45 m/s is the car's speed at the time of impact.
m=1000 kg
F=90 kN= 90000 N
T= 0.5 seconds
F=mv/t
v=Ft/m
v=90000×0.5 ÷1000
V=45 m/s
Speed is a scalar variable that expresses how much an object's location varies over time or how much it moves per unit of time. It is frequently abbreviated as "s."
The distance traveled by an object during a period of time divided by the length of the period gives the average speed of the object throughout that period.
The speed-related measures are time divided by distance. The most prevalent unit of speed in daily life is the kilometer per hour (kph), but the SI measure of speed is the meter per second (m/s).
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3.a box sits on an inclined plane without sliding. as the angle of inclination increases, the normal force a) increases. b) decreases. c) does not change. d) is directed straight down.
As the angle of inclination increases, the normal force A) increases.
What is normal force ?
In mechanics, the normal force is the component of the contact force normal to the surface in contact with the object. Because normal in this case is used in the geometric sense to mean perpendicular, as opposed to its usual usage meaning "usually" or "usually". A person standing still on the platform would be subject to the gravitational pull toward the core of the Earth, if not for the reaction force from the drag forces of the platform's molecules. This force is called the "normal force".
Normal force is a type of ground reaction force. If a person is standing on a slope and not sinking to the ground or sliding down the slope, the total ground reaction force can be divided into two components:
Vertical forces perpendicular to the ground and frictional forces parallel to the ground.
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What is the distance between two objects if one (a 185,000 kg object) experiences a gravitational force of 0.00200 N due to a 225,000 kg object
Using the gravitational force, the mass of item 1 and object 2, and the Newton's law of gravity calculator, one may calculate the distance between two objects.
How is gravitational distance determined?g = GM/r2, where M is the Earth's mass, r is its radius (or the distance from the Earth's center to where you are standing), and G is the gravitational constant. The gravitational constant is G (without the subscripts), while the speed of light is c.
How is the gravitational force between two objects calculated?By applying Newton's equation, we can accomplish this quite easily: forcegravity is defined as G M m2 separation. Suppose that you weigh 60 kilograms and your colleague weighs 70 kilograms. The center-to-centre distance, r, is 1 m, and the gravitational constant, G, is 6.67 10 -11 newtons square meter kilogram-2.
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Uv rays are a type of ""ionizing radiation"" and are energetic enough to damage biological tissue such that they degrade into ions and electrons. What other forms of electromagnetic radiation do you think could be ionizing?.
Other forms of electromagnetic radiation you think could be ionizing are x-rays and gamma rays.
Ionizing radiation, including nuclear radiation, consists of subatomic debris or electromagnetic waves which have sufficient strength to ionize atoms or molecules by using detaching electrons from them.
Ionizing radiation is a shape of power that acts by using casting off electrons from atoms and molecules of materials that include air, water, and dwelling tissue. Ionizing radiation can journey unseen and bypass these materials. whilst ionizing radiation interacts with cells, it is able to purpose damage to the cells and genetic fabric (i.e., deoxyribonucleic acid, or DNA). If now not properly repaired, this damage can result in the death of the mobile or probably dangerous adjustments in the DNA (i.e., mutations.
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A helium-filled weather balloon is held at ground level. The volume of the balloon is 4800 m3. The pressure of the helium is 98 kPa.
The balloon is released and rises to a height where the volume of the balloon is 7200 m3.
(i) Calculate the new pressure of the helium. Assume that the temperature stays constant.
65.3 kPa is the new pressure of the helium.
V1= 4800 m3
V2= 7200 m3.
P1= 98 kPa.
P2=?
P1V1=P2V2
P2=P1V1/V2
P2= 98×4800÷7200
P2=65.3 kPa.
The definition of pressure is force/area. For instance, the weight of the snow divided by the area of the roof would represent the pressure from snow on a roof. Gases are often where pressure in chemistry originates from. Vacuum is the term for the lack of pressure. Since "nature abhors a vacuum," humans have believed that vacuums are both impossible and unnatural for hundreds of years. This isn't really the case.
The amount of pressure units is insane! The torr or mmHg is a common unit. Simply put, this refers to the height of a mercury column. The atmospheric pressure is about 760 torr, or mmHg. You may also see mmH2O, which employs the same notion, but in this instance the atmospheric pressure is around 10.3 mH2O since water is less dense than mercury.
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A marathon runner is running with an initial velocity of 3.95 m/s. As the runner approaches the finish line, she increases her velocity to 4.17 m/s. What is the acceleration of the runner approaching the finish line?
Given that the time between when the marathon runner changes her velocity and the finish line is t, the acceleration of the runner approaching the finish line is 0.22/t m/s² .
What is acceleration?The acceleration of a body is the change in the velocity of a body with time.
Acceleration is a vector quantity as it takes into account the change in velocity as well as the change in the direction of the body.
Hence, a body is accelerating if either or both of these two conditions apply:
a change in the velocity occursa change in the direction of the bodyMathematically;
acceleration = change in velocity / time takenThe change in velocity of a body = Final velocity - initial velocity
Change in velocity of the runner = 4.17 - 3.95
Change in velocity of the runner = 0.22 m/s
Time taken for this change = t
Hence;
acceleration = 0.22/t m/s²
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How did Copernicus influenced newton
Copernicus influenced Newton as the Copernican Revolution was brought to a close by Sir Isaac Newton's Philosophiae Naturalis Principia Mathematica.
How was Newton influenced?Copernicus, the father of modern astronomy, was a Polish astronomer and mathematician. He was the first European scientist to propose the heliocentric theory of the solar system, which states that Earth and other planets revolve around the sun.
By developing the heliocentric theory of Earth's relationship to our Sun, Nicolaus Copernicus altered how educated people saw the world. The heliocentric theory, which is now widely accepted, states that Earth and the other planets revolve around the Sun.
His laws of planetary motion and universal gravitation were developed to explain the presumed motion of the heavens by asserting a gravitational force of attraction between two objects.
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light that is polarized along the vertical direction is incident on a sheet of polarizing material. only 87% of the intensity of the light passes through the sheet. what angle is the axis of the polarizer oriented, with respect to the vertical?
Polarized light waves are those that have only one plane of vibration. Polarization is the process by which non-polarized light is converted into polarised light. There are numerous ways to polarise light.
A characteristic of transverse waves called polarisation identifies the geometric angle of the oscillations. A transverse wave's oscillation direction is perpendicular to the wave's motion direction.
given
Only 72.0% of the light's intensity makes it through the sheet and hits another sheet of polarising material. The second sheet lets no light flow through it.
Given that no light passes through the second sheet because both sheets are crossed, the angle the transmission axis of the second sheet makes with the vertical is
θ₂ = θ₁ + 90°
= 31.94° + 90°
= 1 21.94°
for the first sheet and
Icos²θ₁ = I
I/I₀ = 0.72
θ₁ = cos⁻¹√(0.72)
= 31.94°
for the second sheet, respectively. This is because the malus law states that I = Iocos²θ₁ for the first sheet.
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Why did the ball move the same distance when it was on the flatbed truck that accelerated 0. 2 m/s?.
The ball moves the same distance when it was on the flatbed truck because of Relative velocity.
The relative velocity of the ball with respect to the truck is same as of truck with respect to ball at equal times.
Relative velocity - Relative velocity is velocity of an object in relation to another object
It is the measure of how fast two objects are moving with respect to each other.
The distance travelled by each object is determined by product of velocity and time of motion
d = vt
where, d= distance
v = velocity
t = time
so here we can say that if the ball is moved the same distance when it was on truck, then the relative velocity of the ball with respect to truck is same as of truck with the ball.
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8. A bullet is fired horizontally from a gun. At the same time and from the same height,
a bullet is dropped. If we neglect the effects of air resistance, how will the time the
two bullets spend in the air compare to each other?
a. the bullet that is fired will spend less time in the air, hitting the ground first.
b. there is not enough information to determine this.
c. both bullets will spend the same amount of time in the air, landing at the same time.
d. the bullet that is fired will spend longer in the air, landing later.
Answer:
C hit the ground at the same time
Explanation:
Both bullets have to fall the same VERTICAL distance and are affected by gravity the same way in this regard.
an 8.0 kg object has a moment of inertia of 1.00 kg m2. what torque is needed to give the object an angular acceleration of 1.5 rad/s2?
The torque required to give the object an angular acceleration of 1.5 rad/s² is 1.5 Nm.
TorqueObjects that move in a translational manner use Newton's II law (∑F = ma)and objects that move in a rotational manner also use the same concept of Newton's laws, but the quantity use rotational quantity . Then, Newton's Second Law for objects that move in a rotational manner or move in a circle uses the formula:
τ = (the moment inertia) x (the angular acceleration of the object)
With,
τ = is the total torque acting on the object (Nm)
I = is the moment of inertia of the object (kgm²)
α = is the angular acceleration of the object (r4d/s²)
So, the required torque is:
τ = (1.00 kgm²) (1.5 r4d/s²)
= 1.5 Nm
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an electric fan is plugged into an outlet and the circuit completed, making the fan blades spin. which of the following correctly describes this situation? responses mechanical energy is transformed into electrical energy. mechanical energy is transformed into electrical energy. mechanical energy is destroyed, and electrical energy is created. mechanical energy is destroyed, and electrical energy is created. electrical energy is transformed into mechanical energy. electrical energy is transformed into mechanical energy. electrical energy is destroyed, and mechanical energy is created. electrical energy is destroyed, and mechanical energy is created.
The situation is correctly described as Electrical Energy is transformed into mechanical energy.
Recalling the working of a fan, i.e. as the circuit is closed, the electrons start flowing in the wires, producing current and hence the current reaches the fan, which rotates due to the magnets in it. Hence the Electrical energy is transformed into Mechanical Energy which is the kinetic energy produced due to rotation of wings of fan.
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A baseball player dives head-first into
second base and slows down while sliding on the infield dirt.
Of the forces listed, identify which act upon the player.
1.Normal
2.Gravity
3.Applied
4.Friction
5.Tension
6. Air Resistance
Answer:
Explanation:
Discussion
The ones that are certain are
Normal GravityFrictionIf you have a normal, and the player slides into 2nd, and stops (which he must before he is tagged), then there must be friction involved. There must be gravity, or he would keep going up.
I don't think there is tension. There might be some Air Resistance, but that force is very tiny. Don't be surprised if you answer includes Air Resistance, but I won't try it to begin with.
Fill in the blanks below
Since the diagram above shows fossils and rock features, X is an intrusion that is younger than layers Y and Z. Therefore, the correct answer option is: intrusion, younger than layers Y and Z.
What is a fossil?In Science, a fossil can be defined as the mineral impression or remains of both living and non-living organisms that are generally considered to be prehistoric in nature.
Additionally, rock strata (layers) that are found in various parts of the world are usually unique and different from one another because they are all composed of distinct geological history of planet Earth, which are commonly referred to as fossils.
This ultimately implies that, fossils are ancient organisms such as plants and animals that were formed into rocks.
By critically observing the rock strata (layers) shown in the image attached above, we can reasonably infer and logically deduce that X would be classified as an intrusion and it is younger than rock layers Y and Z.
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a constant torque of 31.4 space n times m is exerted on a pivoted wheel. if the angular acceleration is 4 pi space rad divided by s squared, then the moment of inertia will be
The moment of inertia will be 2.5kgm².
Inertia method an item will keep its present-day movement till a few force causes its speed or course to change. The term is nicely understood as shorthand for "the principle of inertia" as described with the aid of Newton in his first regulation of motion.
Inertia is a property of count number that causes it to withstand changes in pace (pace and/or path). consistent with Newton's first regulation of movement, an object with a given speed maintains that velocity except acted on by an external pressure.
Inertia is the pressure that holds the universe together. literally. without it, count number would lack the electric forces vital to shaping its present-day arrangement. Inertia is counteracted by way of the warmth and kinetic strength produced with the aid of transferring debris.
Calculation:-
τ=Iα
31.4=I×4π
31.4=I×4(3.14)
⟹I=2.5kgm²
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6. Borax was mined in Death Valley, California, during the nineteenth century. It
was transported from the valley by massive wagons, each pulled by a team of
21 mules. Suppose each mule's power output was 746 W (about 1 hp). If in a
certain time interval the total work done by the team on the wagon was
2.35x 10' J, how long was that interval of time?
The interval of time it takes for the team to do a work of 2.35×10⁷ J is 15000 seconds.
What is time?Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.
To calculate the time interval the work was done by the team on the wagon, we use the formula below.
Formula:
t = W/P........... Equation 1Where:
t = Interval of time it takes the team to do the workW = Total work done by the team on the wagonP = Power output of the teamFrom the question,
Given:
W = 2.35×10⁷ JP = 746×21 ( If each mole power output is 746 W)P = 15666 WSubstitute these values into equation 1
t = 2.35×10⁷/15666t = 1500 seconds.Hence, the interval of time it takes to the the work is 15000 seconds.
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A horizontal pipe 10. 0 cm in diameter ha a mooth reduction to a pipe 5. 00 cm in diameter. If the preure of the water in the larger pipe i 8. 00 104 Pa and the preure in the maller pipe i 6. 00 104 Pa, at what rate doe water flow through the pipe?
The rate at which water flow through the pipe is 12.83 kg/s.
What is Bernoulli’s equation?Bernoulli's theorem, is based upon law of conservation of energy. Equalize the total energy (pressure energy, potential energy, and kinetic energy) of a flowing liquid at different points flowing under a constant pressure difference. Bernoulli's equation states that points 1 and 2 are on the streamline, the liquid has a constant density, and the flow is stable with no friction.
D₁ = 10 cm
D₂ = 5 cm
P₁ = 8×10⁴ Pa
P₂ = 6×10⁴ Pa
Let's apply Bernoulli’s equation for the wide and reduced part of this pipe:
P₁+ ¹/₂ρυ₁² = P₂ + ¹/₂ρυ₂²
Now, apply continuity equation:
A₁v₁ = A₂v₂
(D₁²π/4) v₁ = (D₂²π/4) v₂
D₁² v₁ = D₂² v₂
v₂ = (D₁/ D₂)² v₁
v₂ = (10/ 5)² v₁
v₂ = 4 v₁
Now,
P₁+ ¹/₂ρυ₁² = P₂ + ¹/₂ρ4υ₁²
P₁+ ¹/₂ρυ₁² = P₂ + 8ρυ₁²
P₁ - P₂ = 8ρυ₁² - ¹/₂ρυ₁²
P₁ - P₂ = 15/2ρυ₁²
Substitute the values in above equation:
8×10⁴ - 6×10⁴ = 15/2×1000υ₁²
υ₁ = 1.63 m/s
So, volume flow rate is:
ρA₁v₁ = ρ(D₁²π/4)v₁
= 1000×(10²×3.14/4)×1.63
= 12.83 kg/s
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a particle is projected horizontally at 10m/s from the top of a tower 20m high.
calculate the horizontal distance travelled by the particle.( g=10m/s^2)
figure shows a silver ribbon whose cross section is 1.0 cm by 0.20 cm. the ribbon carries a current of 110 a from left to right, and it lies in a uniform magnetic field of magnitude 1.25 t. using a charge density value of n
72.828×[tex]10^{-7}[/tex]Volt is the Hall potential between the edges of the ribbon.
We know that Hall potential is given by =IB/qnd where
I is the current flowing
,B is the magnetic field ,
q is the charge of the electron,
n is the charge density of electron,
and d is the thickness
So, we are given that current(I)=110Ampere,magnetic field(B)=1.25Tesla,
charge of electron(q)=1.6×[tex]10^{-19}[/tex]C, charge density (n)= 5.9x1028,thickness
(t) as 2.cm
So, putting the values of the respected quantities on the above formula ,we get
Hall potential([tex]V_h[/tex])=(110×1.25)/(1.6×[tex]10^{-19}[/tex]×5.9×[tex]10^{28}[/tex]×0.2×[tex]10^{-2}[/tex])
=>([tex]V_h[/tex])=[137.5/1.888]×[tex]10^{-7}[/tex]
=>([tex]V_h[/tex])=72.828×[tex]10^{-7}[/tex]Volt.
Hence, the Hall potential is 72.828×[tex]10^{-7}[/tex]Volt.
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(Complete question) is:
Figure shows a silver ribbon whose cross section is 1.0 cm by 0.20 cm. The ribbon carries a current of 110 A from left to right, and it lies in a uniform magnetic field of magnitude 1.25 T. Using a charge density value of n = 5.9x1028 electrons per cubic meter for silver, find the Hall potential between the edges of the ribbon.
A spring has an unstretched length of 11 cm . It exerts a restoring force F when stretched to a length of 12 cm. For what total stretched length of the spring is its restoring force 3F? At what compressed length is the restoring force 2F?
Using the spring constant relation, the required length and compressed length of the spring at the given force values are 14 cm and 9 cm respectively.
A.) Using the given formula,
F = ke
Where k = spring constant , e = extension and e = (Final length - Initial length)
Initial length, l = 11
Final length = L1 = 12
F = k(12 - 11)
F = k(1)
F = k
Length for a restoring force of 3F ;
3F = k (Final length - Initial length)
k = F
3F = F(L1 - 10)
3F = - 11F + F(L1)
F(L1) = 3F + 11F
F(L1) = 14F
L1 = 14 cm
Hence, required length is 14 cm
B.) Let compressed length = c
2F = F(initial length - compressed length)
2F = F(10 - c)
2F = 11F - F(c)
F(c) = 11F - 2F
F(c) = 9F
c = 9F / F
c = 9 cm
Therefore, the required compressed length is 9 cm
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Since the drag force is proportional to the square of speed, what can you do to improve your car’s gas mileage?.
The answer is Aerodynamic Shaping.
Aerodynamic Shaping can reduce the drag force of an automobile and hence Increase the car's gas mileage. Integrated into the overall shape of an aerodynamic car are the wheel arches and headlights that reduce drag while also reducing wind resistance.
AeroDynamics is basically the study of how air move arround the things which deal with lift, drag, thurst and weight.
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a car is traveling 21 m/s when the driver sees a child standing in the road. he takes 0.8s to react then steps on the breaks and slows at 7.5m/s^2. how far does the car go before it stops?
The distance traveled by the car before it stops when moving with a velocity of 21 m/s is 19.2 m.
What is distance?Distance is the total length between two points.
To calculate the distance the car move before stopping, we use the formula below.
Formula:
S = ut+at²/2......... Equation 1Where:
S = Distanceu = Initial velocityt = Timea = accelerationFrom the question,
Given:
u = 21 m/st = 0.8 sa = 7.5 m/sSubstitute these values into equation 1
S = (21×0.8)+(7.5×0.8²/2)S = 16.8+2.4S = 19.2 mHence, the distance traveled by the car before it stops is 19.2 m.
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If it takes an object 3.5 seconds to make one revolution, what is its frequency?
If it takes an object 3.5 seconds to make one revolution, its frequency is 0.286 Hz.
What is frequency?The number of vibrations counted per second is called frequency. A wave is a group of vibrations that are referred to as energy. The bottom node is known as the crest, and the top node is known as the trough.
The frequency of an alternating current is the number of full cycles per second. The hertz, also known as Hz, is the accepted unit of frequency. The frequency of a current is 1 Hz if one cycle is completed per second; 60 cycles per second equals 60 Hz.
Frequency = 1/t
Frequency = 1/3.5
Frequency = 0.286 Hz
If it takes an object 3.5 seconds to make one revolution, its frequency is 0.286 Hz
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2. A 10kg block of wood is pulled across a level ground by fore of 15N applied at
an angle of 30 degree from the horizontal. How much work is done, if it is moved
to a distance of 3m?
(Note: F applied = 15N x cos 30 degree, cos 30 degree = 0.5)
Answer:
about 19.49J
Explanation:
Work = F × D × Cosine(θ)
Substitute values :D:
Work= 15N x cos 30 degree x 3m x cos 30
Work= 7.5 x 3 x cos 30
Work= about 19.49 joules
Why aren’t there solar and lunar eclipses every month?
A. Because clouds in Earth’s atmosphere block the Moon’s shadow.
B. Because of the gravitational effects of Jupiter on the Sun.
C. Because the Moon’s orbit is tilted with respect to Earth’s orbit.
D. There are, it’s just that we cannot detect all of them.
Answer:
The answer is C.
When Earth is positioned precisely between the Moon and Sun, Earth's shadow falls upon the surface of the Moon, dimming it and sometimes turning the lunar surface a striking red over the course of a few hours which is how a lunar eclipse happens.
When the Moon orbits Earth, the Moon moves between the Sun and Earth. When this happens, the Moon blocks the light of the Sun from reaching Earth. This causes an eclipse of the Sun, or a solar eclipse. During a solar eclipse, the Moon casts a shadow onto Earth.
How do you think you can calculate the total distance traveled if you were running at a constant speed?.
Distance = Speed x Time is a formula for calculating the total distance one covered while running at a constant speed.
To determine the total distance travelled if one is running at a constant speed we use formula:
d = s x t
d = distance covered
s = speed of the object
t = time taken.
The distance travelled is directly proportional to the amount of time required when the speed is constant.
d ∝ t
(at constant speed)
Distance = Speed x Time, is a formula for calculating the total distance one covered while running at a constant speed.
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A rock suspended by a string weighs 5 n out of water and 3 n when submerged. What is the buoyant force on the rock?.
The buoyant force exerted on the rock is 2 N.
What is buoyant force?Buoyancy is the upward force exerted by a liquid that opposes the weight of a partially or fully submerged object. In a liquid column, the pressure increases with depth due to the weight of the liquid above. Buoyancy exists whether an object is floating or submerged. The SI unit of buoyancy is Newton. The factors on which buoyancy depends are:
Volume of the liquid displacedVolume of the body submerged in liquidFor the given case,
Weight of the rock out of water (W₀) = 5N
Weight of the rock when submerged in water (Wₙ) = 3N
Now what decreases the weight of rock in water? It is the buoyant force exerted by water, which can be can be calculated as:
Fᵇ = W₀ - Wₙ
Fᵇ = 5N - 3N
Fᵇ = 2N
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This question is typical on some driver’s license exams: A car moving at 43 km/h skids
14 m with locked brakes.
How far will the car skid with locked brakes
at 129 km/h? Assume that energy loss is due
only to sliding friction.
Answer in units of m
Answer:
Braking distance 126 meters
Explanation:
Given:
V₁ = 43 km/h = 43 000 m / 3 600 s ≈ 12 m/s
D₁ =14 m
V₂ = 129 km/h = 129 000 m / 3 600 s ≈ 36 m/s
____________________
D₂ - ?
D₁ = V₁² / (2·a)
2·a·D₁ = V₁²
a = V₁² / (2·D₁)
D₂ = V₂² / (2·a) = V₂²·2·D₁ / (2·V₁²) =
= V₂²·D₁ / V₁² = D₁·(V₂ / V₁)²
D₂ = 14·(36 / 12)² = 14·3² = 126 m
The braking distance has increased 9 times!
historically, it turned out that einstein's theory could explain everything newton's theory could, while also explaining more. what quality is it most accurate to say that einstein's theory has based on this brief description?
Scope quality is it most accurate to say that einstein's theory has based on this brief description.
According to Einstein's theory of relativity, the curvature of space and time is what causes what we experience as the gravitational force. This is the fundamental tenet of Einstein's theory of general relativity, which is frequently encapsulated in the sentence: "Matter instructs spacetime to curve, and curled spacetime instructs matter to move." Based on Einstein's astounding discovery that light always moves at a constant speed, regardless of how fast you're moving when you measure it, the theory, which revolutionized our understanding of time and space, was developed. Light in the quantum realm. The photons that make up light, or photons, are tiny energy packets with wavelike characteristics, as demonstrated by Einstein's quantum theory of light. In this theory, Einstein also described the process by which electrons are released from metals after being struck by lightning.
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what is the minimum energy input necessary to place this satellite in orbit? ignore air resistance but include the effect of the planet's daily rotation. (use the following as necessary: re, me, g, m, h, and te for the period of earth's rotation.)
The minimum energy input necessary to place this satellite in orbit is
[tex]\frac{1}{2} m(v^{2} - v_{e} ^{2} ) +GM_{E} m(\frac{1}{r} -\frac{1}{R_{E} } )[/tex]
The mass of the satellite = m
Altitude = h = r
The radius of the Earth = [tex]R_{E}[/tex]
The Mass of the Earth = [tex]M_{E}[/tex]
Speed of the satellite = v
Speed of the Earth = [tex]v_{e}[/tex]
Gravitational Constant = G
The energy at the surface of the Earth will be the sum of the kinetic and potential Energy,
So,
[tex]E_{i} = K.E. +P.E.\\\\ E_{i} = \frac{1}{2} mv_{e} ^{2} -\frac{GM_{E} m}{r}[/tex]
Also, Energy in orbit,
[tex]E_{i} = K.E. +P.E.\\\\ E_{i} = \frac{1}{2} mv^{2} -\frac{GM_{E} m}{R_{E} }[/tex]
Now, The change in energy is the minimum energy required to place this satellite in orbit,
Then, the Change in Energy =
∆E [tex]= \frac{1}{2} m(v^{2} - v_{e} ^{2} ) +GM_{E} m(\frac{1}{r} -\frac{1}{R_{E} } )[/tex]
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. ****an elastic cord is 80. cm long when it is supporting a mass of 10. kg hanging from it at rest at rest. when an additional 4.0 kg is added, the cord is 82.5 cm long. hint: 4 kg stretches the cord 2.5 cm!!
An elastic cord with natural length of 80 cm stretched to 82.5 cm when an additional 4 kg mass attached. The spring constant of the cord is 1600 N/m
According to the Hooke's Law, the force applied on a string is directly proportional to the length of extension ( or compression).
F = kx
Where:
F = applied force
k = spring constant
x = length of extension/compression
Data given from the problem:
Natural length = 80 cm
The length of stretch when an additional 4 kg mass added = 82.5
Hence,
x = length of extension = 82.5 - 80 = 2.5 cm = 2.5 x 10⁻² m
The force = 4 x 10 = 40 N
Hence, the spring constant:
k = F / x = 40 / (2.5 x 10⁻²) = 1600 N/m
Complete question:
an elastic cord is 80. cm long when it is supporting a mass of 10. kg hanging from it at rest at rest. when an additional 4.0 kg is added, the cord is 82.5 cm long. hint: 4 kg stretches the cord 2.5 cm!!
a. What is the spring constant of the cord?
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