When the spring is stretched by 15.2 cm = 0.152 m, the spring exerts a restorative force with magnitude (due to Hooke's law)
[tex]F = kx[/tex]
where [tex]k[/tex] is the spring constant. Solve for [tex]k[/tex].
[tex]49.1\,\mathrm N = k (0.152\,\mathrm m) \implies k \approx 323 \dfrac{\rm N}{\rm m}[/tex]
The amount of work required to stretch or compress a spring by [tex]x\,\mathrm m[/tex] from equilibrium length is
[tex]W = \dfrac12 kx^2[/tex]
Then the work needed to stretch the spring by 15.2 cm is
[tex]W_1 = \dfrac12 \left(343\dfrac{\rm N}{\rm m}\right) (0.152\,\mathrm m)^2 \approx 3.73\,\mathrm J[/tex]
and by 15.2 + 13.7 = 28.9 cm is
[tex]W_2 = \dfrac12 \left(343\dfrac{\rm N}{\rm m}\right) (0.289\,\mathrm m)^2 \approx 13.5\,\mathrm J[/tex]
so the work needed to stretch from 15.2 cm to 28.9 cm from equilibrium is
[tex]\Delta W = W_2 - W_1 \approx \boxed{9.76\,\mathrm J}[/tex]
a force of 3600 n is exerted on a piston that has an area of 0.040 m2 what force is exerted on a second piston that has an area of 0.20 m2 use f1 a1= f2 a2
Using the Pascal's principle formula, the force exerted on the second piston is 18000 N.
What is the force exerted on the second piston?The force on the second piston is determined using the formula from Pascal's principle.
The formula is given below:
[tex]\frac{f_{1}}{A_{1}} = \frac{f_{2}}{A_{2}}[/tex]
Solving for the force on the second piston, [tex]{f_{2}[/tex]
[tex]{f_{2} = \frac{A_{2}\times f_{1}}{A_{1}}[/tex]
[tex]{f_{2} = \frac {0.2\times3600}{0.04} = 18000 N[/tex]
In conclusion, the force on the second piston is 18000 N.
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The force of gravity, just as all forces, is an action on an object. Forces appear due to the interactions between pairs of objects. Therefore, for the force of gravity to act on a falling object, there should be another object that, in a sense, is creating that force. Which object is responsible for creating the force of gravity observed on falling objects
The Earth as a whole is responsible for creating the force of gravity observed on falling objects.
How is earth responsible?As the earth pulls the objects lower due to its gravity, the objects typically fall towards the earth by Gravitational force.
The law of gravitation states that the force of attraction between any two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. Anywhere in the universe, the law is applicable to objects. One claims that this law is ubiquitous.
The mass and density of the planet, 5.97237 1024 kg (1.31668 1025 lbs) and 5.514 g/cm3, respectively, determine the force of Earth's gravity. Because of this, Earth has a gravitational pull of 9.8 m/s2 at its surface or 1 g. This pull naturally weakens the further one goes from the surface.
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How does the area of triangle rst compare to the area of triangle lmn? the area of △rst is 2 square units less than the area of △lmn. the area of △rst is equal to the area of △lmn. the area of △rst is 2 square units greater than the area of △lmn. the area of △rst is 4 square units greater than the area of △lmn.
The area of △rst is equal to the area of △lmn.
The answer is option B.
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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A 50.0-kg person steps on a scale in an elevator. The scale reads 5000 N. What is the magnitude of the acceleration of the elevator
The magnitude of the acceleration of the elevator is 90m/s^2
Due to Newton's Law ∑ Forces in direction of motion is equal to mass
multiplied by the acceleration
We have here two forces 5000 N in direction of motion and the weight of the person in opposite direction of motion
The weight of the person is his mass multiplied by the acceleration of gravity
So ,
W = mg , where m is the mass and g is the acceleration of gravity
m = 50 kg and g = 9.8 m/s²
Substitute these values in the rule above
W = 50 × 9.8 = 490 N
The scale reads 5000 N
F = 5000 N , W = 490 N , m = 50kg
F - W = ma
5000 - 490 = 50 a
4510 = 50 a
Divide both sides by 50
a = 90.2 m/s²
Hence the acceleration is 90m/s^2
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Lexy used the formula shown to calculate the force of gravity on a space shuttle.
Fg = GStartFraction (3 times 10 Superscript 5 Baseline kilograms) (6 times 10 Superscript 24 Baseline kilograms) over [(6.4 times 10 Superscript 6 Baseline m) + (1.8 times 10 Superscript 5 Baseline m)] Superscript 2 EndFraction
What does 3 × 105 kg represent?
the difference between Earth’s mass and the space shuttle’s mass
the sum of Earth’s mass and the space shuttle’s mass
the mass of Earth
the mass of the space shuttle
What 3 × 105 kg represents is the mass of Earth. Option D. This is further explained below.
What does 3 × 105 kg represent?Generally, the absence of discernible form in a huge mass of material
In conclusion, Transportation between Earth and space is accomplished by means of the space shuttle.
It gets people to spaceships in orbit. The mass of the space shuttle is 3108 kg.
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Answer:
D
Explanation:
A toy dart gun uses a spring with a spring constant of 35 N/m. To use the dart gun, you compress the spring by pushing in a dart of mass 0.002 kg.
a. If you compress the spring by 0.02 m, what force is the spring exerting on the dart?
b. With the spring compressed 0.02 m, how much elastic potential energy is stored in the spring?
c. If you release the spring, it pushes the dart forward. What is the kinetic energy of the dart when it reaches the natural length of the spring? Explain how you found the answer.
d. What is the speed of the dart when it reaches the natural length of the spring?
(a) The force is the spring exerting on the dart is 0.7 N.
(b) The elastic potential energy stored in the spring is 7 x 10⁻³J.
(c) The kinetic energy of the dart when it reaches the natural length of the spring is 7 x 10⁻³J.
(d) The speed of the dart when it reaches the natural length of the spring is 2.65 m/s.
Force the spring exerting on the dart
F = kx
where;
k is spring constantx is compression of the springF = 35 N/m x 0.02 m
F = 0.7 N
Energy stored in the springU = ¹/₂kx²
U = ¹/₂(35)(0.02)²
U = 7 x 10⁻³ J
Kinetic energy of the dartThe elastic potential energy of the spring will be converted into kinetic energy of the dart, with a magnitude of 7 x 10⁻³ J when it reaches natural length of the spring.
Speed of the dartK.E = ¹/₂mv²
v² = (2K.E)/m
where;
v is the speed of the dartm is mass of the dartv² = (2 x 7 x 10⁻³)/(0.002)
v² = 7
v = 2.65 m/s
Thus, the force is the spring exerting on the dart is 0.7 N.
The elastic potential energy stored in the spring is 7 x 10⁻³J.
The kinetic energy of the dart when it reaches the natural length of the spring is 7 x 10⁻³J.
The speed of the dart when it reaches the natural length of the spring is 2.65 m/s.
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How much horsepower is produced by 2023 z’s 3. 0-liter twin-turbo 6-cylinder engine?.
400 horsepower is produced by 2023 z's 3. 0-liter twin-turbo 6-cylinder engine.
What is horsepower?The power an engine produced is referred to as horsepower. In the British Imperial System, one horsepower equals 33,000 foot-pounds of work per minute, i.e., the force required to lift a mass of 33,000 pounds off the ground in a single motion for one minute.
The new Z's 3.0-liter twin-turbo V6 engine produces 400 horsepower and 350 pound-feet of torque. This is 68 horsepower and 80 lb-ft more than the previous 370Z. The 6-speed manual transmission that comes standard or the optional 9-speed automatic transmission with paddle shifters are both paired with this one engine option.
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The work required to accelerate an object initially at rest to a speed v0 is W. What is the additional work needed to increase its speed from v0 to 2v0? Group of answer choices W W/2 2W 3W None of them
The additional work needed to increase its speed from v0 to 2v0 is D)3W.
Work done is equal to a change in kinetic energy
w = 1/2mv^2-0
= 1/2mv^2
When v is 2v
w new = 1/2*m*(2v)^2 - 1/2mv^2
= 4 * 1/2mv^2 - 1/2mv^2
=4w-w
=3w
Kinetic electricity is a shape of electricity that an item or a particle has with the aid of the purpose of its motion. If work, which transfers energy, is carried out on an object by applying an internet pressure, the item quickens and thereby profits kinetic strength.
Types of Kinetic Energy.
radiant, thermal, sound, electrical,mechanical.Kinetic energy (KE) is the energy of a frame in movement, because of this, it's essentially the power of all moving items. it's far one of the fundamental forms of power, together with capability energy, which is the saved electricity contained inside items for relaxation.
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The additional work needed to increase its speed from v0 to 2v0 is D)3W.
Work done is equal to a change in kinetic energy
w = 1/2mv^2-0
= 1/2mv^2
When v is 2v
w new = 1/2*m*(2v)^2 - 1/2mv^2
= 4 * 1/2mv^2 - 1/2mv^2
=4w-w
=3w
Kinetic electricity is a shape of electricity that an item or a particle has with the aid of the purpose of its motion. If work, which transfers energy, is carried out on an object by applying an internet pressure, the item quickens and thereby profits kinetic strength.
Types of Kinetic Energy.
radiant,thermal,sound,electrical,mechanical.Kinetic energy (KE) is the energy of a frame in movement, because of this, it's essentially the power of all moving items. it's far one of the fundamental forms of power, together with capability energy, which is the saved electricity contained inside items for relaxation.
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A 4.0-kg and a 6.0-kg box rest side-by-side on a perfectly smooth, level floor. A horizontal force of 15 N is applied to the 4.0-kg box pushing it against the 6.0-kg box, and, as a result, both boxes slide along the floor. How hard do the two boxes push against each other
7.5 N against each other
Given the mass of the two boxes are 4 kg and 6 kg
calculate the common acceleration of the two boxes when they join together
F = ma; m = (4 +6)kg and F = 15N
a = F/m
a = 15/10 = 1.5 m/s²
Calculate the impact force of 4 kg box on 6 kg box
F = ma
F = 4 X 1.5 = 6 N
Calculate the force of 5kg box when it accelerate on 1.5m/s²
F = ma
F = 5 X 1.5 = 7.5N
Calculate the opposing force of 5kg box
F = 15N -7.5N = 7.5N
Therefore, each box exerts a force of 7.5 to the other in opposite direction.
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A mass m is placed on an inclined plane (m > 0) and slides down the plane with constant speed. If a similar block (same m) of mass 2m were placed on the same incline, it would:
A mass m is placed on an inclined plane (m > 0) and slides down the plane with constant speed. If a similar block (same m) of mass 2m were placed on the same incline, it would
For 2m, the gravitational force pressing downward on the plane is twofold. However, the normal force is also doubled, and as a result, so is the friction force (the same factor). This indicates that the two forces continue to cancel and produce a net force of zero.Gravitational forceThe force that binds all masses in the universe together, particularly the pull of the earth's mass on objects that are close to its surface.The attracting force that the earth exerts on all other objects in the cosmos is known as gravitational force. A ball being flung high and then falling back to the earth as a result of gravitational force is an example of gravitational force.Learn more about gravitational force here:
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A total of 590 C of charge passes through a flashlight in 0.470 h. What is the average current in milliamperes
Answer:
I = Q / t = 590 C / (.47 * 3600 sec) = .349 amperes
.349 amps * 1000 milliamps / amp = 349 milliamperes
The weight of a person on Earth is 67.0 N. If the gravitational acceleration on the moon is 1.62 m/s2, calculate the person’s weight on the moon.
Group of answer choices
A) 56.0 N
B) 11.0 N
C) 108 N
D) 4.00 N
Answer:
[tex] \large{ \boxed{ \tt{b) \: 11.0 \: N}}}[/tex]- Please see the attached picture for full solution!:)
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what is one standard kilogram
The Kilogram was for many years the only one of the seven SI base standards that was not defined in terms of a fundamental attribute of nature.
It was specified as the weight of a platinum-iridium cylinder stored in a lab outside of Paris under inert conditions.
The problem with that is that it needs to be managed in order to use such a standard for calibrating exact copies. No matter how meticulously you do it, surface molecules must experience some minimal impact.
Therefore, efforts have continued to find a replacement standard that is not a tangible thing. With the suggestion for a new Standard Kilogram utilizing a gadget called the Kibble Balance, it now seems that the quest is over.
Answer:
one standard kilogram is the mass of cylinder made up of platinum-iridum alloy with equal diameter and base kept Ar international bureau of weight and measures near paris
In a game of tennis, a ball traveling at is hit by a racket and travels in the opposite direction at . True or False: There is a change in momentum.
The momentum is changed when the ball is hitted by racket in the tennis game.
To find the answer, we need to know about the momentum.
What's momentum?Momentum of an object is given by the product of mass and the velocity of the ball.Also the rate of change of the momentum with time is called as force.How does the momentum change when a ball hitted by racket?In the game of tennis, the ball is hitted by the racket. And at the time of hitting a delta force is given to that ball.As a force is applied to the ball, so we must find a change in momentum in very small time interval.Thus, we can conclude that the momentum is changed when the ball is hitted by racket in the tennis game.
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A student has three springs A, B and C. He measures the length of each spring, in turn, when
different weights are placed on the end of each spring.
His table of results is shown in Fig. 3.1
(a)(i) The spring C has been stretched past the limit of proportionality.
(ii) Spring stretched within the limit of proportionality is equal to the increase in weight and in turn increase in the length of spring.
(iii) The un-stretched length of spring A is 4.5 cm.
What is weight?The weight of any object is the mass times the acceleration due to gravity on Earth or any other planet.
Weight W = mg
where g = 9.81 m/s²
Given, a student has three springs A, B and C. He measures the length of each spring, in turn, when different weights are placed on the end of each spring. His table of results is shown in Figure.(a)
(i) The spring C has been stretched past the limit of proportionality.
(ii) Spring stretched within the limit of proportionality is equal to the increase in weight and in turn increase in the length of spring.
In case of spring C, there is an unequal increase in weight and length of spring of 0.8 cm, when weight change from 1 to 1.5 N and 1.8 cm increase , when weight change from 2 to 2.5 N.
(iii) The natural length of spring be Xo and X is the increase in length due to 1N weight.
So, the equations formed will be
Xo + X = 6.1 cm....................(1)
Xo + 2X = 7.7 cm....................(2)
Solving both the equations, we get
X = 1.6 cm and Xo = 4.5 cm
Thus, the un-stretched length of spring A is 4.5 cm.
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Question )
A snail covers a distance of 90 meter in 24 hours calculate the average speed of the snail.
Answer:
1.042 × 10⁻³ m/s
Explanation:
average speed = [tex]\frac{total \space\ distance \space\ covered}{time \space\ taken}[/tex]
In this case,
• distance covered = 90 m,
• time taken = 24 hours = 24 × 60 = 1440 min = 1140 × 60 = 86400 s
Substituting these values into the formula:
average speed = [tex]\frac{90}{86400}[/tex]
= 1.042 × 10⁻³ m/s
Answer:
3.75 meters per hour
Explanation:
[tex]\boxed{\sf Speed = \dfrac{Distance}{Time}}[/tex]
Given:
Distance = 90 metersTime = 24 hoursSubstitute the given values into the formula to calculated the speed:
[tex]\implies \sf Speed = \dfrac{90\:m}{24\:h}[/tex]
[tex]\implies \sf Speed = 3.75\:m/h[/tex]
Therefore, the average speed of the snail is 3.75 meters per hour.
To calculate the speed in meters per minute, divide by 60:
[tex]\implies \sf Speed = \dfrac{3.75\:m/h}{60}=0.0625\:m/min[/tex]
To calculate the speed in meters per second, divide by 60 again:
[tex]\implies \sf Speed = \dfrac{0.0625\:m/min}{60}=0.001042\:m/s\:\:(4\:s.f.)[/tex]
True or false cells of humans and plants are same.
How are mircowaves similar to radio waves
Microwaves is similar to radio waves such that they are both an electromagnetic wave of lower wavelength and high frequency.
What is a Wave?This is referred to a disturbance which carries energy without movement of the particles.
Microwaves and radio waves both have a low wavelength and high frequency which makes them similar to each other.
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The speed that a tsunami can travel is modeled by the equation , where s is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?.
0.32 km
How to reach the answer:
The formula below provides the tsunami's speed in response to the query.
s = 356√d
when the tsunami's speed is 200 km/h, the equation's "s" is changed to "200," and the equation of speed is then expressed as follows.
200 = 356√d
The equation can be changed to compute the depth of the water as,
√d = 200÷356
√d = 0.562
Now on squaring both sides:
(√d)² = (0.562)²
d = (0.562)² = 0.316 or 0.32
Therefore the approximate depth of water for a tsunami travelling at 200km/h is 0.32 km
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If someone was to
place a cool lid on this
pot of boiling water,
what would happen?
A. The water particles will lose energy once they touch
the lid.
B. The water particles will gain energy once they touch
the lid.
C. The water particles will get locked in place once they
touch the lid.
Answer:B. The water particles will gain energy once they touch
the lid.
Explanation:
A mass is undergoing simple harmonic motion. When its displacement is 0, it is at its equilibrium position. At that moment, its speed is _______ and its acceleration is _______.
Answer:
When X = 0
Speed = maximum V (max) = ω A
Acceleration = zero a(max) = - ω^2 A
From x = A sin ω t sin = 0 so displacement = zero
V = ω A cos ω t cos = 1 and speed = maximum
a = - A ω^2 sin ω t sin = 0 and acceleration = zero
What is the angular displacement (in rad) of an object that starts from rest and accelerates at a rate of 4 rad/s2 for a time of 4 seconds? (Please leave your answer with one decimal places with no units)
An object which starts from its resting place & accelerates at a speed of 4 rad/sec², the angular displacement is 8 rad.
An object's angular displacement is described in the following:
Angle displacement is equal to θ[tex]f[/tex]-θ[tex]i[/tex].
The following methodology must also be applied to determine angular displacement when the object's acceleration, starting velocity, and time are known:
θ=ωt+ 1/2αt²
[where θ= the angular displacement of an object,
ω= initial angular velocity,
α= angular acceleration,
t= time]
In this case, the object starts from the rest position.
So, the initial angular speed, ω= 0 rad/sec
Provided angular acceleration ,α = 4 rad/sec²
Time ,t= 4 sec
So, θ= [tex]0*4+ (1/2)*4*4[/tex]
⇒θ= 0+ 8
⇒θ= 8 rad
Therefore, it is concluded that the angular displacement is 8 rad.
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7. Suppose a force of 15 N is required to stretch and hold a spring 0.25 m from its equilibrium position. a. Assuming the spring obeys Hooks law, find the spring constant k. b. How much work is required to compress the spring 0.2 m from its equilibrium position
Spring constant k = 75 N/m
Hooke's law for this spring F(x) = 75x
Work = 1.5 J
What is work?When an object is moved over a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. This is known as work.The amount of work required to move an object down a line from point a to point b in the direction of a variable force F is[tex]$W=\int_{a}^{b} F(x) d x$[/tex]
First solutionAccording to Hooke's law, the spring must be held stretched at x=0.2m by a force of 15N.
F (0.2) = k (0.2 m) = 15 N
Solve for k
k = 75 N/m
Hence, Hooke's law is F(x) = 75x
Second solution
The spring is compressed from x = 0 to X = 0.2,
[tex]$W=\int_{0}^{0.2} 75 x d x=\left.\left(\frac{75 x^{2}}{2}\right)\right|_{0} ^{0.2}$[/tex]
W = 1.5 J
So, the work is required to compress the spring 0.2 m from its equilibrium position W = 1.5 J
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A steady current flows through an inductor. If the current is doubled while the inductance remains constant, the amount of energy stored in the inductor:.
If the current is doubled while the inductance remains constant, the amount of energy stored in the inductor 2LI².
Energy stored in inductor
The amount of energy stored in the inductor is given as;
E = ¹/₂LI²
where;
L is inductance I is current in the inductorWhen the current doubles, the new energy stored in the inductor;
E = ¹/₂L(2I)²
E = ¹/₂L(4I²)
E = 2LI²
Thus, if the current is doubled while the inductance remains constant, the amount of energy stored in the inductor 2LI².
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A satellite orbits the earth at a speed of 8.0x 10^3m/s . Calculate the period of orbit of the satellite if the distance between the centre of the earth and the satellite is 6400km?
Hi there!
The period of an orbit can be found by:
[tex]T = \frac{2\pi r}{v}[/tex]
T = Period (? s)
r = radius of orbit (6400000 m)
v = speed of the satellite (8000 m/s)
This is the same as the distance = vt equation. The total distance traveled by the satellite is the circumference of its circular orbit.
Let's plug in what we know and solve.
[tex]T = \frac{2\pi (6400000)}{8000} = \boxed{5026.55 s}[/tex]
What is electromagnet
Answer:
Electromagnetic is used to describe the electrical and magnetic forces or effects produced by an electric current.
The velocity of a 0.25kg model rocket changes from 15m/s [up] to 40m/s [up] in
0.60s. The gravitational field intensity is 9.8N/kg. Calculate the force the escaping
gas exerts of the rocket.
Since g is constant, the force the escaping gas exerts on the rocket will be 10.4 N
What is Escape Velocity ?This is the minimum velocity required for an object to just escape the gravitational influence of an astronomical body.
Given that the velocity of a 0.25kg model rocket changes from 15m/s [up] to 40m/s [up] in 0.60s. The gravitational field intensity is 9.8N/kg.
To calculate the force the escaping gas exerts of the rocket, let first highlight all the given parameters
Mass (m) of the rocket 0.25 KgInitial velocity u = 15 m/sFinal Velocity v = 40 m/sTime t = 0.6sGravitational field intensity g = 9.8N/kgThe force the gas exerts of the rocket = The force on the rocket
The rate change in momentum of the rocket = force applied
F = ma
F = m(v - u)/t
F = 0.25 x (40 - 15)/0.6
F = 0.25 x 41.667
F = 10.42 N
Since g is constant, the force the escaping gas exerts on the rocket is therefore 10.4 N approximately.
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A handball of mass 0.10 kg, traveling horizontally at 30 m/s, strikes a wall and rebounds at 24 m/s. What is the change in the momentum of the ball
The change in momentum of the ball is 0.6Kgm/s.
To find the answer, we need to know about the momentum.
What's the expression of change in momentum during collision?The change in momentum= final momentum - initial momentum of the objectsAnd momentum= mass × velocityHere the initial momentum= 0.10×30=3Kgm/sFinal momentum= 0.10×24= 2.4Kgm/sChange in momentum= 3-2.4= 0.6Kgm/sThus, we can conclude that the change in momentum is 0.6Kgm/s.
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Which of the following graphs represents the equation y-2 = 3(x-1)?
Answer:
Graph b
Explanation:
I used Desmond calculator which is a calculator where you can graph an equation! :)
Hello!
The slope-intercept form is :
y - 2 = 3(x - 1)
y - 2 = 3x - 3
y = 3x - 1
Two points that are found to be on the line :
(0, -1) and (1, 2)
∴ The graph which contains both points is Graph B.
A gas cylinder contains only the gases radon, nitrogen, and helium. The radon has a pressure of 222 torr while the nitrogen has a pressure of 446 torr. If the total pressure inside the cylinder is 771 torr, what is the pressure that is due to the helium?.
Answer:
103 torr
Explanation:
The remainder is due to the helium
771 - 222 - 446 = 103 torr due to helium