference. Therefore, metals are considered to be the best conductors.

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Answer:

It remains Stationary

Explanation:

stationary.

The free body diagram of the ball as shown shows al the forces that acts on the ball as it rolls on the floor.

We know that a free body diagram is the diagram that shows the forces that act on an object. Force is a vector quantity thus we must consider the magnitude and the direction of the force. An object can be acted upon by a system of forces. The system of forces would only cause the object to move when the forces are unbalanced. If the system of forces is balanced, the object would not move at all.

In this case, we have a ball that is rolling on a floor. There are four main forces that are acting on the ball as we can see from the free body diagram. These are;

1) The weight of the ball that acts downwards

2) The normal reaction that acts upwards

3) The force that moves the ball forward

4) The force of friction that resists the forward motion of the ball.

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Answer:

Burn symptoms vary depending on the severity or degree of the burn. Symptoms are often worse during the first few hours or days after the burn. Burn symptoms include:

Blisters.

Pain.

Swelling.

White or charred (black) skin.

Peeling skin.

Explanation:

How are burns managed or treated?

Burn treatment varies depending on the cause and severity. You need to keep all burns clean and apply proper bandages/dressing depending on the severity of the wounds. Treating the person’s pain is key: inadequate control can interfere with wound care.

Continue to check wounds for signs of infection and other long term issues, such as scarring and tightening of the skin over joints and muscles, which makes them difficult to move.

Treatments by burn type include:

First-degree burns: Run cool water over the burn. Don’t apply ice. For sunburns, apply aloe vera gel. For thermal burns, apply antibiotic cream and cover lightly with gauze. You can also take over-the-counter pain medication.

Second-degree burns: Treatment for second and first-degree burns is similar. Your healthcare provider may prescribe a stronger antibiotic cream that contains silver, such as silver sulfadiazine, to kill bacteria. Elevating the burned area can reduce pain and swelling.

Third-degree burns: Third-degree burns can be life-threatening and often require skin grafts. Skin grafts replace damaged tissue with healthy skin from another of uninjured part of the person’s body. The area where the skin graft is taken from generally heals on its own. If the person does not have enough skin available for graft at the time of injury, a temporary source of graft can come from a deceased donor or a human-made (artificial) source but these will eventually need to be replaced by the person’s own skin. Treatment also includes extra fluids (usually given intravenously, with an IV) to keep blood pressure steady and prevent shock and dehydration.

Third-degree burns that are deep and affect a large portion of the skin are very serious and can be life-threatening. Even first- and second-degree burns can become infected and cause discolouration and scarring. First-degree burns don’t cause scarring.

Potential complications of third-degree burns include:

Arrhythmia, or heart rhythm disturbances, is caused by an electrical burn.

Dehydration.

Disfiguring scars and contractures.

Oedema (excess fluid and swelling in tissues).

Organ failure.

Pneumonia.

Seriously low blood pressure (hypotension) may lead to shock.

Severe infection that may lead to amputation or sepsis.