Test your prediction through calculation for the situations of the clay bob and the bouncy ball. Assume each has a mass of 100 grams, and each has an initial velocity of 20 m/s straight at the door. Ignore the effects of gravity. Calculate the change in momentum of

Answers

Answer 1

Answer:

a) Δp = -2.0 kgm / s,  b)   Δp = -4 kg m / s

Explanation:

In this exercise the change in moment of a ball is asked in two different cases

a) clay ball, in this case the ball sticks to the door and we have an inelastic collision where the final velocity of the ball is zero

         Δp = p_f - p₀

         Δp = 0 - m v₀

         Δp = - 0.100 20

         Δp = -2.0 kgm / s

b) in this case we have a bouncing ball, this is an elastic collision, as the gate is fixed it can be considered an object of infinite mass, therefore the final speed of the ball has the same modulus of the initial velocity, but address would count

         v_f = - v₀

        Δp = p_f -p₀

        Δp = m v_f - m v₀

        Δp = m (v_f -v₀)

        Δp = 0.100 (-20 - 20)

        Δp = -4 kg m / s


Related Questions

krichoffs law of current questions​

Answers

Answer:

Explanation:

       Kirchhoff's Current Law, often shortened to KCL, states that “The algebraic sum of all currents entering and exiting a node must equal zero.

           #I AM ILLITERATE

Monochromatic light is incident on a metal surface and electrons are ejected. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons

Answers

Answer:

Increase the rate and the same maximum energy of the electrons

Explanation:

According to the photoelectric effect we can say:

The number of electrons, or the electric current, has a linear behaviour with the intensity of the light and a constant behaviour whit the frequency. Therefore, the rate of electrons increases.

The kinetic energy of the ejected electrons has a linear dependence on the frequency of the light and has a constant behaviour with the intensity. So, we can say there is the same maximum energy.

I hope it helps you!

When you have a straight horizontal line on a velocity time graph, what does this tell you about the object’s motion in terms of velocity and acceleration?

Answers

Answer:

It tell you that the velocity is constant, what means that there's no acceleration

Two divers, G and H, are at depths 20 m and 40 m respectively
below the water surface in lake. The pressure on G is P, while
the pressure on H is P2 if the atmospheric pressure is equivalent
to 10 m of water, then the value of P2/P1 is.
A. 1.67.
B. 2.00.
C. 0.50.
D. 0.60.

Answers

Answer:

B

Explanation:

P1/P1 = 40/20

=2

Which of the following describes an electric conductor

Answers

The following describes an electric conductor : A material that has low resistance and allows the charges to move freely. The correct option is D.

What is conductor?

A conductor is a material or metal which allows the electrons to flow through it. In other words, a conductor allows the current to pass through them.

A battery also called as the voltage source, provides sufficient voltage or energy to excite electrons in the conductor.

Opposition offered to the flow of current is called as the resistance. The electrical element used in the circuit is the resistor.

So, an electric conductor is a material that has low resistance and allows the charges to move freely.

Thus, the correct option is D.

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In order to test an intentionally weak adhesive, the bottom of the small 0.15-lb block is coated with adhesive and then the block is pressed onto the turntable with a known force. The turntable starts from rest at t = 0 and uniformly accelerates with a = 2 rad/s^2. If the adhesive fails at exactly t = 3 s, then determine:

a. the magnitude of the ultimate shear force that the adhesive supports
b. the angular displacement of the turntable at the time of failure

Answers

Answer:

answer

Explanation:

it is the answer which was presented in the year

The car has a mass of 0·50 kg. The boy
now increases the speed of the car to 6·0
ms-1 . The total radial friction between
the car and the track has a maximum
value of 7.0 N. Show by calculation that
the car cannot continue to travel in the circular path.

Answers

Answer:

A solenoid is a type of electromagnet, the purpose of which is to generate a controlled magnetic field through a coil wound into a tightly packed helix. The coil can be arranged to produce a uniform magnetic field in a volume of space when an electric current is passed through it.

The car cannot continue to travel in the circular path, if the radius of the circular track is less than 2.57 m.

What is meant by centripetal force ?

Centripetal force is described as the force applied to a body that is travelling in a circular motion and is pointed in the direction towards the center of the circular path.

Here,

Mass of the car, m = 0.5 kg

Velocity of the car, v = 6 m/s

Radial friction between the car and the track, f = 7 N

The necessary centripetal force for the car to execute the circular motion is provided by the maximum radial frictional force between the car and the track.

So, the condition that the car cannot continue to travel in the circular path is that the centripetal force required is greater than the maximum radial friction.

So,

mv²/r > f

0.5 x 6²/r > 7

Therefore, the radius of the circular track,

r < 18/7

r < 2.57 m

Hence,

The car cannot continue to travel in the circular path, if the radius of the circular track is less than 2.57 m.

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A rabbit is moving in the positive x-direction at 2.70 m/s when it spots a predator and accelerates to a velocity of 13.3 m/s along the positive y-axis, all in 2.40 s. Determine the x-component and the y-component of the rabbit's acceleration.

Answers

Answer:

the answer is nearly 5.655 [tex]ms^{-2}[/tex]

Explanation:

Given,

[tex]v_{x}=2.7 ms^{-1}[/tex]

[tex]v_{y}=13.3 ms^{-1}[/tex]

[tex]t=2.4 s[/tex]

[tex]a_{x}=\frac{2.7}{2.4}=1.125 ms^{-2}[/tex] (as  [tex]a=\frac{v-u}{t}[/tex])

[tex]a_{y}=\frac{13.3}{2.4}=5.542 ms^{-2}[/tex]

[tex]a=\sqrt{a_{x}^{2}+a_{y}^{2} }[/tex]

[tex]=\sqrt{1.125^{2}+5.542^{2} }[/tex]

[tex]=5.655 ms^{-2}[/tex]

hope you have understood this...

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A mountain biker takes a jump in a race and goes airborne. The mountain bike is travelling at 10.0 m/s before it goes airborne. If the mass of the front wheel on the bike is 750 g and has radius 35 cm, what is the angular momentum of the spinning wheel in the air the moment the bike leaves the ground?

Answers

Answer:

Explanation:

The formula for angular momentum is

L = mvr where L is the angular momentum, m is the mass of the object, v is the velocity of the object, and r is the radius of the object. The problem we have that prevents us from just throwing those numbers in there is that mass has to be in kg and it's not, and radius has to be in meters and it's not.

Changing the mass to kg:

750 g = .750 kg

Changing the radius to m:

35 cm = .35 m

Now we can fill in the variables with their respective values:

L = .750(10.0)(.35) gives us

[tex]L=2.625\frac{kg*m^2}{s}[/tex]

Question 3 of 10
What has the same value no matter where it is located in the universe?
A. Volume
B. Weight
C. Mass
D. Density
Reset Selection

Answers

Answer:

C. Mass

Explanation:

A 150g copper bowl contains 220g of water, both at 20.0oC, A very hot 300 g copper cylinder is dropped into the water, causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 100oC, Neglect energy transfers with the environment.
a) How much energy (in calories) is transfered to the water as heat?
b) How much to the bowl?
c) What is the original temperature of the cylinder?

Answers

We have that the  energy (in calories) is transferred to the water as heat,to the bowl and  the original temperature of the cylinder  is mathematically given as

Qw=20.3 kcal Q= 1.11 kcal Ti=873°C

Energy

Generally the equation for the   is mathematically given as

(a)

The heat transferred to the H20

Qw= CwMwdT+Lvms

Qw=((220g)(100°C-20.0T)+(539 caVg)(5.00 g)

Qw=20.3 kcal .

(b)

The heat transferred to the bowl is

Qb= CbmbdT

Q= (0.0923 cal/gC)(150g)(100°C-20.0°C)

Q= 1.11 kcal

(c)  

original temperature of the cylinder

-Qw- Qb = CcMc(T2-T1)

[tex]T1=\frac{Qw+Qm}{CcMc}+T2[/tex]

T1=873C

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elastic wire extend by 1.ocm when a load on 20g range from It, what additional load will it be required Cause the futher extension of 2.0cm​

Answers

Answer:

40g

Explanation:

20g range > 1.0cm

Therefore,

40g range > 2.0cm

A 1.50 kg book is sliding along a rough horizontal surface. At point A it is moving at 3.21 m/s , and at point B it has slowed to 1.25 m/s .
Part A
How much work was done on the book between A and B ?
Part B
If -0.750J of work is done on the book from B to C , how fast is it moving at point C ?
Part C
How fast would it be moving at C if 0.750J of work were done on it from B to C ?

Answers

I assume friction is the only force acting on the book as it slides.

(A) By the work-energy theorem, the total work performed on the book as it slides is equal to the change in its kinetic energy:

W = ∆K

W = 1/2 (1.50 kg) (1.25 m/s)² - 1/2 (1.50 kg) (3.21 m/s)²

W-6.56 J

(B) Using the work-energy theorem again, the speed v of the book at point C is such that

-0.750 J = 1/2 (1.50 kg) v ² - 1/2 (1.50 kg) (1.25 m/s)²

==>   v = 0.750 m/s

(C) Take the left side to be positive, then solve again for v.

0.750 J = 1/2 (1.50 kg) v ² - 1/2 (1.50 kg) (1.25 m/s)²

==>   v1.60 m/s

a standard bathroom scale is placed on an elevator. A 34 kg boy enters the elevator on the first floor and steps on the scale. What will the scale read (in newtons) when the elevator begins to accelerate upward at 0.4 m/s2

Answers

Answer:F = 255 N

Explanation:

It is given that,

Mass of the boy, m = 25 kg

Acceleration of the elevator,  

The elevator is accelerating in upward direction. The net force acting on the boy is given by :

g is the acceleration due to gravity

F = 255 N

The scale reading is 255 N as it begins to accelerate upward. hence, this is the required solution.

Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. In order to cause electrons to be ejected from the surface of this metal you should: ___________

a. use light of the same wavelength but increase its intensity.
b. use light of a shorter wavelength.
c. use light of the same wavelength but decrease its intensity.
d. use light of a longer wavelength.

Answers

Answer:

use light of the same wavelength but decrease it's intensity

What is hydroelectric power ?

Answer quickly..!

Answers

Answer:

It's electricity produced from hydropower. It's also a form of energy that controls the power of water motion.

Explanation:

One pro about hydroelectric power is that it's renewable energy. But one con about hydroelectric power is that it can impact the environment in a negative way.

g Light that is incident upon the eye is refracted several times before it reaches the retina. As light passes through the eye, at which boundary does most of the overall refraction occur?

Answers

Answer

Explanation

:giác mạc

What is the order of magnitude of the distance of Sun to nearest star in meters?

Answers

Answer:

Approximating the Milky Way as a disk and using the density in the solar neighborhood, there are about 100 billion stars in the Milky Way.

Explanation:

Since we are making an order of magnitude estimate, we will make a series of simplifying assumptions to get an answer that is roughly right.

Let's model the Milky Way galaxy as a disk.

The volume of a disk is:

V

=

π

r

2

h

Plugging in our numbers (and assuming that

π

3

)

V

=

π

(

10

21

m

)

2

(

10

19

m

)

V

=

3

×

10

61

m

3

Is the approximate volume of the Milky Way.

Now, all we need to do is find how many stars per cubic meter (

ρ

) are in the Milky Way and we can find the total number of stars.

Let's look at the neighborhood around the Sun. We know that in a sphere with a radius of

4

×

10

16

m there is exactly one star (the Sun), after that you hit other stars. We can use that to estimate a rough density for the Milky Way.

ρ

=

n

V

Using the volume of a sphere

V

=

4

3

π

r

3

ρ

=

1

4

3

π

(

4

×

10

16

m

)

3

ρ

=

1

256

10

48

stars /

m

3

Going back to the density equation:

ρ

=

n

V

n

=

ρ

V

Plugging in the density of the solar neighborhood and the volume of the Milky Way:

n

=

(

1

256

10

48

m

3

)

(

3

×

10

61

m

3

)

n

=

3

256

10

13

n

=

1

×

10

11

stars (or 100 billion stars)

Is this reasonable? Other estimates say that there are are 100-400 billion stars in the Milky Way. This is exactly what we found.

Answer:

Mercury, 46,001,272 km from the sun at the nearest point.

Explanation:

Do you believe in ghost​

Answers

Answer:

well its about our thinking but i do believe in ghost a little

1. Estimate the buoyant force that air exerts on a man. (To do this, you can estimate his volume by knowing his weight and by assuming that his weight density is about equal to that of water. Assume his weight is 940 N.) answer in N
2.On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 17000 N.
(a) What is the weight of the displaced air?
answer in N
(b) What is the volume of the displaced air?
answer in m^3

Answers

Solution :

1. We know that : Buoyant force = weight of the liquid displace

                                                  = volume displaced x density of the fluid

Now volume of the man = [tex]$\frac{\text{mass}}{\text{density}}$[/tex]

Mass = weight / g

         [tex]$=\frac{940}{9.8}$[/tex]

         = 95.92 kg

And density = 1000 [tex]kg/m^3[/tex]

Therefore,

[tex]$\text{volume} = \frac{\text{mass}}{\text{density}}$[/tex]

           [tex]$=\frac{95.92}{1000}$[/tex]

           = 0.0959 [tex]m^3[/tex]

We know density of air = 1.225 [tex]kg/m^3[/tex]

∴ Mass of air displaced = 0.0959 x 1.225

                                       = 0.1175 kg

Weight of the air displaced = 1.1515 N

Therefore, the buoyant force = 1.1515 N

2). As the balloon is not accelerated, the net force acting on it is zero.

Thus the weight that acts downwards = buoyant force upwards

So, the weight of the air displaced = weight of the balloon

                                                          = 17000 N

Therefore, the mass of the air displaced = volume of the air displaced (volume of the balloon) x density of air

[tex]$\frac{17000}{9.8} = \text{volume of air} \times 1.225$[/tex]

[tex]$\text{Volume of air displaced} = \frac{1700}{9.8 \times 1.225}$[/tex]

                                     = 1416.0766 [tex]m^3[/tex]

A cylindrical wire made of an unknown alloy hangs from a support in the ceiling. You measure the relaxed length of the wire to be 16 m long; and the radius of the wire to be 3.5 m. When hang a 5 kg mass from the wire, you measure that it stretches a distance of 4 x 10 m The average bond length between atoms is 2.3 x 10^0 m for th alloy.

Required:
What is the stiffness of a typical interatomic bond in the alloy

Answers

Answer: hello  some of your values are wrongly written hence I will resolve your question using the right values

answer:

stiffness =  1.09 * 10^-6 N/m

Explanation:

Given data:

Length ( l ) = 16 m

radius of wire ( r ) = 3.5 m

mass ( m ) = 5kg

Distance stretched (  Δl ) = 4 * 10^-3 m ( right value )

average bond length ( between atoms ) = 2.3 * 10^-10 m ( right value)

first step : calculate the area

area ( A ) = πr^2 = π * ( 3.5)^2 = 38.48 m^2

        γ          = MgL / A Δl

                    = [ (5 * 9.81 * 16 ) / ( 38.48 * (4.3*10^-3) ) ]

                    = 784.8 / 0.165 = 4756.36 N/m^2

hence : stiffness =   γ  * bond length

                           =  4756.36 * 2.3 * 10^-10  = 1.09 * 10^-6 N/m

Two long straight wires are suspended vertically. The wires are connected in series, and a current from a battery is maintained in them. What happens to the wires? What happens if the battery is replaced by an a-c source?

Answers

Answer:

(i) When a battery is connected inseries to two long parallel wires, the currents in the two wires will be in opposite directions. Due to which a force of repulsion will be acting between them and they are moving further apart.

(ii) When a battery is connected in parallel to two long parallel wires, the currents in the two wires will be in same direction. Due to it, a force of attraction will be acting between them and they are coming closer to each other.

hope it's help you ....!!!!!

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Explanation:

Hope it will helps you lot!

A roller coaster has a total track length of 500 yards. A complete ride on the roller coaster is considered two times around the track. The start and stop places for the ride are virtually the same. What are the distance and displacement for a ride on the roller coaster? Explain your answers.

Answers

Answer:

Explanation:

its 1000 yards if its going around the track 2 times and that if one whole  around the track is 500 its 500 x 2

Two circular coils are concentric and lie in the same plane.The inner coil contains 120 turns of wire, has a radius of 0.012m,and carries a current of 6.0A. The outer coil contains 150turns and has a radius of 0.017 m. What must be the magnitudeand direction (relative to the current in the inner coil) ofthe current in the outer coil, such that the net magnetic field atthe common center of the two coils is zero?

Answers

Answer:

[tex]I_2=6.8A[/tex]

Explanation:

From the question we are told that:

Turns of inner coil [tex]N_1=120[/tex]

Radius of inner coil [tex]r_1=0.012m[/tex]

Current of  inner coil [tex]I_1=6.0A[/tex]

Turns of Outer coil [tex]N_2=150[/tex]

Radius of Outer coil [tex]r_2=0.017m[/tex]

Generally the equation for Magnetic Field is mathematically given by

[tex]B =\frac{ \mu N I}{2R}[/tex]

Therefore

Condition for the net Magnetic field to be zero

[tex]\frac{N_1* I_1}{( 2 * r_1 )}=\frac{N_2 * I_2}{2 * r_2}[/tex]

[tex]I_2=\frac{(N_1* I_1)*(( 2 * r_2)}{( 2 * r_1)*N_2}[/tex]

[tex]I_2=\frac{(120*6.0)*(( 2 * 0.017)}{( 2 * 0.012)*150}[/tex]

[tex]I_2=6.8A[/tex]

RATIO of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is:
1) 7/29
2) 9/31
3) 5/27
4) 5/23​

Answers

Answer:

[tex]5/27[/tex]

Explanation:

wavelengths for Lyman series

[tex]\lambda=\frac{1}{R(1-\frac{1}{4} })=\frac{4}{3R}[/tex]

wavelengths for Balmer series

[tex]\lambda_B=\frac{1}{R(\frac{1}{4}-\frac{1}{9}) } =\frac{1}{R(\frac{5}{36}) } =\frac{36}{5R}[/tex]

[tex]\frac{ \lambda_L}{ \lambda_B} =\frac{4}{3R} \times\frac{5R}{36} =5/27[/tex]

OAmalOHopeO

The ratio of longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is 5/27. The correct option is 3.

What is Lyman and Balmer series?

Lyman and Balmer series are sets of spectral lines in the emission spectrum of hydrogen, which result from the transitions of the electron from higher energy levels to lower energy levels.

The Lyman series consists of spectral lines that are produced by transitions of the electron from higher energy levels to the n=1 energy level. These transitions release energy in the form of ultraviolet photons. The lowest energy level in hydrogen is the n=1 energy level, which is also called the ground state. Therefore, the Lyman series includes the transition of the electron from any energy level greater than or equal to n=2 to the ground state.

The Balmer series consists of spectral lines that are produced by transitions of the electron from higher energy levels to the n=2 energy level. These transitions release energy in the form of visible photons. The lowest energy level in the Balmer series is the n=2 energy level. Therefore, the Balmer series includes the transition of the electron from any energy level greater than or equal to n=3 to the n=2 energy level.

Lyman and Balmer's series are named after the scientists who discovered them. The Lyman series is named after Theodore Lyman, an American physicist who discovered the series in 1906. The Balmer series is named after Johann Balmer, a Swiss mathematician who discovered the series in 1885.

Here in the Question,

The longest wavelength in the Lyman series of the hydrogen spectrum corresponds to the transition from the n = 2 energy level to the n = 1 energy level, while the longest wavelength in the Balmer series corresponds to the transition from the n = 3 energy level to the n = 2 energy level.

The wavelengths of these transitions can be calculated using the Rydberg formula:

1/λ = R(1/n1^2 - 1/n2^2)

where λ is the wavelength of the photon emitted, R is the Rydberg constant (1.097 × 10^7 m^-1), and n1 and n2 are the initial and final energy levels of the electron.

For the longest wavelength in the Lyman series, we have n1 = 2 and n2 = 1, so:

1/λ_lyman = R(1/2^2 - 1/1^2) = 3R/4

For the longest wavelength in the Balmer series, we have n1 = 3 and n2 = 2, so:

1/λ_balmer = R(1/3^2 - 1/2^2) = 5R/36

Therefore, the ratio of the longest wavelengths in the Lyman and Balmer series is:

λ_lyman/λ_balmer = (3R/4)/(5R/36) = 27/20

Simplifying this ratio gives:

λ_lyman/λ_balmer = 27/20

Multiplying both the numerator and denominator by 1/3R, we get:

λ_lyman/λ_balmer = (1/2)/(1/3) = 3/2

Therefore, the ratio of the longest wavelengths in the Lyman and Balmer series is 3:2, or 3/5 in fractional form. Simplifying this ratio gives:

λ_lyman/λ_balmer = 5/3

Taking the reciprocal of both sides, we get:

λ_balmer/λ_lyman = 3/5

Therefore, the correct answer is (3) 5/27.

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A race car goes from a complete stop at the start line to 150 miles per hour in 5 seconds. What is its acceleration? Show your work.

Answers

Answer:

Explanation:

150/5  = 30

30mph per 1 second

explain why our sweat is salty?​

Answers

Answer:

Sweat also contains ammonia and urea, which are produced by the body when it breaks down proteins from the foods you eat.

Hope this helps..

Earth’s Moon has a diameter of 3,474 km and orbits at an average distance of 384,000 km. At that distance it subtends and angle just slightly larger than half a degree in Earth’s sky. Pluto’s moon Charon has a diameter of 1,186 km and orbits at a distance of 19,600 km from the dwarf planet. Compare the appearance of Charon in Pluto’s skies with the Moon in Earth’s skies. Describe where in the sky Charon would appear as seen from various locations on Pluto.

Answers

The result of the comparison of the appearance of Charon on Pluto and   times the Moon from Earth is that; Charon as seen from Pluto appears approximately 7 times larger than the Moon

Charon is directly overhead from the side of Pluto locked to the side of Charon

Charon appears at the horizon from the poles of the axis of rotation of Jupiter around Charon

The reason for arriving at the above solutions is as follows:

The given dimensions and distance from the Earth of the Moon are;

The diameter of the Moon, d = 3,474 km

The average distance of the Moon from the Earth, R = 384,000 km

Required:

The comparison between Charon's appearance in Pluto and the Moon's appearance on Earth Earth

Solution:

The distance of the Moon's travels in an orbit, C = 2·π·R

∴ C = 2 × π × 384,000 km

The angle subtended by the Moon, θ = d/C × 360°

∴ θ = 3,474/(2 × π × 384,000) × 360° ≈ 0.518°

Pluto's moon Charon, has the following parameters;

The diameter of the Charon, d₂ = 1,186 km

The average distance of the Charon from Pluto, R₂ = 19,600 km

Therefore, the distance of the Moon's travels in an orbit, C₂ = 2·π·R₂

∴ C₂ = 2 × π × 19,600 km

The angle subtended by the Moon, θ₂ = d₂/C₂ × 360°

∴ θ₂ = 1,186/(2 × π × 19,900) × 360° ≈ 3.415°

The angle subtended by Charon in Pluto's sky ≈ 3.415°

Charon therefore, appears 7 times larger in Pluto's skies than the Moon's appearance in Earth's skies

Required:

The appearance of Charon as seen from different locations on Pluto

Solution:  

Charon is gravitationally locked to Pluto, therefore, the same side of Pluto is faced with the same side of Charon

Therefore;

Charon appears constantly overhead from the side of Pluto locked to CharonCharon appears constantly at the horizon from the poles on either side of the axis of rotation of Pluto and Charon

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Which of the following measures is equal to 700 km?

Answers

Answer:

1km=1000m

700km=

700×1000=700000

=700000metres

hope this helps

Two masses of 3 kg and 5 kg are connected by a light string that passes over a smooth polley as shown in the Figure.
QL
Determine:
i. the tension in the string,
ii. the acceleration of each mass, and
iii. the distance each mass moves in the first second of motion if they start from rest​

Answers

i. [tex]T = 36.8\:\text{N}[/tex]

ii. [tex]a = 2.45\:\text{m/s}^2[/tex]

iii. [tex]x = 1.23\:\text{m}[/tex]

Explanation:

Let's write Newton's 2nd law for each object. We will use the sign convention assigned for each as indicated in the figure. Let T be the tension on the string and assume that the string is inextensible so that the two tensions on the strings are equal. Also, let a be the acceleration of the two masses. And [tex]m_1 = 3\:\text{kg}[/tex] and [tex]m_2 = 5\:\text{kg}[/tex]

Forces acting on m1:

[tex]T - m_1g = m_1a\:\:\:\:\:\:\:(1)[/tex]

Forces acting on m2:

[tex]m_2g - T = m_2a\:\:\:\:\:\:\:(2)[/tex]

Combining Eqn(1) and Eqn(2) together, the tensions will cancel out, giving us

[tex]m_2g - m_1g = m_2a + m_1a[/tex]

or

[tex](m_2 - m_1)g = (m2 + m_1)a[/tex]

Solving for a,

[tex]a = \left(\dfrac{m_2 - m_1}{m_2 + m_1}\right)g[/tex]

[tex]\:\:\:\:= \left(\dfrac{5\:\text{kg} - 3\:\text{kg}}{5\:\text{kg} + 3\:\text{kg}}\right)(9.8\:\text{m/s}^2)[/tex]

[tex]\:\:\:\:= 2.45\:\text{m/s}^2[/tex]

We can solve for the tension by using this value of acceleration on either Eqn(1) or Eqn(2). Let's use Eqn(1).

[tex]T - (3\:\text{kg})(9.8\:\text{m/s}^2) = (3\:\text{kg})(2.45\:\text{m/s}^2)[/tex]

[tex]T = (3\:\text{kg})(9.8\:\text{m/s}^2) + (3\:\text{kg})(2.45\:\text{m/s}^2)[/tex]

[tex]\:\:\:\:= 29.4\:\text{m/s}^2 + 7.35\:\text{m/s}^2 = 36.8\:\text{N}[/tex]

Assuming that the two objects start from rest, the distance that they travel after one second is given by

[tex]x = \frac{1}{2}at^2 = \frac{1}{2}(2.45\:\text{m/s}^2)(1\:\text{s})^2 = 1.23\:\text{m}[/tex]

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