The same resultant force acts on objects 1 and 2. Object 1 accelerates at 2m/s² and Object 2 accelerates at 5m/s². Which object has the greater mass?

Answer:

 α = [tex]\frac{2 \mu \ N}{m \ r}[/tex]

Explanation:

For this exercise we use Newton's equation for rotational motion

           ∑ τ = I α

the troque is

           α = Fr .r

the moment of inertia of a cylinder is

           I = ½ m r²

we substitute

         fr r = (½ m r²) α

the expression friction is

         fr = μ N

we substitute

         μ N r = ½ m r² α

         α = [tex]\frac{2 \mu \ N}{m \ r}[/tex]

There is strong evidence to support the idea that the universe is expanding. One of the main pieces of evidence for this is the observation of the cosmic microwave background radiation, which is a faint glow of microwave radiation that permeates the entire universe. This radiation is thought to be a residual heat left over from the Big Bang, the event that is believed to have marked the beginning of the universe.

The cosmic microwave background radiation has a very even temperature throughout the universe, but if the universe were not expanding, we would expect to see some regions that are slightly hotter or cooler than others due to differences in density. However, measurements of the cosmic microwave background radiation show that it has a very uniform temperature, which suggests that the universe must be expanding in order to even out any temperature differences that may have existed in the past.

Other evidence for the expansion of the universe includes the observation of supernovae in distant galaxies, which are explosions of massive stars that can be used to measure the distances to those galaxies. These measurements have shown that the most distant galaxies are moving away from us at a speed that is proportional to their distance, which is consistent with the expansion of the universe.

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An object has 100 J of kinetic energy. If the object’s mass doubles, then its kinetic energy will be 200J and is denoted as option C.

This is referred to as the type of energy that it possesses due to its motion and can also defined as the work which is needed to accelerate a body of a given mass from rest to its stated velocity.

The unit is in Joules and the formula is 1/2mv² where m is the mass and v is the velocity of the body or object. In a scenario where the mass is doubled or tripled and the velocity is constant then the kinetic energy will also be doubled or tripled respectively.

For instance, lets assume initial mass is 50kg and the v² is 50m/s then the kinetic energy is  1/2mv²  which is 1/2 × 50 × 50 = 1250J. When the mass is doubled it becomes 100kg which 1/2 × 100 × 50 = 2500J which depicts that  it was also doubled.

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The options are:

A.  50 Joules.

B.  100 Joules.

C.  200 Joules.

D.  400 Joule

Assuming an object has 100 Joules of kinetic energy. If the object’s mass doubles, its kinetic energy would be equal to: C. 200 Joules.

In Science, kinetic energy can be defined as a type of energy that's possessed by a physical object or body, especially due to its motion or a change in velocity (acceleration).

This ultimately implies that, a physical object or body would gain more of kinetic energy as it falls back toward the Earth because it is in motion.

Mathematically, kinetic energy can be calculated by using this formula:

K.E = 1/2 × mv²

Where:

Since the mass of the object doubles, its kinetic energy would be twice that of its initial kinetic energy;

Kinetic energy = 2 × initial kinetic energy

Kinetic energy = 2 × 100

Kinetic energy = 200 Joules.

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Complete Question:

A.  50 Joules.

B.  100 Joules.

C.  200 Joules.

D.  400 Joules.

Answer:

a)[tex]W=0.8J[/tex]

b) [tex]d_t=0.20m[/tex]

c) [tex]\triangle K.E=0.267J[/tex]

Explanation:

From the question we are told that:

Mass of cart 1 [tex]M_1=1.0kg[/tex]

Mass of cart 1 [tex]M_2=0.05kg[/tex]

Force on  cart 1 [tex]F_1=4.0N[/tex]

Push Distance of cart 1 [tex]d_1=0.20m[/tex]

Slide Distance of cart 1 [tex]d_1'=0.35m[/tex]

a)

Generally the equation for work-done is mathematically given by

[tex]W=f*d\\W=4*0.20\\W=0.8J \\[/tex]

b)

The systems center of mass moved a net totally of (while being pushed)

Mass 1 =0.20m

Mass 2=0

Therefore

[tex]d_t=d_1+d_2[/tex]

[tex]d_t=0.20+0[/tex]

[tex]d_t=0.20m[/tex]

c)

Since work-done is equal to K.E energy of cart 1

Therefore

[tex]W=1/2mv^2[/tex]

[tex]V_1=\sqrt{\frac{W}{1/2m}}[/tex]

[tex]V_1=\sqrt{\frac{0.8}{1/2(1)}}[/tex]

[tex]V_1=1.264[/tex]

Therefore Kinetic energy before collision is

[tex]K.E_1=1/2mv^2[/tex]

[tex]K.E_1=1/2*1*1.264^2[/tex]

[tex]K.E_1=0.768[/tex]

Generally from the equation for conservation  of momentum the Velocity of cart 2 is mathematically given by

[tex]v_2=\frac{m_1V_1}{m_1+m_2}[/tex]

[tex]v_2=\frac{1*1.264}{1+0.5}[/tex]

[tex]V_2=0.842m/s[/tex]

Therefore the final K.E is mathematically given by

[tex]K.E_2=(1/2)(m_1+m_2)V_2^2[/tex]

[tex]K.E_2=1/2*(1.5)(0.842)^2[/tex]

[tex]K.E_2=0.531J[/tex]

Generally the Change in K.E is mathematically given by

[tex]\triangle K.E=K.E_1-K.E_2[/tex]

[tex]\triangle K.E=0.798-0.531[/tex]

[tex]\triangle K.E=0.267J[/tex]

Therefore the will force change the kinetic energy of the system's center of mass by

[tex]\triangle K.E=0.267J[/tex]

(a) The work done by you when you push the cart at a constant force is 0.8 J.

(b) The distance moved by the center mass of the two cart system is 0.23 m.

(c) The change in kinetic energy of the system center of mass is 0.271 J.

The work done by you when you push the cart at a constant force is calculated as follows;

W = Fd

W = 4 x 0.2

W = 0.8 J

Xcm = (m₁x₁ + m₂x₂)/(m₁ + m₂)

Xcm = (0.5(0) + 1(0.35)) / (1 + 0.5)

Xcm = (0.35)/(1.5)

Xcm = 0.23 m

F = ma

a = F/m

a = (4)/1 = 4 m/s²

v² = u² + 2as

v² = 0 + 2(4)(0.2)

v² = 1.6

v = √1.6

v = 1.265 m/s

m₁u₁ + m₂u₂ = v(m₁ + m₂)

1(1.265) + 0 = v(1 + 0.5)

1.265 = 1.5v

v = 0.84 m/s

K.E(initial) = ¹/₂m₁u₁² + ¹/₂m₂u₂²

K.E(initial) = ¹/₂(1)(1.265)² + ¹/₂(0.5)(0) = 0.8 J

K.E(final) = ¹/₂(m₁ + m₂)v²

K.E(final) = ¹/₂(1 + 0.5)(0.84)²  = 0.529 J

Δ K.E = 0.8 J - 0.529 J = 0.271 J

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Answer:

The force of friction opposes the motion of an object, causing moving objects to lose energy and slow down. When objects move through a fluid, such as air or water, the fluid exerts a frictional force on the moving object. The frictional force from a fluid is called a drag force.

Answer:

the person on the boat is moving 15mph on the boat and throws the ball 10mph. you add that together its 25mph. the other person is standing on land so their  is no extra speed.

Explanation:

its common

The person on the boat is moving 15 mph on the boat and throws the ball 10 mph. you add that together its 25 mph. the other person is standing on land so their  is no extra speed.

The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity.

The two observation are different because of relative speed is measured as one with observer in the rest or zero speed in other case observer is in the motion with some speed so these are different.

The person on the boat is moving 15 mph on the boat and throws the ball 10 mph. you add that together its 25 mph. the other person is standing on land so their  is no extra speed.

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Answer: 3.3·10^6 m/s

Explanation: Ionization energy of H is 13.6 eV. So the kinetic energy of electron is 31,2 eV.  Kinetic Energy of Electron is  E = ½mv^2

1 eV = 1.60·10^-19 J and  m = 9.1·10^-31 kg.   Solving speed v = √( 2E / m)

v = √(2·31.2·1.60·10^-19 J /9.1·10^-31 kg) = 3.3·10^6 m/s

The resultant (x,y) coordinate of vector B is  (- 5, 3) and that of A is (9,3). Then, the sum of x components of vector A and B is 4.

Vectors are physical quantities having both magnitude and direction. For example force, velocity, displacement etc .are vector quantities. Coordinates are used to describe the position of these vectors.

The coordinates of tail of  the vector A is (0, 0) and the head is (9,3)

Then the coordinate of A is (9 -0, 3-0) = (9,3)

Similarly, the tail coordinate of B is (9,3) and head is (4,6). The coordinates of B vector is (4-9, 6-3) = (-5, 3)

Now the sum of x components of A and B is = - 5 + 9 = 4.

Therefore, option b is correct.

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Answer:

The angle when it leaves is the same as the angle when it hits.

Explanation:

think of it as a mirror, mirrors show exactly what you display.

Answer:

a)   [tex]\omega=9.10*10^{-4}rad/sec[/tex]

b)   [tex]V=1.8217*10^{-3}[/tex]

Explanation:

From the question we are told that:

Mass of woman [tex]M_w=55kg[/tex]

Radius of merry go round [tex]r=2.0m[/tex]

Rotational inertia [tex]i= 1250 kg-m2[/tex]

Mass of rock [tex]M_r=350g \approx 0.350kg[/tex]

Speed of rock [tex]V_r=2.0m/s[/tex]

Tangent angle to the outer edge [tex]\theta=1[/tex]

a)

Generally the equation for conservation of momentum is mathematically given by

[tex]M_r(ucos\theta)r=(I+M_wr^2)\omega[/tex]

[tex]0.350(2.0cos1)(2.0)=(1250+(55)(2.0)^2)\omega[/tex]

[tex]1.3998=1470\omega\\\omega=\frac{1.339}{1470}[/tex]

[tex]\omega=9.10*10^{-4}rad/sec[/tex]

b)

Generally the equation for linear speed V is mathematically given by

[tex]V=r\omega\\V=2.0*9.10*10^{-4}[/tex]

[tex]V=1.8217*10^{-3}[/tex]

The gravitational field strength on Oobla is 20.75 m/s².

The gravitational field is the gravitational force exerted per unit mass on a small mass at a point in the field.

To calculate the gravitational field strength on Ooobla, we use the formula below

Formula:

Where:

From the question,

Given;

Substitute these values into equation 1 and solve for g'

Hence, the gravitational field strength is 20.75 m/s².

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The  average velocity of the airplane  between  Milwaukee and Chicago  is 1083.33 meter/second.

The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.

The total distance between  Milwaukee and Chicago = 130 kilometer

= 1,300,000 meter.

Time interval = 20 minute = 20×60 second = 1200 second.

The  average velocity of the airplane = total distance/time interval

= 1,300,000 meter / 1,200 second.

= 1083.33 meter/second.

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Answer:

B. Electromagnetism is the forces and fields associated with charge.

Complete Question:

A horizontal force of 5N is required to maintain a velocity of 2m/s for a block of 10kg mass sliding over a rough horizontal surface. The work done by this force in one minute is:

Answer:

Workdone = 600 Joules.

Explanation:

Given the following data;

Force = 5N

Velocity = 2 m/s

Time = 1 minute to seconds = 60 seconds.

Mass = 10 kg

To find the work done;

First of all, we would determine the distance covered by the block.

Distance = speed * time

Distance = 2 * 60

Distance = 120 seconds

Mathematically, workdone is given by the formula;

[tex] Workdone = force * distance[/tex]

Substituting into the formula, we have;

[tex] Workdone = 5 * 120 [/tex]

Workdone = 600 Joules.

Therefore, the work done by this force in one minute is 600 Joules.

Answer:

Explanation:true

Answer:

Explanation:

amplitude of oscillation A = .06 m .

maximum velocity = ω A where ω is angular frequency .

ω A = 3.2 m/s ( Given )

ω x .06  = 3.2

ω = 53.33 rad /s .

velocity when the displacement is x can be given by the expression

v² = ω²( A² - x² )

x = .04 m

v² = 53.33²( .06² - .04² )

=  2844.1( .0036 - .0016 )

= 5.688

kinetic energy = 1/2 m v²

= .5 x .050 x 5.688

= .1422 J .

=

Answer:  La valeur du poids dépend de la pesanteur et de la masse. ... La masse est une grandeur positive liée à la quantité de matière contenue dans un objet. ... qui correspond à la force d'attraction exercée par l'astre sur lequel il se trouve (et qui ... 1 kg n'aura pas le même poids à la surface de la Lune ou à la surface de la Terre.

Explanation:

As a well-known serial killer, David Berkowitz was infamous for starting fires and then reporting some of them to various fire officials. He started over 500 fires annually.

David Berkowitz, also known as Son of Sam, was apprehended on August 10, 1977 – 11 days after he committed his final murder—and later received six consecutive sentences of 25 years to life in prison.

Since the 18th century, arson has changed from a bad individual act to a powerful tool for group violence. The privatization of common land in England starting in 1750 restricted the access of peasants to resources like game and firewood.

Therefore, Son of Sam, also known as David Berkowitz, was apprehended by authorities after going on a homicidal rampage in New York City in the 1970s.

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Answer:

everything

Explanation:

Used to refer to a thing, no matter what

Answer:

the film's minimum thickness to make the reflected light enhanced in brightness is 112.8 nm

Explanation:

Given the data in the question;

wavelength λ = 600 nm  

index of refraction = 1.33

so the film's minimum thickness to make the reflected light enhanced in brightness = ?

condition for maxima for reflected light is;

2nt = [ ( 2m + 1 )λ ] / 2

we solve for t

4nt = [ ( 2m + 1 )λ ]

t =  [ ( 2m + 1 )λ ] / nt

Now, for minimum thickness m = 1

t = λ / 4n

so we substitute in our values;

t = 600 nm / ( 4 × 1.33 )

t = 600 nm / 5.32

t = 112.78195 ≈ 112.8 nm  { one decimal place }

Therefore, the film's minimum thickness to make the reflected light enhanced in brightness is 112.8 nm

The reason that Silent Spring was so influential at the time is option D: It was the first time that the public was being made aware of the long-term impacts of pollution.

Silent Spring, a book written by Rachel Carson and published in 1962, was influential at the time because it was the first book to bring awareness to the negative impacts of pesticides on the environment and human health.

Therefore, The book provided evidence and detailed accounts of the harmful effects of pesticides on wildlife and ecosystems, and it argued that the widespread use of pesticides was unsustainable and could have long-term consequences for the environment and human health.

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The coefficient of kinetic friction between the block and the rough surface is -0.6.

Kinetic friction is a type of friction that occurs when two objects are in contact and moving relative to each other. It is also known as sliding friction or dynamic friction. Kinetic friction is caused by the interaction of the two surfaces as they move against each other. The force of kinetic friction acts in the opposite direction of the motion of the two objects and is proportional to the normal force between them. The coefficient of kinetic friction is a measure of the amount of friction between two surfaces and is determined by the materials of the two surfaces.

The coefficient of kinetic friction can be found using the equation:
μk = (vf - vi) / (d * a)
where μk is the coefficient of kinetic friction, vf is the final velocity, vi is the initial velocity, d is the distance traveled, and a is the acceleration due to gravity (9.8 m/s2).
Plugging in the given values, we get:
μk = (6 - 18) / (30 * 9.8)
μk = -0.6
Therefore, the coefficient of kinetic friction between the block and the rough surface is -0.6.

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The statement that a doctor who is monitoring the health of astronauts in space has just received a signal that indicates one of the astronauts may be experiencing low blood sugar. The mission control personnel that would communicate this to the astronaut on board the space craft is CAPCOM is true. So the correct option is A.

When there is a mission in which astronauts do space exploration, there will be mission control on the ground made up of members who will take over from the astronauts on earth, this will be the CAPCOM. These people will transmit the decision-making of the mission director who will be from the ground and will also communicate the needs of the astronauts to the people who control the mission.

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Answer:

Explanation:

circumference = diameter * [tex]\pi[/tex]

circumference = 65 * [tex]\pi[/tex]

circumference = 204.2035225m

350 km/h = 97.222222 m/s

0.4761 revolutions per second

The parallel component of the force of gravity is the net force. The perpendicular component of the force of gravity is directed opposite the normal force and as such balances the normal force.

In order to balance the normal force, the perpendicular component of gravity is pointed in the opposite direction. No other force can counteract the parallel component of the gravitational force.

The presence of an imbalanced force will then cause the object to accelerate downward along the inclined plane. This acceleration is brought on by the parallel part of the gravitational force. The net force is a parallel part of the gravitational force.

FGravity=m×g

where m is the object's mass and g is gravity's acceleration, which is 9.8 m/s2. In this case, the negative indicates that the force is downward-directed.

FParallel=FGravity×Cos(Θ)

FParallel=FGravity×Sin(Θ)

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The value of mA is the equation of conservation of linear momentum is determined as mA = [ mB (vBi - vBf) ] / [  (vAf - vAi ) ].

The principle of conservation of linear momentum states that in a closed or isolated system, the total momentum of the system is always conserved.

Mathematically, the formula for the principle of conservation of linear momentum is given as;

Pi = Pf

where;

mAvAi + mBvBi = mAvAf + mBvBf

where;

To find the value of mA, we will make mA the subject of the formula as follow;

mAvAf  - mAvAi = mBvBi - mBvBf

mA (vAf - vAi ) = mB (vBi - vBf)

mA = [ mB (vBi - vBf) ] / [  (vAf - vAi ) ]

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Answer:

In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

Answer:

option ( a ) is correct .

Explanation:

Escape velocity on the earth = √ ( 2 GM / R )

where G is universal gravitational constant , M is mass of the earth and R is radius .

V₀ = √ ( 2 GM / R )

escape velocity on the planet where mass is equal is earth's mass and radius is 4 times that of the earth

Radius of the planet = 4 R

escape velocity of planet = √ ( 2 GM / 4R )

= .5 x √ ( 2 GM / R )

= .5 V₀

option ( a ) is correct .

Answer:

Newton's first law, also known as the law of inertia, states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. In other words, an object will not change its velocity on its own, it will only do so if something else pushes or pulls on it. This law is a fundamental principle of classical mechanics, and it helps to explain the behavior of objects under various conditions.

Explanation:

Answer: Newton first law states that an object at rest tends to stay at rest. an object in motion tends to stay in motion in a straight line at a constant speed until another force acts on the object.  It is also called the law of inertia

Explanation: Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.

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Answer:

Photoelectric-type alarms aim a light source into a sensing chamber at an angle away from the sensor. Smoke enters the chamber, reflecting light onto the light sensor; triggering the alarm.

Explanation:

nfpa.org is the website with theanswer