At the bottom of the “ride,” when the jumper momentarily stops
I am not sure how to approach this question.
Answer:
35.2 AU
Explanation:
Kepler's Third Law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
[tex]\boxed{T^2 \propto a^3 \implies T^2=ka^3}[/tex]
Kepler's Third Law
[tex]T^2=\dfrac{4 \pi^2}{GM}a^3[/tex]
where a is the semi-major axis of the ellipse.
If expressed in the following units:
T = Earth years.a = Astronomical units AU (a=1 AU for Earth).M = Solar masses.then:
[tex]\implies\dfrac{4 \pi^2}{GM}=1[/tex]
Therefore Kepler's Third Law can be expressed as:
[tex]\boxed{T^2=a^3}[/tex]
Given:
T = 75.6 yearsFrom inspection of the given diagram:
[tex]\implies 2a=x+0.57[/tex]
[tex]\implies a=\dfrac{x+0.57}{2}[/tex]
Substitute these values into the equation and solve for x:
[tex]\implies (75.6)^2=\left(\dfrac{x+0.57}{2}\right)^3[/tex]
[tex]\implies (75.6)^\frac{2}{3}=\dfrac{x+0.57}{2}[/tex]
[tex]\implies 2(75.6)^\frac{2}{3}=x+0.57[/tex]
[tex]\implies x=2(75.6)^\frac{2}{3}-0.57[/tex]
[tex]\implies x=35.1883819...[/tex]
[tex]\implies x=35.2\; \text{AU}[/tex]
Starting from rest, a car accelerates at 2.2 m/s2 up a hill that is inclined 5.2 ∘ above the horizontal. How far horizontally has the car traveled in 13 s ?
The horizontal distance travelled by the car in the given time period of 13 seconds is determined as 168.3 m.
What is the horizontal distance travelled by the car?The horizontal distance travelled by the car is calculated as follows;
s = ut + ¹/₂acosθ(t²)
where;
v is the final horizontal speed of the caru is the initial horizontal speed of the cara is the acceleration of the cart is the time of motion of the carθ is the angle of inclination of the planes = 0 + ¹/₂(2) x cos(5.2) x (13)²
s = 168.3 m
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15. A hybrid automobile traveling at 5.0 km/h, steadily increases its speed to 20.0 km/h in 10.0 s
a. Calculate its average acceleration, b. Calculate the distance the automobile travels during this
period of acceleration.
6. A race car traveling:
The average acceleration of the hybrid automobile is 0.42 m/s².
The distance travelled by the hybrid automobile during the period of acceleration is 34.5 m.
What is the average acceleration of the hybrid automobile?
The average acceleration of the hybrid automobile is the rate of change of velocity of the hybrid automobile with time.
Mathematically, the formula for average acceleration is given as;
a = Δv/Δt
where;
Δv is change in velocity of the automobileΔt is change in time of motion of the automobilea = (v - u)/t
where;
v is the final velocity of the hybrid automobile = 20 km/h = 5.56 m/su is the initial velocity of the hybrid automobile = 5 km/h = 1.389 m/sa = (5.56 - 1.389)/10
a = 0.42 m/s²
The distance travelled by the automobile during the period of acceleration is calculated as follows;
v² = u² + 2as
2as = v² - u²
s = (v² - u²)/(2a)
s = (5.56² - 1.389²) / (2 x 0.42)
s = 34.5 m
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What is the sun 70% made of?
Answer:
hydrogen
Explanation:
The Sun is a huge, glowing sphere of hot gas. Most of this gas is hydrogen (about 70%) and helium (about 28%). Carbon, nitrogen and oxygen make up 1.5% and the other 0.5% is made up of small amounts of many other elements such as neon, iron, silicon, magnesium and sulfur.
The sun is 70% made of Hydrogen.
What is hydrogen?
The element hydrogen has the sign H and the atomic number 1. The lightest element is hydrogen. Under normal conditions, hydrogen is a gas composed of diatomic molecules with the formula H2. It has no colour, no odour, no taste, is non-toxic, and is extremely flammable. Hydrogen is the most prevalent chemical element in the universe, accounting for approximately 75% of all normal matter. The Sun and other stars are mostly made up of hydrogen in the plasma state. The majority of hydrogen on Earth resides in molecule forms like water and organic substances. Each atom of hydrogen's most common isotope (symbol 1H) has one proton, one electron, and no neutrons.
The sun is around 70% made of Hydrogen and 28% Helium
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Question 15 of 34
Which of the following would increase the mechanical advantage of a lever?
A. Moving the fulcrum closer to the output force
O B. Moving the fulcrum farther from the output force
C. Decreasing the input force without moving the fulcrum
D. Increasing the input force without moving the fulcrum
The option that would increase the mechanical advantage of a lever is option A. Moving the fulcrum closer to the output force.
What influences a lever's mechanical advantage?Mechanical advantage quantifies a lever's effectiveness (how easy it is to lift the load). - When compared to the distance between the load (resistance) and the fulcrum, the advantage relies on the distance between the effort and the latter (effort arm) (resistance arm).
Note that in Levers of Class 1:
The mechanical advantage will increase when the fulcrum is brought closer to the load.The mechanical advantage will increase when the effort is moved further from the fulcrum. You might need a longer lever for this.Learn more about mechanical advantage from
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QUESTION: What 2 pieces of text evidence
did you find to support the claim: Science
Influences Technology?
RESPONSE: My 1st piece of text evidence
said
My 2nd piece of text evidence said
QUESTION: How does the engineer use the science behind mass, force, and
velocity to influence how a wheelchair is made?
RESPONSE: Engineers use mass, force, and velocity to design different
wheelchairs by.
Science employs technology to create new discoveries, while technology uses science to address problems. Science and technology, however, pursue distinct objectives. Science seeks to provide answers and advance knowledge. The purpose of technology is to resolve real-world issues. Despite having differing objectives, science and technology coexist and support one another. For the development of new technologies like the space telescope, scientific knowledge is used.
There are numerous such instances that demonstrate how science and technology may collaborate.
The microscope is one instance. Galileo might have created it at the same time as the telescope. The development of the microscope was based on scientific understanding of light and lenses, just like the development of the telescope.
How do you believe the development of the microscope aided in the advancement of science?
The microscope enabled researchers to see a universe of microscopic things they had never seen before. Numerous significant scientific advancements resulted from it, including the identification of cells—the fundamental constituents of all living things.
Therefore, science and technology help each other evolve and develop.
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a nickel wire with a resistance of 25 Ω is connected across the terminals of a 3.0 v of a flashlight battery, how much current is in the wire?
The amount of current flowing in the wire, given that it has a resistance of 25 Ω and connected to a 3.0 V is 0.12 A
How do I determine the current in the wire?From Ohm's law, we understood that the voltage, current and resistance are related according to the following formula:
Voltage (V) = Current (I) × resistance (R)
V = IR
With the above formula, we can obtain the current in wire. Details below.
The following data were obtained from the question:
Resistance (R) = 25 ΩVoltage (V) = 3.0 VCurrent (I) =?Thus, the current can be obtained as follow:
Voltage (V) = Current (I) × resistance (R)
3 = Current × 25
Divide both sides by 25
Current = 3 / 25
Current = 0.12 A
Thus, we can conclude that the current in the wire is 0.12 A
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why does kinetic energy have two maxitans minimum values during each oscillation?
Answer:
it has water
Explanation:
water is good
given an angle of incidence of ice as 40 degree and angle of refraction of 25.9 degree what is the refractive index of the ice
Answer:sin40∘=0.643) Hint: The relationship of angle of incidence and angle of refraction at interface of two media is given by Snell's law.
Explanation:
Magnets are used in an electric door bell as well as in a magnetic compass. State three differences between the two magnets
Answer:hope this helpsss
Explanation:
A permanent magnet that is always aligned with the magnetic field of the earth makes up the magnetic needle of a magnetic compass, which is used for navigation.
The magnetic field is produced by an electric current in an electromagnet. Because they are transient magnets, electromagnets lose their magnetic properties as soon as the current is interrupted.
What work is done by a forklift raising a 583 kg box a distance of 1.2 m?
The work that is done by a forklift raising a 583 kg box a distance of 1.2m is 699.6N.
How to calculate work done?Work refers to the measure of energy expended in moving an object. It is most commonly calculated by multiplying the force by the distance.
This means that no work is done if the object does not move. This means that the work done can be calculated as follows:
Work done = Force × distance
According to this question, a forklift raises a 583kg box over a distance of 1.2m. The work done can be calculated as follows:
Work done = 583kg × 1.2m
Work done = 699.6N
Therefore, 699.6N is the force required to lift the box.
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Kate was doing some resistance training where she would push against a brick wall
for 30 seconds. Which of the following statements best explains this situation in
terms of Work and Energy.
Kate did not do any work on the wall, because the wall did not move.
Kate used stored energy in her body which was likely converted to heat energy-
Kate did not change the Kinetic Energy of the wall; she did not change the
gravitational potential energy of the wall; and she did not change the elastic
potential energy of the wall.
All of the above statements are true.
Answer:
Kate did not do any work on the wall , because the wall did not move
A model of a helicopter rotor has four blades, each of length 3.4 m from the central shaft to the blade tip. The model is rotated in a wind tunnel at a rotational speed of 600 rev/min.
What is the radial acceleration of the blade tip expressed as a multiple of the acceleration due to gravity, g ?
Express your answer as a multiple of g .
The radial acceleration of the blade tip is 1370 g rad/s².
What is radial acceleration?Radial acceleration is defined as "the acceleration of the object is along the radius, directed towards the center" in uniform circular motion.
Given parameters:
Rotational speed of the helicopter rotor: ω = 600 rev/min
= 600 × 2π/60 rad/min.
= 20π rad/min.
Length of the blade: r = 3.4 m.
Then, the radial acceleration = ω²r = (20π)²× 3.4 rad/s².
= {(20π)²× 3.4}/9.8 g rad/s².
= 1370 g rad/s².
Hence, the radial acceleration of the blade tip is 1370 g rad/s².
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Compare the momenta of a 6300-kg elephant walking 0.11 m/s and a 50-kg dolphin swimming 10.4 m/s.
Answer:
Explanation:
p₁ = m₁·V₁ = 6300·0.11 = 693 kg·m/s
p₂ = m₂·V₂ = 50·10.4 = 520 kg·m/s
693 kg·m/s > 520 kg·m/s
Describe a situation in which the median of a data set would be more useful than the mean
Answer:
mean extremely affect by the two level of values
highest and lowest points
950 kg
3.
If the car has 30.400 J of kinetic
energy, how fast is it moving?
Using the page from the Chart of the Nuclides, select a nuclide that is radioactive and decays (changes) to another nuclide by emitting an Alpha particle. Is the new element radioactive and if it is, how do you know that? If the new nuclide is radioactive, what does it decay to?
Do the same thing with a nuclide that emits a Beta particle.
If a rock contains 75% lead 206 (Pb206) and 25% uranium 238 (U238), how old is the rock? Explain how you determined the answer.
Is it possible to have a rock of that age on Earth, and what is the reason for your answer?
The age of the rock is 9 * 10^9 years and there is no rock that can be as old as this age on earth.
What is radioactive decay?The term radioactive decay has to do with the process by which a radioactive nuclide disintegrates so as to obtain the daughter nucleus. The radioactive decay may occur by alpha or by beta radiation.
In this case, we are told that only 25% of the original uranium 238 isotope of half life 4.5 * 10^9 years still remains.
Using the formula;
0.693/[tex]t_{\frac{1}{2}[/tex] = 2.303/t log (No/N)
[tex]t_{\frac{1}{2}[/tex] = half life of the isotope
N= amount of isotope at time t
No = amount of isotope initially present
Then;
0.693/4.5 * 10^9 = 2.303/t log(No/0.25No)
1.54 * 10^-10 = 1.39/t
t = 1.39/1.54 * 10^-10
t = 9 * 10^9 years
There is no rock that is this much old since the average age of the earth is 4.5 billion years.
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Pls help :)
An astronaut lands on an alien planet. He places a pendulum (L = 0.200 m) on the surface and sets it in simple harmonic motion, as shown in this graph.
Answer the following questions:
What is the period and frequency of the pendulum’s motion?
How many seconds out of phase with the displacements shown would graphs of the velocity and acceleration be?
What is the acceleration due to gravity on the surface of the planet in ? Determine the number of g-forces.
Show any necessary calculations.
a. ) The period is 1/frequency = 5sec / 9 cycles = 0.555 seconds
b.) the seconds out of phase with the displacements shown would graphs of the velocity and acceleration be 5/18 (0.2777...) sec delayed with respect to displacement
c.) Gravity = (324 π²) (0.2) / 25 = 25.582 m/sec²
What is gravity?
Gravity is defined as a fundamental interaction which causes mutual attraction between all things with mass or energy.
Solving for the acceleration due to gravity on the surface of the planet, we have the following:
For small swing angles, the period of an ideal pendulum anywhere is
T = 2pi √(length / local gravity) .
The astronaut has already done the pendulum and transmitted the data to us, so
we can use his data and this formula to calculate the local gravity where he is located
P = 2pi √(length / local gravity)
5/9 sec = 2π √(0.2m / gravity)
√(0.2m / gravity) = 5/9sec / 2π
Take the reciprocal of each side: √(gravity) / √(0.2) = 18π / 5
Multiply each side by √(0.2): √(gravity) = 18π √(0.2) / 5
Square both sides: Gravity = (324 π²) (0.2) / 25 = 25.582 m/sec²
The value gotten is about 2.608 times the Earth's gravity.
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10. If an evaporator has a pressure drop of 10 psig and the low side pressure is 15 psig, what is the pressure at the
inlet of the evaporator?
a.5 psig
b.10 psig
c.15 psig
d.25 psig
If an evaporator has a vapour pressure drop of 10 psig and the low side pressure is 15 psig, pressure at the inlet of the evaporator will be 25 psig
change pressure= low side pressure-pressure drop
change pressure=15-(-10)
change pressure=25 psig
The vapor pressure of a liquid, sometimes referred to as the equilibrium pressure of a vapor above its liquid, is the pressure of the vapor produced by the evaporation of a fluid (or solid) over a sample of the liquid (or solid) in such a closed container (or solid).
Vapor pressure is the term for the force that is produced as liquids evaporate. Three factors commonly have an effect on a vapor press: surface area, intermolecular forces, and temperature. The vapor pressures of molecules change with temperature.
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State the name given to reflected sound waves
Echo
Explanation:
It is termed as Echo. Echo is a reflection of sound that arrives at the listener with a delay after the direct sound.
Two stars, one twice as massive as the other, are 1.0 light-year (ly) apart. One light year is the distance light travels in one year at the speed of light, 3.00×10^8m/s. The gravitational potential energy of this double-star system is −6.5 ×10^34J.
Q: What is the mass of the lighter star?
The mass of the lighter star is 2.15 x 10³⁰ kg.
What is the mass of the light star?The mass of the lighter star is obtained by applying the formula force gravitational potential energy between the two stars.
According to Newton's law of universal gravitation, every two objects in the universe attracts each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between the two objects.
U = F x r
U = Gm₁m₂/r² x r
U = Gm₁m₂/r
where;
G is universal gravitation constantm₁ is the mass of the first starm₂ is the mass of the second starr is the distance between the two starsr = 3 x 10⁸ m/s x 3.154 x 10⁷ s/yr
r = 9.46 x 10¹⁵ m
let the lighter star = m₁
then, the heavier star = 2m₁
U = (G x m₁ x 2m₁)/r
U = 2Gm₁²/r
Ur = 2Gm₁²
m₁² = Ur/2G
m₁ = √(Ur/2G)
m₁ = √(6.5 x 10³⁴ x 9.46 x 10¹⁵ / 2 x 6.626 x 10⁻¹¹)
m₁ = 2.15 x 10³⁰ kg
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A weightlifter curls a 25 kg bar, raising it each time a distance of 0.50 m. How many times must he repeat this exercise to burn off the energy in one slice of pizza? Assume 25% efficiency. Energy content of one slice of pizza is 1260 kJ .
42 times must he repeat this exercise to burn off the energy in one slice of pizza.
What is energy?
Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.
Energy burn by the weightlifter = potential energy
Potential energy = mgh
Potential energy = 25.(9.8)(0.50)
Potential energy = 122.5 Joule.
Assume 25% of efficiency so energy burn = 122.5*25/100
energy burn = 30.625 joule
Number of times = 1260/30.625
Number of times = 42 times.
42 times must he repeat this exercise to burn off the energy in one slice of pizza.
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Katie pulls her wagon by the handle. She exerts a force of 60 N 30 degrees above the
horizontal. The force of friction from the sidewalk on the wagon is 30 N. The wagon has
a mass of 20 kg. What is the normal force on the wagon?
a. 226 N
b. 196 N
c. 166 N
d. 136 N
Answer: D: 136 N
..
..
5. If I shoot a cannonball (m = 4.5 kg) straight up from a cannon that exerts a force of 7000 N through a
barrel length of 4.00 meters, how high will the cannonball go?
With the use of formulas, the maximum height reached by the cannonball is 635.4 meters
Motion Under GravityThe motion of an object under gravity is the vertical motion of the object under the influence of acceleration due to gravity.
If I shoot a cannonball (m = 4.5 kg) straight up from a cannon that exerts a force of 7000 N through a barrel length of 4.00 meters, the acceleration of the cannonball in the barrel can be calculated by using the formula
F = ma
Where
F = 7000 Nm = 4.5 Kga = ?Substitute all the parameters into the formula
7000 = 4.5a
a = 7000/4.5
a = 1555.6 m/s²
By using the below formula, we will find the velocity at which the ball leaves the barrel.
Where
u = 0a = 1555.6 m/s²s = 4 mv² = u² + 2as
v² = 0 + 2 × 1555.6 × 4
v² = 12444.4
v = √12444.4
v = 111.6 m/s
The same speed will be the initial velocity at the entrance of the barrel. How high will the cannonball go can be known by using the formula
v² = u² - 2gH
Where
v = 0 (at maximum height)u = 111.6 m/sg = 9.8 m/s²H = ?Substitute all the parameters into the formula
0 = 111.6² - 2 × 9.8 × H
19.6H = 12454.56
H = 12454.56/19.6
H = 635.4 m
Therefore, the cannonball will go as high as 635.4 m
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An ordinary workshop grindstone has a radius of 8.50 cm and rotates at 5500 rev/min.
(a)
Calculate the magnitude of the centripetal acceleration at its edge in meters per second squared and convert it to multiples of g.
magnitude m/s2
magnitude g
(b)
What is the linear speed in m/s of a point on its edge?
m/s
(a.i) The magnitude of the centripetal acceleration at its edge is 28,197.04 m/s².
(a. ii) In terms of multiple of g, the centripetal acceleration is 2,874.3 g.
(b) The linear speed is determined as 48.96 m/s.
What is the magnitude of the centripetal acceleration?The magnitude of the centripetal acceleration of the workshop grindstone is calculated by applying the following kinematic equation.
a = v²/r = ω²r
where;
v is the linear speed of the grindstoneω is the angular speed of the grindstoner is the radius of the grindstoneThe given parameters include;
ω = 5500 rev/min
ω = 5500 rev/min x 2π rad/rev x 1 min / 60 s
ω = 575.96 rad/s
a = (575.96²) x (0.085)
a = 28,197.04 m/s²
In terms of acceleration due to gravity (g);
a = 28,197.04 m/s² / 9.81 = 2,874.3 g
The linear speed of the grindstone is calculated as follows;
v = ωr
v = 575.96 rad/s x 0.085 m
v = 48.96 m/s
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State Newtown's second law of motion in words
Answer:
Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.
Explanation:
Answer:
The acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.
(also, you have a typo. it's Newton, not Newtown)
Two balls of the same radius but densities p1 = 2 p and p2 = 4 pare placed in a
liquid of density p. What is the ratio (the weight of ball 1 in the liquid / the weight of
ball 2 in the liquid)?
Answer:
W1 = d1 V
W2 = d2 V weight of balls in air (both have same volume0
w2 = (d2 - p) V apparent weight of ball 2 (p * V = buoyant force
w2 / w1 = (d2 - p) / (d1 - p) the liquid exerts the same buoyant force on each ball
Let p be in units of kg / m^3 * g say 1 N / m^3
Suppose d1 = 2 and d2 = 3 N/m^3 and p = .5 N/m^3
The ratio of apparent weights would be
w2 / w1 = (3 - .5) / (2 - .5) = 1.67 to 1
Excluding air pressure, there is how many force or force(s) acting on a book lying at rest on a tabletop?
Answer: 2 Forces
Explanation:
1. Normal force- object is on a surface
2. Weight
Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.4 km in 15 s , starting from rest.
The coefficient of static friction needed for a drag racer to cover the given distance is 1.27.
What is the acceleration of the slipping tires?
The magnitude of the acceleration of the slipping tires is calculated by applying the kinematic equation for average distance travelled by the slipping tires as shown below.
s = ut + ¹/₂at²
where;
u is the initial velocity of the slipping tires = 0t is the time of motion of the slipping tiresa is the average acceleration of the slipping tiress is the average distance moved by the slippings = 0 + ¹/₂at²
s = ¹/₂at²
at² = 2s
a = 2s/t²
a = (2 x 1,400 m) / (15 s)²
a = 12.44 m/s²
The coefficient of static friction needed for a drag racer to cover the given distance is calculated as;
μ = a/g
where;
g is acceleration due to gravity = 9.81 m/s²μ = 12.44 / 9.81
μ = 1.27
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A set of lights consists of 20 lamps connected in series to the 230 V mains electricity supply. 1. (a) When the lights are switched on and working correctly, the current through each lamp is 0.25 A. (i) What is the total current drawn from the mains supply?
The total current that is drawn from the mains supply is 5 A.
What is current?The term current has to do with the flow of charges in a circuit. Now we have been told that A set of lights consists of 20 lamps connected in series to the 230 V mains electricity supply. It was also said in the question that when the lights are switched on and working correctly, the current through each lamp is 0.25 A.
Now we have the following information;
Current passing through each lamp = 0.25 A
Number of lamps = 20 lamps
Hence;
Total current = 0.25 A * 20
= 5 A
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