1. Calculate the impedance for a series RLC circuit with a 10 kA resistor, a 4400 pF capacitor, and a 3.5 mH inductor in series, if the input current has a frequency of f = 600 MHz, (Note f is not the same as w!) 2. What is the resonance frequency for the above circuit? 3. Does the resonance frequency depend on the resistance? Why or why not?
Answers
1. The impedance of a series RLC circuit can be calculated using the formula Z = √((R^2) + ((Xl - Xc)^2)), where R is the resistance, Xl is the inductive reactance and Xc is the capacitive reactance.
At a frequency of 600 MHz, the inductive reactance can be calculated using the formula Xl = 2πfL, where L is the inductance. Thus, Xl = 2π(600 x 10^6)(3.5 x 10^-3) = 1319.5 Ω. The capacitive reactance can be calculated using the formula Xc = 1/(2πfC), where C is the capacitance. Thus, Xc = 1/(2π(600 x 10^6)(4400 x 10^-12)) = 543.63 Ω. Therefore, Z = √((10,000^2) + ((1319.5 - 543.63)^2)) = 10,990.7 Ω.
2. The resonance frequency for a series RLC circuit can be calculated using the formula f = 1/(2π√(LC)), where L is the inductance and C is the capacitance. Thus, f = 1/(2π√(3.5 x 10^-3)(4400 x 10^-12)) = 615.5 MHz.
3. The resonance frequency does not depend on the resistance in a series RLC circuit because at resonance, the reactances of the inductor and capacitor cancel each other out and the circuit becomes purely resistive. Therefore, the resistance does not affect the resonance frequency.
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Related Questions
27. Beyond "c", the speed of the rocket is;
(A) constant.
(B) continuously increasing.
(C) continuously decreasing.
(D) increasing for a while and constant thereafter.
(E) constant for a while and decreasing thereafter.
Answers
Beyond "c", the speed of the rocket is; (D) increasing for a while and constant thereafter.
How quickly does a rocket move?The space shuttle must accelerate from zero to 8,000 metres per second (nearly 18,000 miles per hour) in eight and a half minutes to reach the minimum height necessary to circle the Earth.
The orbital velocity is 7.9 kilometres per second, which translates to more than 20 times the speed of sound. A rocket attaining orbital velocity (1st cosmic velocity) will enter orbit around the Earth (C), whereas a faster rocket would follow an elliptical trajectory (D).
On Earth, air tends to prevent exhaust gases from exiting the engine. This lessens the thrust. However, because there is no atmosphere in space, the exhaust gases may depart considerably more easily and quickly.
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What happens if both the speed and radius of a circular path of a body doubled and what will be the effect of it on centripetal acceleration?
Answers
If both the speed and radius of a circular path of a body are doubled then centripetal acceleration will also be doubled.
What Is Centripetal Acceleration?The characteristic of an object moving in a circular path is known as centripetal acceleration. Centripetal acceleration is the term for any moving object whose acceleration vector is directed toward the center of the circle. The centripetal acceleration formula is as follows:
\(a_c=v^2 /r\)
where v is the angular speed and r is the radius.
Now for the given question,
Original centripetal acceleration,
\(a=v^2 /r\)
New centripetal acceleration,
\(a^{'} =(2v)^2 /2r\\\\=2v^2/r\\=2a\)
Hence, centripetal accelearation is also doubled.
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New York is roughly 3000 miles from Seattle. When it is 8:00 a.m. in Seattle, it is 11:00 a.m. in New York. Using this information, estimate the following.
(a) the rotational speed of the surface of Earth
mi/h
(b) the circumference of Earth
mi
(c) the radius of Earth
mi
Answers
The estimated rotational speed of the surface of Earth is 1000 miles per hour. The estimated circumference of Earth is 72000 miles. The estimated radius of Earth is approximately 11459.5 miles.
To estimate the rotational speed of the surface of Earth, we can calculate the time difference between Seattle and New York and the distance between them.
The time difference is 11:00 a.m. - 8:00 a.m. = 3 hours.
The distance between Seattle and New York is given as roughly 3000 miles.
Rotational speed = Distance / Time = 3000 miles / 3 hours = 1000 miles per hour.
Therefore, the estimated rotational speed of the surface of Earth is 1000 miles per hour.
To estimate the circumference of Earth, we can use the distance between Seattle and New York and the time difference.
The time difference of 3 hours corresponds to a time zone difference of approximately 1/24th of a full rotation around Earth.
Circumference of Earth = Distance / Time Difference = 3000 miles / (1/24) = 72000 miles.
Therefore, the estimated circumference of Earth is 72000 miles.
To estimate the radius of Earth, we can use the circumference calculated in the previous step and the formula for the circumference of a circle.
Circumference of Earth = 2π × Radius
72000 miles = 2π × Radius
Radius = 72000 miles / (2π) ≈ 11459.5 miles.
Therefore, the estimated radius of Earth is approximately 11459.5 miles.
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astronomical observations of our milky way galaxy indicate that it has a mass of about 8 1011 solar masses. a star orbiting near the galaxy's periphery is 5.7 104 light years from its center. (for your calculations, assume that the galaxy's mass is concentrated near its center.) (a) what should the orbital period of that star be?
Answers
The orbital period of the star is about 3,520 years.
To solve this problem, we can use Kepler's Third Law, which relates the period of an orbit (T) to the semi-major axis of the orbit (a) and the mass of the central body (M) as follows:
\(T^2 = 4\pi^2a^3/GM\)
where G is the gravitational constant.
Since the star is orbiting near the periphery of the Milky Way, we can assume that its orbit is circular, and the distance from the center of the galaxy to the star is equal to the radius of its orbit (r = a = 5.7x10^4 light years).
Converting this distance to meters and the mass of the Milky Way to kilograms, we get:
\(r = 5.7x10^4 light years x 9.461x10^15 meters/light year = 5.398x10^20 meters\)
M = \(8x10^11 solar masses x 1.989x10^30 kg/solar mass\) = \(1.594x10^42 kg\)
Plugging these values into Kepler's Third Law, we can solve for the period:
\(T^2 = (4\pi^2/6.674x10^-11 m^3/kg s^2)(5.398x10^20 m)^3/(1.594x10^42 kg) = 1.24x10^21 s^2\)
T = \(sqrt(1.24x10^21 s^2)\) = 1.11x10^11 seconds
Converting this to years, we get:
T = \(3.52x10^3 years\)
Therefore, the orbital period of the star is about 3,520 years.
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Newton’s first law of motion was a giant leap forward in scientific thought during Newton’s time. Even today, the idea is sometimes difficult at first for people to understand. Which statement is the best example of an object and motion that would make it hard for people to believe Newton’s first law? A rolling ball eventually slows down and comes to a stop. A wagon must be pushed before it begins to move. The heavier the load in a cart, the harder the cart is to turn. A box does not move when pushed equally from opposite sides.
Answers
Answer: A rolling ball eventually slows down and comes to a stop.
Explanation: Right on Edge2020, not C or B or D.
Answer:
A
Explanation:
Person above me might be right
what is the common name of the equation used to represent conservation of mass?
Answers
The common name of the equation used to represent the conservation of mass is the "Continuity Equation." The Continuity Equation is a fundamental principle in physics and fluid dynamics, stating that mass is conserved within a closed system or within a flowing fluid.
In its simplest form, the Continuity Equation relates the mass flow rate of a fluid to the fluid's velocity and cross-sectional area. Mathematically, it is expressed as:
ρAv = constant
Where ρ represents the density of the fluid, A is the cross-sectional area through which the fluid is flowing, and v is the velocity of the fluid.
The Continuity Equation is widely applicable in various fields, including fluid mechanics, hydraulics, and thermodynamics. It is used to analyze and predict fluid behavior, ensure mass conservation in fluid systems, and study phenomena like fluid flow through pipes, nozzles, and channels.
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a body weights 28N at a height of 3200km from the earth surface.What will be the gravitational force on that body if its lies on the earth surface.
Answers
Answer:
The object would weight 63 N on the Earth surface
Explanation:
We can use the general expression for the gravitational force between two objects to solve this problem, considering that in both cases, the mass of the Earth is the same. Notice as well that we know the gravitational force (weight) of the object at 3200 km from the Earth surface, which is (3200 + 6400 = 9600 km) from the center of the Earth:
\(F_G=G\,\frac{M_E\,m}{d^2} \\28\,\,N=G\,\frac{M_E\,m}{9600000^2}\)
Now, if the body is on the surface of the Earth, its weight (w) would be:
\(F_G=G\,\frac{M_E\,m}{d^2} \\w=G\,\frac{M_E\,m}{6400000^2}\)
Now we can divide term by term the two equations above, to cancel out common factors and end up with a simple proportion:
\(\frac{w}{28} =\frac{9600000^2}{6400000^2} \\\frac{w}{28} =\frac{9}{4} \\\\ \\w=\frac{9\,*\,28}{4}\,\,\,N\\w=63\,\,N \\\)
Assignment
S
of
write the Symbol
Told, mercury and
Cooper, Iron,
Lead
Answers
Answer:
Check explanation
Explanation:
Gold - Au (Aurum)
Mercury - Hg (Hydrargyrum)
Copper - Cu (Cuprum)
Iron - Fe (Ferrum)
Lead - Pb (Plumbum)
These elements in the periodic table are some of the elements represented by letters not in line with their names.
This is because, these elements were known in ancient times and therefore, they are represented by letters from their ancient names.
Energy is the energy an object has because of its motion. True or False
Answers
That depends on what word you skipped at the beginning of the question.
If it's supposed to be "Potential" energy, then the statement is false.**
If It's supposed to be "Kinetic" energy, then the statement is true.
** It's also false if the missing word is "Chemical", "Mechanical", "Thermal", "Nuclear", "Electrical", "Electromagnetic", or "Nervous".)
what happens when air filled balloon is left with its mouth downwards and allowed the air to escape
Answers
Answer:
As their is a high pressure inside the balloon, air would gush out of the ballon.
Due to Newton's Third Law of Motion, When this air exerts a force downwards , the surrounding medium would also exert an equal and opposite force on the ballon.. due to which it would fly upwards.
Explanation:
Before Collision:
2,000 kg 4 m/s 4,000kg 0 m/s
After collision: 2,000 kg + 4,000kg Vt = ?
I will give Brainliest to the first person. Please show work
Answers
Answer:
4/3 m/s
Explanation:
Assuming momentum is conserved, the sum of products of mass and speed before the collision is the same as after:
(2000 kg)(4 m/s) +(4000 kg)(0 m/s) = (2000 +4000 kg)(Vt)
Vt = (8000 kg·m/s)/(6000 kg) = 4/3 m/s
The speed of the combined objects after the collision is 4/3 m/s.
Question 53 Marks: 1 The recommended distance from the bottom of the trench to the ground water table or rock is 62 inches.Choose one answer. a. True b. False
Answers
The above statement is True. The recommended distance from the bottom of the trench to the groundwater table or rock is indeed 62 inches. This distance helps ensure proper wastewater treatment and prevents contamination of groundwater resources.
Groundwater table The water table is an underground boundary between the soil surface and the area where groundwater saturates spaces between sediments and cracks in the rock. Water pressure and atmospheric pressure are equal at this boundary
Groundwater, which is in aquifers below the surface of the Earth, is one of the Nation's most important natural resources. Groundwater is the source of about 37 percent of the water that county and city water departments supply to households and businesses (public supply).
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active mountain belts are most likely to be found
Answers
Active mountain belts are most likely to be found along the margins of continents.
Where do we find active mountain belts?Most mountains and mountain ranges are part of a mountain range formed where two lithospheric plates converge, and in most cases continue to converge.In fact, many mountain belts mark the boundaries of lithospheric plates, and these boundaries intersect other such boundaries.Many of the sedimentary rocks are of marine origin, as mountain belts typically form along tectonic coasts and across subduction zones.Sediments are often part of accretionary complexes that have been folded and compacted by plate tectonic processes and transported to continents.What is a mountain belt?A mountain system or belt is a group of mountain ranges of similar shape structure and orientation that arise from the same cause, usually mountain building. Individual mountains within the same mountain range do not necessarily have the same geological structure or rocks.
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Water has a density of 1000 kg/m3. A piece of rubber has a density
of 1024 kg/m3. Explain what would happen if the rubber was put in
a pool of water?
Answers
Explanation:
if the rubber was put in a pool of water then the rubber sinks in water because the density of rubber (1024 kg/m³) Is more than that of water (100 kg/m³) . As we know if the density is greater than water then the substance sinks in water.
Hope it will help :)
which contributions did johannes kepler make? select three options.
Answers
The three contributions made by Johannes Kepler are:
He solved Ptolemy's model by proving elliptical orbits.He determined that planets move faster when closer to the Sun.He discovered laws of planetary motion. Options 2, 4, and 5.Johannes Kepler was a German astronomer and mathematician who lived from 1571 to 1630. He is best known for his contributions to the field of astronomy, particularly his work on the motion of planets. One of Kepler's most important contributions was his discovery that the orbits of planets are not circular, as previously believed, but elliptical. This discovery was based on years of meticulous observations of the planets, particularly Mars, which allowed him to develop his Three Laws of Planetary Motion.
Kepler's First Law states that planets move in elliptical orbits with the Sun at one of the foci. His Second Law, also known as the Law of Equal Areas, states that a planet will sweep out equal areas in equal times as it travels around the Sun. This means that a planet moves faster when it is closer to the Sun than when it is farther away. Kepler's Third Law, also known as the Harmonic Law, relates the orbital period of a planet to its distance from the Sun.
Kepler's work on planetary motion was groundbreaking and had a significant impact on the way astronomers understood the solar system. His discoveries laid the foundation for Isaac Newton's later work on gravitation and planetary motion. Kepler's contribution to astronomy is widely recognized and celebrated, with various scientific awards and honors named after him.
The complete question is
Which contributions did Johannes Kepler make? Select three options.
He revived Aristotle’s model of the solar system. He solved Ptolemy’s model by proving elliptical orbits. He proved Galileo’s calculations were incorrect. He determined that planets move faster when closer to the Sun. He discovered laws of planetary motion.To know more about the Johannes kepler, here
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Use the drop-down menus to answer the questions. How do objects with the same charge interact? how do objects with opposite charges interact? how do uncharged objects interact?.
Answers
Answer:
1. They repel each other
2. They attract each other
3.They have no affect on each other
Explanation:
got em right
The interaction between the objects with same charge is repulsion.
The interaction between the objects with opposite charge is attraction.
There is no interaction between the uncharged objects.
What is meant by electrostatic force ?Electrostatic force is defined as the force of attraction or repulsion that happens between two charged particles.
Here,
The interaction between the two charged particles is due to the electrostatic force of attraction or repulsion.
Case-1
Interaction between objects with the same charge.
When two objects with same charge are placed at a distance from each other, the force existing between them is the electrostatic force of repulsion. This is because they are two like charges and we know like charges never attracts each other. So, the interaction between them is repulsion.
Case-2
Interaction between objects with opposite charges.
When two objects with opposite charges are placed at a distance from each other, the force existing between them is the electrostatic force of attraction. This is because, they are two unlike charges and we know unlike charges will always attract each other. So, the interaction between them is attraction.
Case-2
Interaction between uncharged objects
When two uncharged objects are placed at a distance from each other, there will be o force of attraction or repulsion between them. This is because the electrostatic force acts between two particles that have charge. So, there is no interaction between the uncharged objects.
Hence,
The interaction between the objects with same charge is repulsion.
The interaction between the objects with opposite charge is attraction.
There is no interaction between the uncharged objects.
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different between clinical And laboratory thermometer.give me 4 points of each
Answers
A pendulum has a length of 7.46 m. Find its period. Theacceleration of gravity
is 9.8 m/s2. Answer in units of s. How long wouldthe pendulum have to be to
double the period? Answer in units of m.
Answers
The pendulum must be 0.401 m to double the period.
Period of a pendulum: The period of a pendulum is the time it takes for it to complete one full back-and-forth movement, also known as a swing.
According to the given question, the length of the pendulum is 7.46 m, and the acceleration of gravity is 9.8 m/s^2. So, we will use the formula for period of a pendulum which is given by: `\(T=2\pi \sqrt{l/g}\)`
where T is the period of the pendulum, l is the length of the pendulum, and g is the acceleration due to gravity. So, substituting the given values, we have: \(T = 2\pi \sqrt{7.46/9.8}\\T = 5.35\ s\)
Therefore, the period of the pendulum is 5.35 s. We are now going to calculate how long the pendulum has to be to double the period. To accomplish that, we'll use the formula for period of a pendulum to calculate the new length of the pendulum.
We will equate the new length to twice the length of the original pendulum. i.e, \(2l = 2\pi \sqrt{(2l)/g}\)
Therefore, we get \(2l/g = \pi \sqrt{(2l)/g}\)
We will now solve the equation for l: \(2 = \pi \sqrt{(2l)/g}\)
Square both sides of the equation: \(4 = \pi^2(2l)/g\)
Divide both sides by π^2 to isolate the value of l:
\(l = 4g/4\pi^2\\l = 0.401 m\)
Hence, the pendulum must be 0.401 m.
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18/5 kmph into m/s (velocity)
By dimensional analysis
Answers
Answer: 1 m/s
Explanation: 1 km = 1000 m (1 kilometer is equal to 1000 meters)
1 hour = 3600 seconds (1 hour is equal to 3600 seconds)
The mass fractions of total ferrite and total cementite in an iron-carbon alloy are 0. 88 and 0. 12, respectively. Is this a hypoeutectoid or hypereutectoid alloy? why?.
Answers
This is a hypoeutectoid alloy because the mass fraction of carbon is less than the eutectoid composition of 0.8%.
What is hypoeutectoid?
The ductility of the eutectoid alloy has decreased by the a factor of three, while that of the hypoeutectoid steel has decreased by the a factor of three. The additional, fragile cementite just on pearlite grain boundaries in hyper-eutectoid alloys reduces the alloy's ductility even more. The proeutectoid cementite limits fracture to the fragile grain boundary zone and limits plastic deformation to a ferrite lamellae inside the pearlite. Such alloys must be chosen for their composition to balance such properties to the requirements of the design in order to be used in light-strong structures. Although a front fork on the a bicycle must meet certain requirements, one of those requirements is high toughness, which necessitates tailoring this same carbon content to provide the required ductility.
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Differences between Pascal's Law & Law of flotation
Answers
Answer:
Pascal's principle states that pressure increases by the same amount throughout an enclosed or confined fluid. Archimedes' principle states that the buoyant force acting on a submerged object is equal to the weight of the volume of fluid displaced by the object.
a sprinter runs 100.0 m in 9.87 seconds. if he travels at constant acceleration for the first 75.0 m and then at constant velocity for the final 25.0 m, what was his acceleration during the first 75.0 m?
Answers
The acceleration of the sprinter during the first 75.0 m was 1.44 m/\(s^2.\)
We can use the kinematic equations of motion to solve this problem. Let's assume that the sprinter has an initial velocity of zero at the starting point, and a final velocity of v at the end of the 75.0 m distance. We can also assume that the time taken to cover the first 75.0 m is \(t_1,\) and the time taken to cover the last 25.0 m is \(t_2\).
For the first 75.0 m, we can use the following kinematic equation:
\(d = (1/2)at1^2\)
where d is the distance covered, a is the acceleration, and t1 is the time taken to cover the distance.
For the last 25.0 m, we can use the following kinematic equation:
\(d = vt_2\)
where d is the distance covered, v is the final velocity, and \(t_2\) is the time taken to cover the distance.
We can also use the following kinematic equation for the entire 100.0 m distance:
\(d = (1/2)at^2\)
where d is the distance covered, a is the acceleration, and t is the total time taken to cover the distance.
Using the given values of distance and time, we can write the following three equations:
75.0 m = \((1/2)at1^2\) (equation 1)
25.0 m =\(vt_2\) (equation 2)
100.0 m = \((1/2)at^2\) (equation 3)
Since the sprinter covers the last 25.0 m at constant velocity, we know that his final velocity, v, is the same as his average velocity over the last 25.0 m. Therefore, we can write:
v = 25.0 m / t2
Substituting this expression for v into equation 3, we get:
100.0 m = \((1/2)at1^2\) + 25.0 m / \(t_2\)
Simplifying this equation, we get:
200.0 m = at1^2 + 50.0 m / \(t_2\)
Now we can use equation 1 to eliminate t1:
\(t_1 =\sqrt(2d/a)\)
Substituting this expression for t1 into equation 2, we get:
25.0 m = \(v(\sqrt(2d/a))\)
Simplifying this equation, we get:
\(v^2\)= 50.0ad
Substituting this expression for \(v^2\) into the previous equation, we get:
200.0 m = (a/2)(2d/a) + (d/a) \(v^2\)
Simplifying this equation, we get:
200.0 m = d(1/2 + 1/2)
or
d = 200.0 m
Substituting this value of d into equation 3, we get:
200.0 m = \((1/2)at^2\)
Simplifying this equation, we get:
a =\((2d/t^2)\)
Substituting the given values of distance and time, we get:
a = (2 x 75.0 m / (9.87 \(s)^2)\)
a = 1.44 m\(/s^2\)
Therefore, the acceleration of the sprinter during the first 75.0 m was 1.44 m/\(s^2.\)
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Find the altitude of the triangle in the figure
below.
50˚
12 m
Answer in units of m.
Answers
9.19m
the altitude of the triangle in the figure below. 50˚ and 12 m
As per figure,
AD is the altitude of the triangle
also AD is perpendicular to BC
so TRIANGLE ABD is a right angled triangle
sin50° = AD/AB = AD/12
AD = 12sin50°
AD = 9.19m
A triangle is said to be right or right-angled if any angle between any two of its sides is 90 degrees or a right angle.One of the most significant geometrical constructions is the right triangle. Base, height, and hypotenuse are the three angles that make up a right triangle. The hypotenuse, or side opposite the right angle, is where the height and base meet at a 90° angle. Since a triangle's interior angles add up to 180 degrees, and one of those angles is 90 degrees, the total of the other two angles must likewise be 90 degrees. The triangle is referred to as an isosceles right triangle if the two angles are equal and 45° each.To know more about right angled triangle visit : https://brainly.com/question/12381687
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When you switched the direction of the voltage on the battery the magnetic compass needle moved. Which of the following is the best explanation for the movement of the compass needle?
A- The copper wire magnetized the compass needle.
B- The compass needle magnetized the copper wire.
C- The current in the wire produced a magnetic field.
D- The compass needle moved due to the Earth's magnetic field and was unaffected by the electromagnet.
Answers
The correct explanation for the movement of the compass needle when the direction of the voltage on the battery is switched is (C) The current in the wire produced a magnetic field.
What is voltage?Voltage, also known as electric potential difference, is a measure of the electric potential energy per unit of charge in an electrical circuit. It is the force that drives the flow of electric charge in a circuit. Voltage is usually measured in volts (V) and is represented by the symbol "V".
When an electric current flows through a wire, it creates a magnetic field around the wire. The direction of the magnetic field depends on the direction of the current flow.
This magnetic field interacts with the Earth's magnetic field and causes the compass needle to move. Therefore, as the direction of the current in the wire changes when the voltage on the battery is switched, the direction of the magnetic field around the wire also changes, causing the compass needle to move.
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please help!
An object is fired up a frictionless ramp, 65° above the horizon. If it’s initial velocity is 35m/s how long does it take for the object to return to starting point?
Answers
Answer:
t= 7.88
Explanation:
Starting with F=ma.
The only force that is going to cause an acceleration is gravity (if we use the coordinate system I described).
F = ma
mgsin65 = ma
a = gsin65
Vf = Vi + at
0 = 35 m/s + (gsin65)t
t = 35/gsin65
multiply it by 2 to get whole time
t = 70/gsin65
t = 7.88 seconds.
A car is going over the top of a hill whose curvature approximates a circle of radius 350 m. At what velocity will the car's occupants appear to weigh 10% less than their average weight?
Answers
The car will appear to be 10% lighter than its normal weight when traveling at a speed of about 16.7 m/s.
Determining the average of an object given the radius of curvature.When the car is going over the top of the hill, the apparent weight of the occupants will be less than their actual weight due to the centrifugal force acting on them.
The centrifugal force acting on the occupants is given by:
Fc = ma
where Fc is the centrifugal force, m is the mass of the occupants, and a is the centripetal acceleration.
The centripetal acceleration is given by:
a = v^2 / r
where v is the velocity of the car and r is the radius of the hill.
The apparent weight of the occupants can be found using:
Wapp = Wactual - Fc
where Wactual is the actual weight of the occupants and Wapp is the apparent weight.
If the occupants appear to weigh 10% less than their average weight, then:
Wapp = 0.9 * Wactual
Substituting the equations for F and a we get:
0.9 * Wactual = Wactual - m * v^2 / r
Simplifying, we get:
m * v^2 / r = 0.1 * Wactual
v^2 = 0.1 * Wactual * r / m
We can express the weight in terms of mass using the formula:
W = m * g
where W is the weight, m is the mass, and g is the acceleration due to gravity.
Substituting, we get:
v^2 = 0.1 * m * g * r / m
v^2 = 0.1 * g * r
Solving for v, we get:
v = √(0.1 * g * r)
Plugging in the values, we get:
v = √(0.1 * 9.81 m/s^2 * 350 m)
v = 16.7 m/s
Therefore, the velocity of the car at which the occupants will appear to weigh 10% less than their average weight is approximately 16.7 m/s.
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Find the net force acting on a box that has a force of 50 newtons pulling at an angle of 30 degrees and a force of 90 newtons pulling at a 160 degree angle
Answers
Answer:
Approximately \(69\; {\rm N}\) at approximately \(126^{\circ}\).
Explanation:
Assume that both angles in the question are relative to the positive \(x\)-axis (towards the positive horizontal direction.)
Horizontal component (\(x\)-component) of the two forces would be:
\((50\; {\rm N}) \, \cos(30^{\circ}) = \left(25\, \sqrt{3}\right)\; {\rm N} \approx 43.3\; {\rm N}\).\((90\; {\rm N}) \, \cos(160^{\circ}) \approx (-84.6) \; {\rm N}\).Note that the \(x\)-component of the \(90\; {\rm N}\) force is negative since this components points away from the positive \(x\!\)-direction.
Hence, the net force in the \(x\)-component would be:
\((50\; {\rm N}) \, \cos(30^{\circ}) + (90\; {\rm N}) \, \cos(160^{\circ}) \approx (-41.3) \; {\rm N}\).
(Again, this component is negative since it points away from the positive \(x\)-axis.)
Similarly, the vertical component (\(y\)-component) of the two forces would be:
\((50\; {\rm N}) \, \sin(30^{\circ}) = 25\; {\rm N}\).\((90\; {\rm N}) \, \sin(160^{\circ}) \approx 30.8 \; {\rm N}\).Hence, the net force in the \(y\)-component would be:
\((50\; {\rm N}) \, \sin(30^{\circ}) + (90\; {\rm N}) \, \sin(160^{\circ}) \approx 55.8\; {\rm N}\).
Refer to the diagram attached. The resultant net force is the vector sum of the components. Apply the Pythagorean Theorem to find this net force:
\(\begin{aligned}(\text{net force}) &= \sqrt{(\text{$x$-component})^{2} + (\text{$y$-component})^{2}} \\ &\approx \sqrt{(-41.3)^{2} + (55.8)^{2})}\; {\rm N} \\ &\approx 69\; {\rm N}\end{aligned}\).
Find the angle of this net force relative to the positive \(x\)-axis using the inverse cosine function \(\arccos\):
\(\begin{aligned}\arccos\left(\frac{(\text{$y$-component})}{(\text{net force})}\right) &\approx \arccos\left(\frac{55.8\; {\rm N}}{69\; {\rm N}}\right) \\ &\approx 126^{\circ}\end{aligned}\).
(The units might need to be converted into degrees.)
Activity 1 MATCH IT
Directions: Match Column A to Column B. Write your answer on the space provided before the number.
COLUMN A
__1. Hiking
__2. Orienteering
__3. Zumba
__4. Volleyball
__5.badminton
COLUMN B
A. It is an outdoor navigational recreational activity using specially drawn and detailed maps.
B. Created through on-the –spot aerobics class using the non- traditional music.
C.Going on an extended walk for the purpose of pleasure and exercise.
D. Can be traced from the ingenuity of William J. Morgan in 1895 at Holyoke Massachusetts.
E. Games are held inside the gym to avoid the effect of air in the flight of the shuttle.
Answers
Answer:
1. A hiking
2. C
3. B
4. D
5. E
Two forces of
411
N and
617
N act on an object. The angle between the forces is
46°.
Find the magnitude of the resultant and the angle that it makes
with the larger force.
Answers
Let's first resolve the two forces into their components as shown in the diagram below: The larger force (617 N) makes an angle of 46° with the horizontal axis.
Therefore, the horizontal component will be given by:
H = 617 cos 46°H = 617 × 0.69H = 425.73 N
The vertical component will be given by:V = 617 sin 46°V = 617 × 0.73V = 450.66 NOn the other hand, the smaller force (411 N) makes an angle of (90° - 46°) = 44° with the horizontal axis. Therefore, the horizontal component will be given by:H = 411 cos 44°H = 411 × 0.72H
= 296.52 N
The vertical component will be given by:V = 411 sin 44°V = 411 × 0.67V = 274.47 N The resultant horizontal component, R will be given by:R = 425.73 + 296.52R = 722.25 N The resultant vertical component, R will be given by:R = 450.66 + 274.47R = 725.13 N The magnitude of the resultant, R will be given by:R² = (722.25)² + (725.13)²R = √(522198.06)R = 722.82 N The angle that R makes with the larger force (617 N) will be given by:θ = tan⁻¹(725.13/722.25)θ = 45.23° Therefore, the magnitude of the resultant is 722.82 N and it makes an angle of 45.23° with the larger force.
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According to newton's second law, if you double the force acting on a body, the acceleration will double.
a. true
b. false
Answers
It is the true statement, that if we double the force acting on a body, the acceleration will double.
What is acceleration?In terms of both speed and direction, acceleration is the rate at which velocity varies over time. Acceleration refers to the change in speed or direction of an item or point travelling straight forward. Due to the constant change in direction, motion on a circle accelerates even while the speed is constant. Both impacts help to accelerate all other types of motion.
In order to be a vector quantity, acceleration must have both a magnitude and a direction. As a vector quantity, velocity is also. A time interval's velocity vector change divided by that interval's duration is the definition of acceleration.
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