Short-duration spacecraft typically have one backup system and carry their own supply of oxygen. A large portion of the required oxygen is produced on long-duration missions, such as the International Space Station (ISS), which has been in orbit since 1998. Different sources provide the oxygen utilized on the ISS. The water electrolyzer is the primary source of metabolic oxygen. As an alternative to the electrolyzer, oxygen candles (also known as SFOGs) can produce metabolic oxygen. Additionally, oxygen is carried up whenever a cargo ship docks and stored in two tanks on the ISS Airlock. The electrolyzer electrolyzes water to create oxygen by running an electric current through it. Since water is a poor electrical conductor by itself, a little quantity of common salt is dissolved in the water to improve its electrical conductivity. Water is split into hydrogen and oxygen throughout the process.
We must keep in mind that oxygen by itself cannot be inhaled; it must be combined in the proper ratio with nitrogen to make it breathable. Two tanks aboard the ISS are used to store nitrogen, and the cargo ships that travel by from time to time also transport nitrogen cylinders. Through the electrical grid of the station, the solar panels on the station supply the necessary electricity for the oxygen generators. The majority of the required water is transported to the station by cargo supply ships. Condensers, which draw water vapor even from the station's air, ensure that not a drop of water is wasted. Using the proper equipment, water is also recycled from the astronauts' urine.
Through a suitable vent, the hydrogen gas produced during the electrolysis process is released into space. Pressurized tanks at the airlock nodes at the space station are pumped with oxygen when the cargo vehicles arrive there. Pressurized tanks there are also pumped with nitrogen. It goes without saying that the station's atmospheric controls combine the gases in the right amounts for the atmosphere of Earth and then distribute the combination throughout the cabin. The production of oxygen in space is impossible.
. A wheel of diameter 0.2 m starts from rest and accelerated with constant angular acceleration to an angular velocity of 900 rev min¹ in 5 s. (a) Find the position at the end of 1 s of a point originally at the top of the wheel. (b) Compute and show in a diagram the magnitude and the direction of the acceleration at the end of 1 s.
(a)The position at the end of 1 s of a point originally at the top of the wheel will be 9.425 radians.
(b)The magnitude and the direction of the acceleration at the end of 1 s will be 1.885 m/sec² clockwise.
What is angular acceleration?Angular acceleration is defined as the pace of change of angular velocity concerning time.
Given data;
Diameter of the wheel,d = 0.2 m
Initial velocity,ω₀ = 0
Angular acceleration,α = c
n = 900 rev min¹
ω = 94.2478 rad /sec
Time of rolling,t = 5 s
From Newton's first equation of motion;
ω = ω₀ + αt
94.2478 rad /sec = 0 + α(5 sec)
α = 18.85 rad/sec²
The position at the end of 1 s of a point is found as;
Θ = ω₀t+1/2(αt²)
Θ = 0+1/2[(18.85 rad/sec²) × (1 sec)²]
Θ = 9.425 radian
The magnitude and the direction of the acceleration at the end of 1 s are found as;
a = αr
a= 18.85 rad/sec² × 0.1 m
a = 1.885 m/sec²
Hence the position at the end of 1 s and magnitude and the direction of the acceleration at the end of 1 s will be 18.85 rad/sec²and the magnitude and the direction of the acceleration at the end of 1 s will be 1.885 m/sec² clockwise.
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The rms voltage is given by the following.
ΔVrms = ΔVmax/[tex]\sqrt{2}[/tex] = 0.707ΔVmax
Substituting the maximum voltage, we obtain
ΔVrms = ΔVmax/[tex]\sqrt{2}[/tex]
= 0.707ΔVmax = 0.707(165 V) = 117 V.
An rms voltage of 117 V corresponds to a maximum voltage of 165 V.
What is the maximum current Imax in the resistor?
The maximum current in the resistor is determined by dividing root mean square current by 0.7071.
Maximum current in the resistor
The maximum current in the resistor is calculated as follows;
I₀ = I(rms)/0.7071
where;
I₀ is the peak current or maximum current in the resistorI(rms) is the root mean - square currentThus, the maximum current in the resistor is determined by dividing root mean square current by 0.7071.
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What is the difference in the weight of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica? The product GMEarth = 3.99 x 10^14 N x m2 x kg-1, the radius of the Earth is 6.38 × 10^6 m, and the height above sea level of the Vinson Massif is 5.14 × 10^3 m. Neglect the flattening of the Earth at the poles.
The difference in weight of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica is -1.847 N
How to find the difference in weight?
To find the difference in weight, we find the change in acceleration due to gravity.
What is acceleration due to gravity?
The acceleration due to gravity is the acceleration exerted by the force of gravity on an object. It is given by
g = GM/r² where
GM = 3.99 × 10¹⁴ Nm²/kg and r = radius of earth = 6.38 × 10⁶ mThe change in acceleration due to gravityNow, to find the change in g, we differentiate g with respect to r,
So, dg/dr = d(GM/r²)
= -2GM/r³
So, the change in acceleration due to gravity, Δg is
Δg = dg/dr × Δr
= -2GM/r³ × Δr
Now, Δr = height above sea level of Vinson Massif = 5.14 × 10³ m
Substituting the values of the variables into the equation, we have
Δg = -2GM/r³ × Δr
Δg = [(-2 × 3.99 × 10¹⁴ Nm²/kg)/(6.38 × 10⁶ m)³] × 5.14 × 10³ m
Δg =[ (-7.98 × 10¹⁴ Nm²/kg)/259.69 × 10¹⁸ m³] × 5.14 × 10³ m
Δg = -0.03073 × 10⁻⁴ N/mkg × 5.14 × 10³ m
Δg = -0.1579 × 10⁻¹ N/kg
Δg = -0.01579 N/kg
The difference in weight of the 117 kg personSince weight W = mg where
m = mass of person and g = acceleration due to gravityThe difference in weight is dW = mdg
Since
m = 117 kg and dg = -0.01579 N/kgdW = mdg
= 117 kg × -0.01579 N/kg
= -1.847 N
So, the difference in weight of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica is -1.847 N
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A 0.10 kg mass is oscillating at a small angle from a light string of length 0.10 m.
What is the period of the pendulum?
The time period of the pendulum is 0.65 second.
What is time period?The time period is a period of time during which a behavior takes place or a condition persists. Depending on the type of activity or condition under consideration, it may be expressed either in seconds or in millions of years.
The mass of the object is = 0.10 kg
Length of the string is = 0.10 m.
Acceleration due to gravity is = 9.8 m/s²
Hence, the time period of the pendulum is = 2π√(0.10/9.8) sec
= 0.65 second.
Hence, the time period of the pendulum is 0.65 second.
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Part A
How did Einstein’s and Newton’s theories differ in terms of explaining the cause of gravity?
Newton thinks that object falls due to gravity whereas Einstein thinks gravity is not the reason behind it.
How did Einstein’s and Newton’s theories differ in terms of explaining the cause of gravity?Newton concluded that objects fall because they are pulled by Earth's gravity. Einstein's thinks that these objects do not fall due to gravity. According to Einstein, these objects and Earth just freely move in a curved spacetime
So we can conclude that Newton thinks that object falls due to gravity whereas Einstein thinks gravity is not the reason behind it.
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A thin flexible gold chain of uniform linear density has a mass of 17.1 g. It hangs between two 30.0 cm long vertical sticks (vertical axes) which are a distance of 30.0 cm apart horizontally (x-axis), as shown in the figure below which is drawn to scale.
Evaluate the magnitude of the force on the left hand pole.
The magnitude of the force on the left-hand pole is mathematically given as
f'=0.167N
[tex]Q=45 \textdegree[/tex]
What is the magnitude of the force on the left-hand pole.?Generally, the equation for Force is mathematically given as
[tex]F=\frac{mg}{sin\theta}[/tex]
Therefore
[tex]F=\frac{17.1*10^{-3}*9.8}{sin45}[/tex]
F=0.237N
Considering horizontal
f'-fcos=0
Therefore
f'=0.237*cos45
f'=0.167N
In conclusion, the slope
[tex]tan\theta=lv/ln\\\\tan\theta=30/30\\\\\theta=tan^{-1}\\\\[/tex]
[tex]Q=45 \textdegree[/tex]
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2. A transformer has 300,000 windings in its primary coil and uses 12,000V AC input. Show your work!
A) (4 points) How many windings would be needed to produce at output of 110V AC? Is this a step down or step up transformer?
B) (3 points) Explain why a transformer only works with AC and not DC currents.
The number of windings that would be needed to produce an output of 110V AC will be 2750.
What is induced voltage?
Electromagnetic induction is what causes the induced voltage. Electromagnetic induction is the process of generating emf (induced voltage) by subjecting a conductor to a magnetic field.
Typically, a transformer's primary winding is attached to the input voltage source and changes electrical power into a magnetic field.
The secondary winding's role is to turn this alternating magnetic field into electricity, generating the necessary output voltage.
The relation between the primary and the secondary winding is;
[tex]\rm \frac{V_s}{V_p}= \frac{N_s}{N_p} \\\\ \frac{110}{12000}= \frac{N_S}{300000} \\\\ N_s = 2750 \[/tex]
Transformers can only operate on AC current, since a flux shift is required for the induction process.
Additionally, since there won't be any flux change phenomena in the DC supply, the induction process can't take place. Transformers are utilized in AC supplies because of this.
Hence, the number of windings that would be needed to produce an output of 110V AC will be, 2750 and a transformer only works with AC.
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To win the game, a place kicker must kick a
football from a point 28 m (30.6208 yd) from
the goal, and the ball must clear the crossbar,
which is 3.05 m high. When kicked, the ball
leaves the ground with a speed of 18 m/s at
an angle of 47.3
◦
from the horizontal.
The acceleration of gravity is 9.8 m/s
2
.
By how much vertical distance does the ball
clear the crossbar?
The answer to the question is that the vertical distance the ball clear the cross bar is 1.465 metres.
We have horizontal distance as 28 m, and velocity as 18 m/s and the angle of projection 46.8 degree.
so, we can say that
In horizontal direction,
28 = (18 cos 46°) t
t = 2.2723 seconds
Now, in vertical direction,
Let be the height of the ball
h = (18 sin 46°)t - (1/2)gt²
h = (18 sin 46°)t - 4.9t²
h = ( (13.1214) × (2.2723) ) - ( (4.9) × (2.2723)² )
h = 4.5154 metre
Vertical distance the ball clear the cross bar = h - 3.05
Vertical distance the ball clear the cross bar = 4.5154 - 3.05
Vertical distance the ball clear the cross bar = 1.465
Thus, we can conclude that after solving and applying the concepts of projectile motion we find out the vertical distance the ball will clear the cross bar is 1.465 metres.
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A force F1 of magnitude 5.90 units acts on an object at the origin in a direction = 36.0° above the positive x-axis. A second force F2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F1 + F2.
The magnitude and direction of the resultant force will be 7.65 units and 40.2°.
What is force?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 push 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
Given data;
Megnitude of force 1, F₁ = 5.90 units
Megnitude of force 2, F₂ = 5.00 units
α is the angle between the two forces=36.0°
Θ is the angle of the resultant force
The megnitude of the resultant force is;
[tex]\rm F =\sqrt{ F_{1}+F_{2}+2F_{1}F_{2}cos \alpha }\\\\ F = \sqrt{5.90 + 5.00 +2 \times 5.90 \times 5 \times cos 36^0 } \\\\ F = 7.65 \ units[/tex]
The direction of the resultant force is;
[tex]\rm \theta = tan^{-1}(\frac{F_{2}}{F_{1}} )[/tex]
[tex]\rm \theta = tan^{-1}(\frac{5.00}{5.90})\\\\ \theta = 40.2 ^0[/tex]
Hence the magnitude and direction of the resultant force will be 7.65 units and 40.2°.
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Latency refers to the 27 seconds of time it takes for someone to refocus on driving after they finish texting or talking on the phone. true false
The term "latency" describes the 27 seconds that pass after someone has finished texting or conversing on the phone before they can concentrate again on driving. The given statement is true.
What is latency?A measure of delay is latency. The amount of time it takes for some data to travel across a network is known as latency.
The amount of time it takes for information to travel from its source to its destination and back is often quantified as a round trip delay.
The 27 seconds that pass after someone has done texting or talking on the phone before they can focus on driving again are referred to as "latency." The assertion is accurate.
Hence, the given statement is true.
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Two straight long parallel wires, separated by a distance of 1.0 m, carry a current of 4.00
each. A third wire is arranged perpendicular to the two parallel wires. If the magnetic field at a point equidistant from all the wires is zero, find the current in the third wire.
The magnitude of the current in the third wire is 8 A.
Total magnetic fieldE₁ + E₂ + E₃ = 0
Equidistance from the two wires = 0.5 m
Apply Biot Savart rule to determine the magnitude of the magnetic field.
μI/2πr₁ + μI/2πr₂ + μI/2πr₃ = 0
(4π x 10⁻⁷ x 4)/(2π x 0.5) + (4π x 10⁻⁷ x 4)/(2π x 0.5) + (4π x 10⁻⁷ x I₃)/(2π x 0.5) = 0
4 x 10⁻⁷ I₃ = -3.2 x 10⁻⁶
I₃ = (-3.2 x 10⁻⁶)/(4 x 10⁻⁷)
I₃ = - 8 A
Thus, the magnitude of the current in the third wire is 8 A.
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6. A student travels 4.0 m east, 8.0 m south, 4.0 m west, and finally 8.0 m north. What is her
displacement?
What distance did she travel?
The student's path traces out a rectangle and she ends up at the same spot, so her displacement is 0 m.
On the other hand, she travels a total distance equal to the perimeter of that rectangle,
4.0 m + 8.0 m + 4.0 m + 8.0 m = 24 m
a bus strats from from rest. if the accleration is 2m/s,find the distance travelled and the velocity after 2 seconds
Answer:
Velocity: 4 m/s
Distance: 4 m
Explanation:
initial velocity: u = 0 m/s
Acceleration: a = 2 m/s²
Time taken: t = 2 seconds
Distance traveled: d = (what we need to find)
Final velocity: v = (what we need to find)
---------------------------------------
v = u + at
v = 0 + 2 × 2
v = 4 m/s
---------------------------------------
d = 0 × 2 + 1/2 × 2 × (2)²
d = 1/2 × 2 × 4
d = 4 m
A long wire carries a current of 3.0 A along the axis of a long solenoid (radius = 3.0 cm, n = 900 turns/m, current = 30 mA). What is the magnitude of the magnetic field at a point 2.0 cm from the axis of the solenoid? Neglect any end effects.
Answer is 45uT, but how do you get this?
Hi there!
Let's break this problem up into two parts.
Part A: Solenoid
The magnetic field everywhere inside a solenoid is constant, and can be found using the equation:
[tex]B = \mu_0 nI[/tex]
B = Magnetic field strength (? T)
μ₀ = Permeability of Free Space (4π × 10⁻⁷ Tm/A)
n = number of turns/meter (900)
I = current (0.03 A)
We are given all of these values, so let's solve.
[tex]B = (4\pi \times 10^{-7})(900)(0.03) = 34\mu T[/tex]
However, we also have a long wire that produces a magnetic field perpendicular to that produced by the solenoid.
Part B: Long wire
The equation for the magnetic field produced by a long wire is found by:
[tex]B = \frac{\mu_0 I}{2\pi r}[/tex]
Where 'r' is the distance from the wire.
Plug in what we know:
[tex]B = \frac{(4\pi \times 10^{-7})(3)}{2\pi (0.02)} = \mu 30 T[/tex]
Now, we must do the vector sum of these two fields to find the total magnetic field. Since they are perpendicular (solenoid field points to the side, wire fire points in or out), we can use the Pythagorean Theorem.
[tex]B_T = \sqrt{B_s^2 + B_w^2}\\\\B_T = \sqrt{(34\mu T)^2 + (30\mu T)^2} \approx \boxed{45\mu T}[/tex]
And here's our answer!
A crate with a mass of 175.5 kg is suspended from the end of a uniform boom with a mass of 94.7 kg. The upper end of the boom is supported by a cable attached to the wall and the lower end by a pivot (marked X) on the same wall.
Calculate the tension in the cable.
The tension in the cable is mathematically given as
T =266.659 N
What is the tension in the cable.?Generally, the equation for the angle of the boom with horizontal is mathematically given as
A = tan-1(5 /10)
[tex]A= 26.57 \textdegree[/tex]
The angle of cable with horizontal
B = tan-1(4 / 10)
B= 21.80 degrees
Hence
175.5 * cos26.57 + 94.7 *cos26.57 * 1/2 = T (sin(26.57+21.80)) * 1
T =266.659 N
In conclusion, the tension in the cable.
T =266.659 N
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A mass of 2kg is attached to the end of a vertical wire of length 2m and diameter 2mm extend the wire by 1mm. Calculate the young modulus of the wire
Which of the following most directly shows how society affects physics? A. Elected officials make decisions about what research is funded. B. Physicists work on projects that will get them nominated for Nobel prize. C. Citizens panel provide input on most research projects. D. Governments budget money for national science- funding agencies
The option above which most directly shows how society affects physics is that physicists work on projects that will get them nominated for Nobel prize.
Who is a physicist?A physicist is a person who who studies physics.
Physics is one of the branches of science which involves the study of matter, light, mechanics...
In conclusion: the option below which most directly shows how society affects physics is that physicists work on projects that will get them nominated for Nobel prize.
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A barber Wants to set up a salon in a measuring Length of 3m by 3m. He has a simple Woden Chair, 3 large mirror and one bulb. a) using the knowledge of shadows and reflection, advice the barber on how to arrange a good salon using the unly items he has. b) without acking more sources of light, how can he enhance the lighting System in his salon? S A barber Wants to set up a salon in a measuring Length of 3m by 3m . He has a simple Woden Chair , 3 large mirror and one bulb . a ) using the knowledge of shadows and reflection , advice the barber on how to arrange a good salon using the unly items he has . b ) without acking more sources of light , how can he enhance the lighting System in his salon ?
Two mirrors are arranged such that they are parallel to each and perpendicular to the third mirror.
Also, the light is placed at the center of the three mirrors to produce multiple images by reflection.
What is reflection of light?Reflection is the bouncing back of light waves of a reflective surface when light shines on that surface.
The knowledge of reflection of light can be used by the Barber to set up a good salon.
The mirrors are arranged in the salon such that two of the mirrors are parallel to each and perpendicular to the third mirror. Also, the light is placed at the center of the three mirrors.
The parallel arrangement of the mirror will ensure that the clients will be able to have a full frontal and back view of themselves.
The parallel and perpendicular arrangement of the mirrors will also ensure that the light placed at the center will produce reflected to produce infinite images thus lighting up the salon.
In conclusion, the reflective properties of the mirrors as well as the angle between mirrors is used to create a well-lit salon by the barber.
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What does newtons 2nd law explain?
Answer asap for brainlist
Answer:
B. why you must push harder to move a car farther.
Explanation:
acceleration (gaining speed) happens when a force acts on a mass (object). FORCE=MASSxACCELERATION
A pan-galactic gargle (an alien) whose mass is 85 kg exploring a large asteroid. What is the force of
gravity holding it down?
The acceleration due to gravity of the asteroid is 833.85 N.
Force of gravity holding the the alien down
F = mg
where;
m is mass of the alieng is acceleration due to gravityAssuming the acceleration due to gravity of the asteroid = 9.81 m/s²
F = 85 x 9.81
F = 833.85 N
Thus, the acceleration due to gravity of the asteroid is 833.85 N.
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Three ropes A, B and C are tied together in one single knot K. (See figure.)
If the tension in rope A is 65.3 N, then what is the tension in rope B?
The tension in the rope B is determined as 10.9 N.
Vertical angle of cable B
tanθ = (6 - 4)/(5 - 0)
tan θ = (2)/(5)
tan θ = 0.4
θ = arc tan(0.4) = 21.8 ⁰
Angle between B and Cθ = 21.8 ⁰ + 21.8 ⁰ = 43.6⁰
Apply cosine rule to determine the tension in rope B;
A² = B² + C² - 2BC(cos A)
B = C
A² = B² + B² - (2B²)(cos A)
A² = 2B² - 2B²(cos 43.6)
A² = 0.55B²
B² = A²/0.55
B² = 65.3/0.55
B² = 118.73
B = √(118.73)
B = 10.9 N
Thus, the tension in the rope B is determined as 10.9 N.
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Lindsay is planning a flight from St. Catherines to Hamilton, which lies due west of St. Catharines.
Her aircraft flies at a speed of 200 km/h in still air. A wind of 50.0 km/h is blowing from [W 60.0° N].
In what direction must she aim the aeroplane to fly directly to Hamilton? (KU, TI)
Lindsay should fly the plane in the direction [W 12.5° S] to get Hamilton.
Using Sine rule to solve this question
Sine rule => SinA/a = SinB/b = SinC/c = constant
The magnitude of wind is 50 with an angle of 60 degrees.
The magnitude of plane is 200 and the angle at which it should fly is unknown and should be θ.
One side is 50 km/hr at an angle of 60 degrees.
sin 60°/200 = sin θ / 50
50 × sin 60° = 200 × sin θ
√3/2 = 4 × sin θ
√3/8 = sin θ
sin θ = 0.2165
θ = sin⁻¹(0.2165)
θ = 12.5°
So Lindsay have to fly the plane in the direction of [W 12.5° S].
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3. a) (4 points) Compare and contrast magnetic and electric fields. Your answer should include at least 2 ways they are similar and 2 ways that they differ.
b) (4 points) Include a diagram of an electric field for a positive test charge and a diagram for a typical bar magnet. Make sure you show the field lines (including direction) and label the charges and poles.
A magnetic field is a field explaining the magnetic influence on an object in space.
A electric field is a field defined by the magnitude of the electric force at any given point in space.
What are magnetic field and electric fields?A magnetic field is a field explaining the magnetic influence on an object in space.
A electric field is a field defined by the magnitude of the electric force at any given point in space.
The difference between magnetic fields and electric filed are:
Electric Filed
Magnetic fields creates an electric charge in surrounding.It is measured as newton per coulomb, volt per meter.An electric field is measured using an electrometer.It is proportional for the electric charge.Magnetic Filed:
Magnetic filed creates an electric charge around moving magnets.It is measured as gauss or tesla.The magnetic field is measured using the magnetometer.It is proportional to the speed of electric chargeSimilarities between Electric and Magnetic Field
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For a vector with origin at coordinate (0, 0) (horizontal, vertical) and end at (6, 8) northeast of the origin,
what is the horizontal component of the vector?
The horizontal component of the vector is determined as 6i.
Horizontal component of the vector
The horizontal component of the vector is calculated as follows;
V = (0 i, 0 j) + (6i, 8j)
V = (6i, 8j)
where;
6i is the horizontal component of the vector8j is the vertical component of the vectorThus, the horizontal component of the vector is determined as 6i.
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20. What is the meaning of intuition?
A. Using facts and observations to make a conclusion
B. Quickly understanding something without needing mental reasoning
C. Praising others instead of criticizing
D. Making decisions with strict requirements
Answer:
B) Quickly understanding something without needing mental reasoning
Answer:
[tex]\huge\boxed{\sf Option \ B}[/tex]
Explanation:
Intuition means:Taking quick decisions.Understanding quickly without using the conscious mind.Instinct.So, Intuition actually means quickly understanding something without needing mental reasoning.
[tex]\rule[225]{225}{2}[/tex]
An archer shoots an arrow at a 74.0 m distant target, the bull's-eye of which is at same height as the release height of the arrow.
(a) At what angle must the arrow be released to hit the bull's-eye if its initial speed is 33.0 m/s? (Although neglected here, the atmosphere provides significant lift to real arrows.)
°
(b) There is a large tree halfway between the archer and the target with an overhanging branch 3.50 m above the release height of the arrow. Will the arrow go over or under the branch?
under
over
A. The angle at which the arrow must be released to hit the bull's-eye is 20.7 °
B. The arrow will go over the branch.
A. How to determine the angleRange (R) = 74 mInitial velocity (u) = 33 m/sAcceleration due to gravity (g) = 9.8 m/s²Angle (θ) = ?R = u²Sine(2θ) / g
74 = 33² × Sine (2θ) / 9.8
Cross multiply
74 × 9.8 = 33² × Sine (2θ)
725.2 = 1098 × Sine (2θ)
Divide both sides by 1098
Sine (2θ) = 725.2 / 1098
Sine (2θ) = 0.6605
Take the inverse of sine
2θ = Sine⁻¹ 0.6605
2θ = 41.3
Divide both sides by 2
θ = 41.3 / 2
θ = 20.7 °
B. How to determine if the arrow will go over or under the branchTo determine if the arrow will go over or under the branch situated mid way, we shall determine the maximum height attained by the arrow. This can be obtained as follow:
Initial velocity (u) = 33 m/sAcceleration due to gravity (g) = 9.8 m/s²Angle (θ) = 20.7 °Maximum height (H) = ?H = u²Sine²θ / 2g
H = [33² × (Sine 20.7)²] / (2 ×9.8)
H = 6.94 m
Thus, the maximum height attained by the arrow is 6.94 m which is greater than the height of the branch (i.e 3.50 m).
Therefore, we can conclude that the arrow will go over the branch
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Need help in showing how to get the final velocity
I don't think the provided solution is correct because it's not dimensionally consistent. The quantity [tex]8h-1[/tex] in particular doesn't make sense since it's mixing a distance with a dimensionless constant.
Here's how I think the proper answer should look:
The net force on the box acting perpendicular to the ramp is
[tex]\sum F_\perp = F_{\rm normal} - mg \cos(\theta) = 0[/tex]
where [tex]F_{\rm normal}[/tex] is the magnitude of the normal force due to contact with the ramp and [tex]mg\cos(\theta)[/tex] is the magnitude of the box's weight acting in this direction. The net force is zero since the box doesn't move up or down relative to the plane of motion.
The net force acting parallel the ramp is
[tex]\sum F_\| = mg\sin(\theta) - F_{\rm friction} = ma[/tex]
where [tex]mg\sin(\theta)[/tex] is the magnitude of the parallel component of the box's weight, [tex]F_{\rm friction}[/tex] is the magnitude of kinetic friction, and [tex]a[/tex] is the acceleration of the box.
From the first equation, we find
[tex]F_{\rm normal} = mg \cos(\theta)[/tex]
and since [tex]F_{\rm friction} = \mu F_{\rm normal}[/tex], we get from the second equation
[tex]mg\sin(\theta) - \mu mg\cos(\theta) = ma[/tex]
and with [tex]\mu = 0.25[/tex] and [tex]\theta=60^\circ[/tex], we get
[tex]a = g\sin(60^\circ) - 0.25g \cos(60^\circ) = \left(\dfrac{\sqrt3}2 - \dfrac18\right) g[/tex]
Let [tex]x[/tex] be the length of the ramp, i.e. the distance that the box covers as it slides down it. Then the box attains a final velocity [tex]v[/tex] such that
[tex]v^2 = 2ax[/tex]
From the diagram, we see that
[tex]\sin(\theta) = \dfrac hx \implies x = \dfrac h{\sin(60^\circ)} = \dfrac{2h}{\sqrt3}[/tex]
and so
[tex]v^2 = \dfrac{4ah}{\sqrt3} = \left(2 - \dfrac1{2\sqrt3}\right) hg = \dfrac14 \left(8 - \dfrac2{\sqrt3}\right) hg[/tex]
[tex]\implies v = \dfrac12 \sqrt{\left(8 - \dfrac2{\sqrt3}\right) hg}[/tex]
A slinky spring 3m long rests on a horizontal bench with one end fixed. When the free end is suddenly pushed forward, the compression pulse travels to the fixed end and back in 2 secs. What is the speed of the longitudinal waves along the spring? What is the wavelength of the longitudinal waves produced when the free end is moved to and fro with a frequency of 2.5Hz? A slinky spring 3m long rests on a horizontal bench with one end fixed . When the free end is suddenly pushed forward , the compression pulse travels to the fixed end and back in 2 secs . What is the speed of the longitudinal waves along the spring ? What is the wavelength of the longitudinal waves produced when the free end is moved to and fro with a frequency of 2.5Hz ?
The speed of the longitudinal waves along the spring is 1.5 m/s.
The wavelength of the longitudinal waves produced when the free end is moved to and fro is 0.6 m.
What is wavelength?The wavelength is the distance between the adjacent crest or trough of the sinusoidal wave. The wavelength is the reciprocal of the frequency of the wave.
Wavelength λ = c/f
where c is the speed of light in vacuum = 3*10⁸ m/s
A slinky spring 3m long rests on a horizontal bench with one end fixed. When the free end is suddenly pushed forward, the compression pulse travels to the fixed end and back in 2 secs.
λ = v/f
v =fλ =λ /T where T is the time period = 2sec
Put the values we get
v = 3/2 =1.5 m/s
Thus, the speed of wave is 1.5 m/s.
Using the same expression for frequency 2.5Hz, wavelength is
λ = v/f
λ = 1.5 /2.5 = 0.6 m
Thus, the wavelength is 0.6m.
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What do we call fixed point around which a lever pivots?
A. A fulcrum
B. A whell and axle
c. A wedge
D. A cylinder
Answer asap for beainlist
Answer:
A
Explanation:
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A treasure chest full of silver and gold coins is being lifted from a pirate ship to the shore using two ropes as shown in the figure. The mass of the treasure chest is 75.6 kg.
What is the tension in rope A?
How much tension does rope B carry?
And what is the tension in rope C?
The tension in rope A is 740.88 N, the tension carried by rope B is 751.4 N and the tension carried by rope C is -124 N.
Angle made by B with respect to horizontaltan θ = Δy/Δx
tan θ = (10 - 4)/(5 - 4)
tan θ = 6
θ = arc tan (6) = 80.53
Net force in vertical directionC sin(0) + B sin(80.53) = A sin(90)
C sin(0) + B sin(80.53) = (75.6 x 9.8)
0 + 0.986 B = 740.88
0.986 B = 740.88
B = 740.88/0.986
B = 751.4 N
Net force in horizontal directionC cos(0) + B cos(80.53) = (75.6 x 9.8) cos(90)
C + 0.165 B = 0
C + 0.165(751.4) = 0
C + 124 = 0
C = - 124 N
Thus, the tension in rope A is 740.88 N, the tension carried by rope B is 751.4 N and the tension carried by rope C is -124 N.
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