A 0.08m long spring is attached vertically to the ceiling. after 66kg mass is attached to the spring it has a length of 2.1m. determine the spring's force constant. use g=10

The spring is stretched about 3.5cm from its natural length as the block moves in this circle.

Acceleration is given by formula = [tex]\frac{v^{2} }{r}[/tex] where,..... (1)

v= velocity and r = total distance

In this case r = L+Δx where,

L is the length of unstretched spring

Δx = Change in Spring length

According to Hooke's law

F=kΔx …..(2) where,

F= force , k is constant and Δx= change in spring length

Also,

F=ma …..(3) where,

F= force , m= mass of body and a = acceleration

From equation (2) and (3)

ma = kΔx

Now, from equation (1)

mv²/L+Δx = kΔx

mv² = kΔx(L+Δx)…. (4)

Total energy(E) = 1/2mv² + 1/2kx²

From equation (4)

E = 1/2kΔx(L+Δx) + 1/2kΔx²

By solving this equation, this becomes

kΔx² + 1/2kΔxL - E = 0

Given,

k=200N/m  L=50cm=0.5m  E=2J

Δx = 0.035 m = 3.5cm

Hence, the spring is stretched about 3.5cm from its natural length as the block moves in this circle.

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The period of the voltage that has a frequency of 60Hz is 0.0166s. Details about period can be found below.

Period in physics refers to the length of time during which the same characteristics of a periodic phenomenon recur.

The period is measured in seconds and is denoted by T. It can be calculated by dividing 1 by the frequency of an oscillation because it is inverse of the frequency.

T = 1/60 = 0.0166s

Therefore, the period of the voltage that has a frequency of 60Hz is 0.0166s.

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The football must have the speed of 0.03 m/s to have the same momentum.

What is momentum conservation:

here,

mass of football, m1 = 150 kg

mass of bullet, m2 = 15 g = 0.015 kg

speed of bullet, v2 = 300 m/s

According to conservation of momentum:

substituting the values in equation,

150* v1 = ( 0.015 )* (300)

v1 =  0.03 m/s

Hence,

The football must have the speed of 0.03 m/s to have the same momentum.

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Answer:

0.0469 gal

Explanation:

177.49 ml is 0.17749 L.

So, 0.17749/3.78 gives the answer

The answer is 0.0469 gallons of chocolate milk a cup can hold which contains 177.44 ml of chocolate milk.

A liquid volume measurement that is equivalent to 231 cubic inches or four quarts is known as Gallon.

To calculate gallons of chocolate milk a cup can hold:

Given,

1 ml = 0.001 L

1 gal = 3.78 L

Convert 177.44 ml to liters:

1 Liter = 1000 ml

177.44 ml * 0.001 L/ml = 0.17744 L

Convert liters (L) to gallons (gal):

= 0.17744 L / 3.78 L/gal

= 0.0469 gal

Thus, a cup that contains 177.44 ml. of chocolate milk holds 0.0469 gal.

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The equation that represents the principle of the lever balance is:

The principle of moments states when a body is in equilibrium, the sum of the clockwise moment about a point equals the sum of anticlockwise moment about that point.

A see-saw represents a balanced system of moments.

The sum of clockwise moment = The sum of anticlockwise moments.

Assuming W1 and W2 are clockwise moments and W3 and W4 are anticlockwise moments.

The equation will b:  W₁ + W₂ = W3 + W4

In conclusion, a balanced see-saw illustrates the principle of the lever balance.

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Diagram A will result in the movement of the block to the left as a result of the forces.

This is referred to an influence which is capable of changing the motion of an object.

Diagram A has equal upward and downward force and left side which is 60N is higher than the right side which has 20N. The block will therefore move to the left.

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If a large star explodes in a supernova and leaves a core that's 10 times the mass of the Sun, the core of the star would collapse.

A star can be defined as a giant astronomical object that contains a luminous sphere of plasma, and it is bounded together by its own gravitational force.

Based on astronomical information, if a large star explodes in a supernova and leaves a core that's 10 times the mass of the Sun, the core of the star would collapse due to its own gravity which creates a violent explosion known as a supernova.

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Answer:

No. They do not undergo any stage of metamorphosis at all. Once they hatch from their eggs, they remain as the same form for the rest of their life. They grow quite a bit, but they do not "morph", or transform, the way caterpillars turn into butterflies.

Voltage is defined as the force that causes electrons to flow. That is option A.

A Voltage is defined as an electromotive force and the potential difference in charge between two points in an electrical field.

It is equally known as the force that causes electrons of a current to flow.

Mathematically, it's = V = current × resistance.

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The act of Adjusting your speed to address one hazard at a time when faced with multiple risks is: (c) Separating

Meaning of separating Hazards

A hazard can be defined primarily as an occurrence that can lead to damage of properties and destruction of live.

separating Hazards can be defined as an act of adjusting one's speed in other to attend to one hazard before another.

In conclusion, The act of Adjusting your speed to address one hazard at a time when faced with multiple risks is: (c) Separating

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I want to examine the surface of a planet that is covered by a thick atmosphere (which includes oxygen and contains a very thick layer of water clouds that never clears). What wavelength of electromagnetic radiation would I be smartest to use: radar waves.

Radars send out electromagnetic waves much like wireless computer networks and cell phones. The signals are despatched out as short pulses which can be reflected by objects of their route, in part reflecting returned to the radar.

The radio waves travel outward from the antenna at the velocity of light (186,000 miles or three hundred,000 km in keeping with the second) and keep going until they hit something.

Then some of them bounce back in the direction of the antenna in a beam of contemplated radio waves also visiting at the speed of light. the speed of the waves is crucially vital.

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The radius of its orbit, measured from Earth's center, will be 1.44 × 10⁷ mm.

Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.

Given data in problem is;

The mass of Earth is, [tex]\rm m_E = 5.98 \times 10^{24} \ kg[/tex]

Gravitational constant, G =6.674 × 10⁻¹¹ N m₂/kg²

The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.

[tex]\rm F_g = \frac{Gm_sm_e}{r^2}[/tex]

The centripetal force due to rotation of the satellite;

[tex]\rm F_c = \frac{m_s v^2}{r}[/tex]

The centripetal and the gravitational force are equal;

[tex]\rm F_g = F_c \\\\ \frac{Gm_sm_e}{r^2} = \frac{m_s v^2}{r} \\\\ r = G \frac{m_E }{v^2 } \\\\ r = G \frac{m_E }{(r \omega )^2 } \\\\ r = \sqrt[3]{\frac{Gm_E}{\omega^2}} \\\\ r = \sqrt[3]{\frac{6.67 \times 10^{-11}(5.98 \times 10^{24})}{(3.63 \times 10^{-4})^2}} \\\\ r = 1.44 \times 10^7 \ mm[/tex]

Hence, the radius of its orbit measured from Earth's center will be 1.44 × 10⁷ mm.

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If the body is in motion, the force operating on it simply produces the motion; however, if the force acting on it is balanced, the body is in a static position and its shape is flexible.

Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body.

Force is explained as the multiplication of mass and acceleration. Its unit is N.

It is the external agent which helps to change the shape and size of an object. Force is used to pushing and pull the object and sometimes changes the direction of motion.

The net force acting on an object is equal to the sum of all forces acting upon it.

F = F1 + F2 + F3

The force is found as;

F=ma

Where,

Force, F

Mass,m

Acceleration,a

Unbalanced forces operating on a body might not modify its dimension, but balanced forces might.

The unbalanced forces act on the body is helps to give the motion to the body and only one application of force can act on the object.

If there is motion in the body the force acting on the body causes only the motion but if the force acting on the body is balanced the body is in static condition and the shape of the body can change.

Hence the given statement is justified unbalanced force acting on a body may not change the dimension and balanced forces may change the dimension.

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Power is needed for (1) acceleration and (2) lifting the loaded chairs. These two parts can be calculated separately and then added together.

(1) Power for acceleration:

The final speed of the lift is

V=(10 km/h)(1 h×1000 m60 sec×1 km)=2.887 m/s.

Then the power needed is

Pa=12m(V2−V20)/Δt=12(50×250 kg)(2.778 m/s)2=9.6 kW.

(2) Power for lift

Assume that the acceleration is constant (i.e. power supply is constant), its value will be

a=ΔVΔt=2.778 m/s5 s=0.556 m/s2.

Then the vertical lift during acceleration will be

(12at2)×(2001000)=1.36 m.

Hence, the power needed to increase the potential energy of the lift is

Pg=mgΔhΔt=(50×250 kg) (9.89 m/s2)(1.36 m)/(5 s)=3.41 kW.

Then the total Power required is

Ptotal=Pa+Pg=9.6+34.1=43.7 kW.

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Answer:

Weight

Explanation:

The second law of motion by Newton can be used to determine weight.

Answer:

because the a and the b both have ones next to them so a is 1 and b is 1 so the sum is 2 and the minus changes because it is within the two lines

Explanation:

The initial amount of electrical energy involved is 120 J

What is Electrical energy:

Here,

we have an initial amount of electrical energy, E.

E is converted into two forms of energy

given light energy, L = 20 J

and the Heat energy, H = 100 J

The law of conservation of energy states that energy cannot be created nor destroyed, but only converted into other forms.

According to The law of conservation of energy:

E = L + H

substituting the values, we get

E = 20 + 100

E = 120 J

So, option D is correct.

The initial amount of electrical energy involved is 120 J

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Your question is incomplete as the figure is missing, but most probably the question was:

How much electrical energy is involved in this transformation?

60 J

80 J

100 J

120 J

Answer:

The acceleration of a point on the wheel is 11.43 m/s² acting radially inward.

Explanation:

The centripetal acceleration acts on a body when it is performing a circular motion.

Here, a point on the bicycle is performing circular motion as the rotation of the wheel produces a circular motion.

The centripetal acceleration of a point moving with a velocity  and at a distance of  from the axis of rotation is given as:

a = v2/r

Here, V = 8m/ s,r = 0.70 m

∴ a = 8/0.70 = 11.43m/ s2

Therefore, the acceleration of a point on the wheel is 11.43 m/s² acting radially inward.
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The magnitude of the second charge needed to propel the first charge is 6,250 C.

The magnitude of the second charge is calculated by applying Coulomb's law as follows;

F = kq₁q₂/r²

where;

Fr² =  kq₁q₂

q₂ = Fr²/kq₁

q₂ = (100 x 750,000²)/(9 x 10⁹ x 1)

q₂ = 6,250 C

Thus, the magnitude of the second charge needed to propel the first charge is 6,250 C.

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0.36 J of work is done in stretching the spring from 15 cm to 18 cm.

To find the correct answer, we need to know about the work done to strech a string.

Thus, we can conclude that the work done is 0.36 J.

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Answer:

Their atoms are spread farther apart

Answer: because gaseous molecules are farther apart

The analogous formula for magnetic fields is the Ampere's law.

To find the answer, we need to know about the Ampere's law of magnetism.

Ampere's law states that the close line integral of magnetic field around a current carrying loop is directly proportional to the current enclosed within it.

Mathematically, Ampere's law is

B•dl= μ₀I

Thus, we can conclude that the analogous formula for gauss law is the Ampere's law in magnetism.

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The ball will return to the thrower's hand with a speed of 10 m/s.

What is straight upward motion:

It is the motion when an object is projected upward, it moves in the opposite direction of the force of gravity.

The velocity is negative while the object moves up and positive while it moves downward due to upward motion.

Here,

A ball is thrown straight upward, u = 10 m/s

final velocity since ball momentarily stops at highest point, v= 0 m/s

According to Newton's 3rd equation of motion:

where,

g = acceleration due to gravity = -9.8 m/s²

h = height

substituting the values,

2(-9.8)h = (0)² - (10)²

h = 100 / 19.6

h = 5.10 m/s

Now, we consider downward motion:

2gh = v² - u²

where,

g  = 9.8 m/s²

h = height = 5.10  m

v = return velocity of ball

u = 0 m/s

substituting the values,

2(9.8)(5.10 m) = V² - (0)²

V = √(99.96)

V = 9.99 m/s

V ≈ 10 m/s

Hence,

the ball will return to the thrower's hand with a speed of 10 m/s.

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The boy has the greater linear velocity.

The linear velocity in a rotatory system is defined as:

v = ω×r

where,

v is the linear velocity

ω is the angular velocity

r is the radius.

As mentioned in the question, they are turning out at a constant rate, so the angular velocities of both the boy and the girl are the same.

The linear velocity now only depends on the radius of the disc, according to the aforementioned inference. The distance from the center has a directly proportional relationship with the linear velocity.

As a result, linear velocity increases as the distance from the center increases.

From the question, it is clear that the boy is farther away from the center than the girl is. The boy has a higher linear velocity as a result.

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Answer:

M au = Fs - M g       au = upwards acceleration; Fs = scale reading

Fs = M (au + g)    scalar quantities where g is positive downwards and au is positive upwards - Fs is the net force acting on the person

If the acceleration is zero Fs = M g  and the scale reads the persons weight

If the elevator is decelerating then au is negative and the scale reading     Fs = (g - au) M     and the scale reading is less than the weight of the person

The wavelengths for frequencies 910 and 2555 MHz are 32.9 and 11.7 cm respectively.

What is frequency:

Frequency describes the number of waves that pass a fixed place in a given amount of time.

What is wavelength:

It is defined as the distance in meter required to complete one circle.

here, two microwave frequencies are given

f1 = 910 MHz = 910* 10^6 Hz

f2 = 2555 MHz = 2555* 10^6 Hz

According to formula of frequency:

where

v is speed of wave.

f is frequency of wave.

All electromagnetic wave moves with same speed v = 3×10⁸ m/s.

for f1:

substituting the values in equation,

λ1 = v / f1

λ1 =  3×10⁸ / 910* 10^6

λ1 = 0.329 m

λ1 = 32.9 cm

for f2:

λ2 = v / f2

λ2 =  3×10⁸ / 2555* 10^6

λ2 = 0.117 m

λ2 = 11.7 cm

Hence,

the wavelengths for frequencies 910 and 2555 MHz are 32.9 and 11.7 cm respectively.

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For this experiment on a solar collector, the variables include the following:

In Science, a variable can be defined as a measurable attribute or physical quantity that changes or varies across an experiment and as such can take on different numerical values.

For this experiment on a solar collector, there are different variables and these include the following:

Furthermore, you should determine both the greatest and smallest rate of temperature change for each of the trials by subtracting the initial temperature from the final temperature based on the numerical values obtained from this experiment.

In conclusion, the trial with the greatest numerical value has the greatest rate of temperature change while the trial with the smallest numerical value has the smallest rate of temperature change

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Complete Question:

1. What are the variables in this investigation?

2. Which trial had the greatest rate of temperature change?

3. Which trial had the smallest rate of temperature change?

Answer:

E = 1/2 M V^2 + 1/2 I ω^2 = 1/2 M V^2 + 1/2 I V^2 / R^2

E = 1/2 M V^2 (1 + I / (M R^2))

For a cylinder I = M R^2

For a sphere I = 2/3 M R^2

E(cylinder) = 1 + 1 = 2       omitting the 1/2 M V^2

E(sphere) = 1 + 2/3 = 1.67

E(cylinder) / E(sphere) = 2 / 1.67 = 1.2

The cylinder initially has 1.20 the energy of the sphere

The PE attained is proportional to the initial KE

H(sphere) = 2.87 / 1/2 = 2.40 m    since it has less initial KE

Block the red and green lights and you get a blue shadow. Block all three lights, you get a black shadow.Block one of the three lights, you get a shadow whose colour is a mixture of the two other colours.

The distribution of colors produced when light is dispersed by a prism.

In this demonstration,

Students experiment with red, green, and blue light to get different shadow colours.

Primary colors are not a fundamental property of light but are related to the physiological response of the eye to light. Light is a continuous spectrum of all of the wavelengths that can be detected by the human eye.

The human eye normally contains only three types of colour ranges of the colour spectrum.

Humans and other species with three such types of color receptors are known as trichromats.

The R, G, B cones are most sensitive to the red, green, and blue wavelengths.

The colours each receptor is the most sensitive to. The blue cone will also pick up purple, blue, and green hues.

Green cones will pick up purple, blue, green, yellow, and orange hues. Red cones will pick up purple, blue, green, yellow, orange, and red hues. The sensitivities of the three cones overlap to let us perceive all visible colours.

Hence,

When red light, blue light, and green light stimulate the three colour receptors on our retinas equally, the signal gets blended in our brain and we see "white" light.

This is why we see sunlight as white light, not as its individual colours.

Slight changes in the relative signals of the cones enable us to see a myriad of different colour combinations, which is why we "see" more than just three colours.

In this demonstration, coloured filters are affixed to flashlights.

The coloured filters block some wavelengths and let others through. The red-filtered flashlight puts out wavelengths from red through to orange and yellow. The green-filtered flashlight puts out yellow, green and blue wavelengths. The blue-filtered flashlight puts out green, blue, and purple wavelengths.

When the three coloured light bulbs all shine on the same surface, we see all the wavelengths from red through to purple, which we perceive as white.

With these three coloured lights you can make shadows of seven different colours:

Blue, red, green, black, cyan (blue-green), magenta (pink), and yellow.

If you block two of the three lights, you get a shadow of the third color.

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A special purpose nozzles that are often lowered through holes or other openings to the cellar of an occupancy are called cellar nozzles.

What is a nozzle:

A nozzle is a device in which steadily flowing fluid can be made to accelerate by a pressure drop along the duct in a cross-sectional area.

So when a fluid flows through a nozzle, its velocity increases continuously and pressure decreases continuously.

There are different types of tips like hollow cone, solid cone or flat fan.

The cellar nozzle (also called a Bresnan nozzle) is designed to be used under the surface the operator is standing on.

Hence,

The cellar nozzles are often lowered through holes or other opening to the cellar of an occupancy.

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