The rocket’s acceleration is [tex]21m/s^2[/tex]
What is acceleration?Acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is vector quantities as it has both magnitude and direction.
It is given by
[tex]a = \frac{v_f-v_0}{t}[/tex]
Where,
[tex]a =[/tex] average acceleration
[tex]v_f=[/tex] final velocity
[tex]v_0=[/tex] starting velocity
[tex]t =[/tex] elapsed time
What is Thrust?The force acting on an object perpendicular to the surface is called thrust. It is vector quantity and SI Unit of thrust is Newton.
[tex]\mathbf{T}=\mathbf{v} \frac{\mathrm{d} m}{\mathrm{d} t}[/tex]
Where,
[tex]T=[/tex] thrust
[tex]v=[/tex] velocity
[tex]dm=[/tex] change of mass
[tex]dt=[/tex] change in time
Given,
Mass of rocket, [tex]m = 5*10^5Kg[/tex]
Thrust,[tex]T = 1.5*10^7N[/tex]
Air resistance [tex]F_a= 4.5*10^6N[/tex]
The net upward force will be
[tex]F_n= T-F_a\\F_n= 1.5*10^7-4.5*10^6\\F_n= 1.05*10^7N[/tex]
Using
[tex]F = ma\\a = \frac{F}{m}\\a = \frac{1.05*10^7}{5*10^5}\\a = 21 m/s^2[/tex]
Thus the acceleration is [tex]21m/s^2[/tex].
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To calculate the rocket's acceleration, subtract air resistance from the engine's thrust to get the net force and then divide it by the rocket's mass according to Newton's second law. The acceleration is found to be 21 [tex]m/s^2[/tex].
To determine the rocket's acceleration, we must apply Newton's second law of motion, which states that force equals mass times acceleration (F = ma). In this scenario, we have two forces to consider: the rocket engine's thrust and the air resistance acting against it. The net force is calculated by subtracting the air resistance from the engine's thrust.
Firstly, we must find the net force acting on the rocket. To do this, we subtract the air resistance from the thrust:
Net Force = Thrust - Air Resistance
[tex]Net Force = 1.50 X 10^7 N - 4.50 X 10^6 N\\Net Force = 10.5 X 10^6 N[/tex]
Now, using Newton's second law, we set up the equation for acceleration (a = F/m), where F is the net force and m is the mass of the rocket:
Acceleration (a) = Net Force (F) / Mass (m)
[tex]Acceleration (a) = \frac{10.5 X 10^6 N}{5.00 X 10^5 kg}\\Acceleration (a) = 21 \ m/s^2[/tex]
Thus, the acceleration of the rocket is 21 meters per second squared.
"you discover a planet orbiting a distant star that has about the same mass as the sun, with an orbital period of 63 days. what is the planet’s orbital distance?"
The planet's orbital distance is approximately 0.028 astronomical units (AU).
Explanation:The orbital distance of a planet can be calculated using Kepler's Third Law. Kepler's Third Law states that the square of the orbital period of a planet is proportional to the cube of its average distance from the Sun. In this case, the planet has an orbital period of 63 days, which is approximately 0.1726 years. The sun's mass is approximately 1 solar mass. We can use these values to solve for the planet's orbital distance.
Using the formula for Kepler's Third Law, we have:
T^2 = (4*pi^2*a^3)/G*M
Where T is the orbital period, a is the orbital distance, G is the gravitational constant, and M is the mass of the Sun.
Plugging in the values we have:
T^2 = (4*pi^2*a^3)/(6.67430 × 10^-11 m^3 kg^-1 s^-2 * 1 solar mass)
Simplifying the equation, we can solve for a:
a^3 = (T^2 * G * M)/(4*pi^2)
Taking the cube root of both sides, we find:
a = ((T^2 * G * M)/(4*pi^2))^(1/3)
Let's plug in the values:
a = ((0.1726^2 * 6.67430 × 10^-11 m^3 kg^-1 s^-2 * 1 solar mass)/(4*pi^2))^(1/3)
a ≈ 0.028 AU
Therefore, the planet's orbital distance is approximately 0.028 astronomical units (AU).
Block b rests upon a smooth surface. if the coefficients of static and kinetic friction between a and b are μs = 0.4 and μk = 0.3, respectively, determine the acceleration of each block if p = 6 lb
Given
Weight of the block A, Wa = 20 lb, weight of block B Wb = 50 lb. Applied force to block A, P = 6lb, coefficient of static friction µs = 0.4, coefficient of kinetic friction µk = 0.3. If a force P is applied to the body, no relative motion will take place until the applied force is equal to the force of friction Ff, which is acting opposite to the direction of motion. Magnitude of static force of friction between block A and block B, Fs = µsN, where N is reaction force acting on block A. Now, resolve the forces Fx = max. P = (mA + mB)a,
6 = (20 / 32.2 + 50 / 32.2)a
2.173a = 6
A = 2.76 ft/s^2
To check slipping occurs between block A and block B, consider block A:
P – Ff = mAaA
6 – Ff = 1.71
Ff = 4.29 lb
And also,
N = wA. We know static friction,
Fs = µsN
Fs = 0.4 x 20
Fs = 8lb
Frictional force is less than static friction. Ff < Fs
Therefors, acceleration of block A, aA = 2.76 ft/s^2, acceleration of block B aB = 2.76 ft/s^2
Between blocks 'a' and 'b', the coefficients of friction come into play. If the force transmitted from block 'b' to 'a' is greater than the maximum static friction, block 'a' will move and its acceleration can be calculated.
Explanation:The smooth surface implies there is no friction between block 'b' and the surface. However, there is friction between blocks 'a' and 'b'. Hence, the given coefficients of static and kinetic friction, μs = 0.4 and μk = 0.3 would apply there. If the force 'p' was applied to block 'b', since there is no friction between 'b' and the surface, 'b' would move freely with acceleration a = F/m (F: applied force, m: mass of the block).
For block 'a', the acceleration would depend on whether the frictional force is able to resist the force being applied through block 'b'. The static friction is given by μs * N (N: Normal force - equal to the weight of block 'a' in this case), which has to be overcome to set the block motion. Once it starts moving, kinetic friction, given by μk * N, comes into effect. If the force transmitted from block 'b' to 'a' is greater than the maximum static friction, block 'a' will start to move and its acceleration can be calculated by subtracting the kinetic friction from the transmitted force and dividing by the mass of block 'a'.
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A wire is wrapped around a piece of iron, and then electricity is run through the wire. What happens to the iron?
With your hand parallel to the floor and your palm upright, you raise a 3-kg book upward with an acceleration of 2 m/s2. what is the magnitude of force that your hand exerts on the book while it is accelerating?
Answer:
35 N
Explanation:
We are using Newton's law of motion.
Here is what we know:
(T-w)= ma
w = 3 kg (we will change to Newtons in a second)
a = 2m/s^2
rearrange equation to solve for T (tension)
T = ma+w
all we need is mass
Now to get the correct mass we need to divide its weight by the gravitational field strength(in our case it is just gravity) but first we want our weight of 3kg to be in Newtons.
1 kg = 9.81 N
w = (3)(9.81) = 29.4N
Now that our weight is 29.4N we need to divide that by gravity.
m = [tex]\frac{29.4}{9.8}[/tex]
Now that we have mass we can plug in our numbers
[tex](\frac{29.4}{9.8}*2)+29.4 = 35.4N[/tex]
Plugging that into our calculator gives us the answer 35.4 or 35 N
(feel free to correct me if my reasonings for any of this stuff is incorrect)
The magnitude of force that your hand exerted on the book while it accelerates is 35.4 N.
The given parameters;
mass of the book, m = 3 kgacceleration of the book, a = 2 m/s²The magnitude of force that your hand exerted on the book while it accelerates is the tension on your hand.
The tension on your hand while the book accelerates is calculated using Newton's second law of motion;
F = ma
T = ma + w
T = ma + mg
T = m(a + g)
T = 3(2 + 9.8)
T = 35.4 N
Thus, the magnitude of force that your hand exerted on the book while it accelerates is 35.4 N.
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Describe the relationship of the Earth’s lithosphere to the asthenosphere.
The Earth's soft putty-like Asthenosphere carries the Lithosphere (which is like a giant jig-saw puzzle fit around the Earth), and the giant continents on its back.
Lithosphere floats on the top of Asthenosphere
Explanation:The earth crust is made up of tectonic plates and these tectonic plates are always in flow. Together the earths crust and mantle beneath it is called lithosphere. On the other hand the area beneath the mantle is called the asthenosphere. Actually lithosphere is solid in nature and asthenosphere is semi solid or liquid nature. The lithosphere floats on the asthenosphere.
A 2.41 kg block is pushed 1.42 m up a vertical wall with constant speed by a constant force of magnitude f applied at an angle of 59.9 ◦ with the horizontal. the acceleration of gravity is 9.8 m/s 2 . 2.41 kg 59 f .9 ◦ if the coefficient of kinetic friction between the block and wall is 0.521, find the work done by f.
Final answer:
The work done by the force can be calculated using the formula: Work = Force * Distance. The magnitude of the force can be found using trigonometry, and then the work is calculated by multiplying the force by the distance moved. The work done by the force ƒ is 15.32 Joules.
Explanation:
The work done by the force ƒ can be calculated using the formula:
ƒ = Fd
where F is the magnitude of the force and d is the distance moved. In this case, the force ƒ is equal to the horizontal component of the applied force. We can find this component using trigonometry:
ƒ = Fcosθ
where θ is the angle between the force and the horizontal direction. Substituting the given values, we have:
ƒ = (20 N)cos(59.9°)
ƒ = (20 N)(0.539)
ƒ = 10.78 N
Now we can calculate the work done by the force ƒ using the formula:
Work = ƒd
where d is the distance moved. In this case, the distance moved is 1.42 m. Substituting the values, we have:
Work = (10.78 N)(1.42 m)
Work = 15.32 J
Therefore, the work done by the force ƒ is 15.32 Joules.
A 231-ω and a 206-ω resistor are connected in series across an unspecified power supply. if the current through the 231-ω resistor is 0.39 a, what is the exact current (in
a.through the 206-ω resistor? do not include units with your answer.
The characteristics of series circuits, we can find that the current in the two resistances the same, the answer is:
i = 0.39 A flows in the 206 Ω resistorElectric circuits are a system formed by resistors, capacitors and coils, through which the electric current flows, these circuits can be classified:
Parallel circuits. In these circuits there are several branches in such a way that the current is divided between each branch according to its resistance, the advantage that if one branch is broken by the others, electricity can continue to flow. Series cicuits In this type of circuit there is only one path for the current, which is why when it breaks, the current in the entire circuit is interrupted.In this case it is indicated that we have a series circuit, for which all the current must flow through the path, consequently all the current of the circuit must pass through the two resistors.
In conclusion, using the characteristics of series circuits, we find that the current in the two resistances the same, the answer is:
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what is the main difference between protons and neutrons
Answer: charges
Explanation: protons are positively charged while neutrons have no charge at all
Racing greyhounds are capable of rounding corners at very high speeds. a typical greyhound track has turns that are 45 m diameter semicircles. a greyhound can run around these turns at a constant speed of 16 m/s . part a what is its acceleration in m/s2? express your answer to two significant figures and include the appropriate units. a = 11 ms2 submitmy answersgive up correct part b what is its acceleration in units of g ? express your answer using two significant figures.
The relationship between acceleration, velocity and radius is given as:
a = v^2 / r
Since we are given a diameter of 45 m, hence the radius is 22.5 m.
a = (16 m/s)^2 / 22.5 m
a = 11.38 m/s^2
In 2 significant figures:
a = 11 m/s^2
A greyhound running around a semicircular racetrack at a constant speed is experiencing centripetal acceleration due to its changing direction, which, in this case, is approximately 5.71 m/s² or 0.58g.
Explanation:A greyhound running around a semicircular racetrack at a constant speed is not accelerating in the linear sense. However, because its direction is continually changing, it is experiencing centripetal acceleration. Centripetal acceleration can be calculated by the formula a = v^2/r, where v is the speed, and r is the radius of the circular path. Plugging in the given values, we obtain an acceleration of approximately 5.71 m/s²
To find the acceleration in units of g, we need to divide this value by the acceleration due to gravity, which is approximately 9.80 m/s². Therefore, the dog's acceleration is approximately 0.58g. In conclusion, the greyhound experiences a centripetal acceleration of about 5.71 m/s², which is equivalent to 0.58g, when it is running around the turns at the given speed.
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Which structure is found in all EUKARYOTIC cells? Large central vacuole, Golgi apparatus, flagella, cilia
Answer:
Golgi apparatus.
Explanation:
What happens to the frequency of a wave if its energy increases?
The wavelength decreases as the frequency increases.
Explanation:The wavelength λ is the distance between successive peaks in a wave.
The frequency f of a wave is the number of complete waves that pass a point in a given time.
Answer: The frequency of a wave will increase.
Explanation:
The relation between the energy and the frequency is as follows;
[tex]E=h\nu[/tex]
Here, h is the planck's constant and [tex]\nu[/tex] is the frequency of the wave.
The energy of the wave is directly proportional to the frequency of the wave. The frequency is inversely proportional to the wavelength. If the energy of the wave increases then the wavelength of the wave decreases.
If the energy of the wave increases then the frequency of the wave will increase.
A 960 kg motorboat accelerates away from a dock at 2.3 m/s2 .t Its propeller provides a thrust force of 4.1 kN .
All of the following are properties of metals except: Question 1 options: malleable ductile luster brittle
A 1100-kg car pulls a boat on a trailer. (a) what total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-n force on the road and produces an acceleration of 0.550 m/s2 ? the mass of the boat plus trailer is 700 kg. (b) what is the force in the hitch between the car and the trailer if 80% of the resisting forces are experienced by the boat and trailer?
The total resistive force against the car, boat, and trailer is 910 N. The force experienced in the hitch between the car and the trailer is 728 N.
Explanation:This is a classic problem that involves applying Newton's second law and the concept of net force. Newton's second law states that Force = mass * acceleration. Let's begin with the first part of the question.
Given that the car has a mass of 1100 kg and it accelerates at 0.550 m/s2, and uses a force of 1900 N, we realize that this force is not just accelerating the car, but also overcoming some resistance. The total force exerted by the car is the sum of the force to overcome the resistance and the force to accelerate both the car and the trailer. We calculate this total force as follows:
Force_moving = (Mass_car + Mass_trailer) * Acceleration
Force_moving = (1100 kg + 700 kg) * 0.550 m/s2
Force_moving = 990 N
The resistive force then is the difference between the force the car exerts on the road and the force needed to move: Force_resistance = Force_exerted – Force_moving = 1900 N – 990 N = 910 N
In the second part of the question, we’re asked to figure out the force in the hitch between the car and the trailer, if 80% of the resisting forces are experienced by the boat and trailer. We simply take 80% of the resisting force:
Force_hitch = 0.80 * Force_resistance = 0.80 * 910 N = 728 N
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The total resisting force to the motion of the car, boat, and trailer is 910N. The force in the hitch between the car and the trailer, experiencing 80% of the resisting force, is 728N.
Explanation:The subject of this question pertains to Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
(a) We can use this equation to calculate the total a total force that resists the motion of the car, boat, and trailer: F = ma. Here, F is the net force, m is the total mass (car + boat + trailer), and a is the acceleration. Plugging in the given values (F = (1100kg + 700kg) * 0.550m/s²), we find the net force is 990 N. Since the car is exerting a force of 1900 N, the force resisting the motion can be found by subtracting this net force from the force exerted by the car (1900N - 990N), which gives 910 N.
(b) If 80% of the resisting forces are experienced by the boat and trailer, then the force on the hitch would be 80% of the total resisting force, i.e., 0.8 * 910 N = 728 N.
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A roller coaster car rapidly picks up speed as it rollsdown a slope. As it starts down the slope its speed is 4m/s. But 3 seconds later, at the bottom of the slope, its speed is 22m/s. What is its average acceleration?
If i play two pure tones, one at 100 hz and the other at 110hz, will we perceive beats? if so, what will be the beat frequency
how much time would it take for an airplane to reach its destination if it traveled at an average speed of 790 km/hr for a distance
What is the function of a diaphragm in a film camera
during the first 50s a truck traveled at constant speed of 25m/s . Find the distance that it traveled
The truck, traveling at a constant speed of 25m/s for 50 seconds, covers a distance of 1250 meters.
Explanation:To calculate the distance the truck travels during the first 50 seconds at a constant speed, we can use the formula for distance based on speed and time:
Distance (d) = Speed (v) × Time (t)
Given that the truck's speed is 25m/s and the time is 50 seconds, we plug these values into the formula:
d = 25m/s × 50s
Upon multiplying, we find the main answer:
d = 1250 meters
Therefore, the truck traveled a total distance of 1250 meters in the first 50 seconds.
Why is it misleading to describe atmospheric pressure as simply the weight of the air only pressing down on a surface?
compare the bouyant force of water and the weight of a piece of wood that floats on the water
A statement that can be proven by observation or measurement is known as a(n): a. opinion b. value c. fact d. belief Please select the best answer from the choices provided
A statement that can be proven by observation or measurement is known as a fact , therefore the correct answer is option C
what is the scientific investigation?Scientific investigation is the process of looking for answers by doing extensive research and finding the answers through experimental results.
The scientific investigation very much relies on true experimental results that can be supported by evidence.
A scientific fact, also known as empirical evidence, is the outcome of persistent, meticulous observation or measurement by experimentation or another method. The development of scientific hypotheses depends on these.
Theories and facts are two distinct concepts. Facts, which can be observed and/or evaluated, and theories, which are scientists' justifications and assessments of the facts, are clearly distinguished in the scientific method.
Thus, a statement that can be proven by observation or measurement is known as a fact , therefore the correct answer is option C
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The velocity of a 40 kg object increases from 20 m/s to 30 m/s in 2 seconds. What is the acceleration of the object during these 2 seconds
A dog sledding team is comprised of a 80.0 kg musher (the person driving the sled), a 21.0 kg sled and four dogs. assume each dog\'s pull is fully transmitted to the sled, applied parallel to the ground and the sled travels along level ground. how much power does each dog supply to pull the sled/driver system at a constant speed of 8.80 m/s where the coefficient of friction between the sled and the snow is 0.150? (the acceleration due to gravity is 9.81 m/s2.)
To find the force in the coupling between the dogs and the sled, use the equation F = ma where F is the force and m is the total mass. For the power supplied by each dog, calculate P = Fv where P is power, F is force, and v is velocity.
Explanation:The magnitude of the force in the coupling between the dogs and the sled: To calculate the force in the coupling, you can use the equation F = ma, where m is the total mass of the sled and rider, and a is the acceleration of the system. By using the force exerted by each dog and the acceleration calculated from that force, you can determine the force in the coupling. Power supplied by each dog: Power is defined as P = Fv, where F is the force applied and v is the velocity. Calculate the total force applied by all four dogs and the velocity of the sled, then use this information to determine the power supplied by each dog.
Identify the total number of protons and neutrons in the nucleus of the most common isotope of manganese
A wheel with radius 0.487 m rotates 5.75 times every second. find the period of this motion.
To find the period of a wheel that rotates 5.75 times per second, use the formula T = 1/f, resulting in a period of 0.174 seconds.
Explanation:To find the period of the motion for a wheel that rotates 5.75 times every second, we can use the relationship between frequency (f) and period (T). The frequency is the number of revolutions per second, which we're given as 5.75 revolutions per second. The period is the time it takes to complete one revolution. The formula that relates frequency and period is T = 1/f.
Plugging in the given frequency:
T = 1/5.75
Calculating this gives us:
T = 0.174 s
Therefore, the period of this motion, which is the time it takes the wheel to make one complete revolution, is 0.174 seconds.
What was his average swimming speed during the second half of the race if he tied the record, which was at an average speed of 2.05 m/s?
I believe this question has additional detail which stated that during the 1st half, his speed was 2.01 m/s. From this we can calculate his speed during the second half, v2, using the formula:
v_ave = (v1 + v2) / 2
2.05 m/s = (2.01 m/s + v2) / 2
v2 = 2.09 m/s
A rocket experiences a constant force even as the amount of fuel in its fuel tanks decreases. What happens to the acceleration of the rocket as it runs out of fuel?
A - The acceleration decreases because the mass increases.B - The acceleration increases because the mass increases.C - The acceleration decreases because the mass decreases.D - The acceleration increases because the mass decreases.
We can answer this question by looking at Newton's second law:
[tex]F=ma[/tex]
which can be rewritten as
[tex]a=\frac{F}{m}[/tex]
where F is the force experienced by the rocket, m is its mass, a is its acceleration. In the rocket's case, the mass of the rocket decreases (because the fuel in the tank decreases), while the force remains constant, so the ratio F/m increases, and therefore the acceleration of the rocket increases.
Therefore, the correct answer is
D - The acceleration increases because the mass decreases.
A microwave oven operates at 2.00 ghz . what is the wavelength of the radiation produced by this appliance? express the wavelength numerically in nanometers.
Answer:
1.5x10^8
Explanation:
According to kinetic-molecular theory, if the temperature of a gas is raised from 100 °c to 200 °c, the average kinetic energy of the gas will ________.
Actually the Kinetic Energy, which is also known as the energy of motion is directly proportional to temperature. So the higher the temperature is, the faster the gas particles move so they have possess more kinetic energy.
This temperature is in absolute units so we convert to Kelvin:
200 C = 473.15 K
100 C = 373.15 K
So the amount increase is:
473.15 / 373.15 = 1.268
It will increase by a factor of 1.268 or 126.8%
The average kinetic energy of the gas will increase by a factor of 1.27
[tex]\texttt{ }[/tex]
Further explanationThe Ideal Gas Law that needs to be recalled is:
[tex]\large {\boxed {PV = nRT} }[/tex]
P = Pressure (Pa)
V = Volume (m³)
n = number of moles (moles)
R = Gas Constant (8.314 J/mol K)
T = Absolute Temperature (K)
Let us now tackle the problem !
[tex]\texttt{ }[/tex]
Given:
initial temperature of the gas = T₁ = 100°C = 373 K
final temperature of the gas = T₂ = 200°C = 473 K
Asked:
ratio of average kinetic energy of the gas = Ek₁ : Ek₂
Solution:
[tex]Ek_1 : Ek_2 = \frac{3}{2}kT_1 : \frac{3}{2}kT_2[/tex]
[tex]Ek_1 : Ek_2 = T_1 : T_2[/tex]
[tex]Ek_1 : Ek_2 = 373 : 473[/tex]
[tex]Ek_2 = \frac{473}{373} Ek_1[/tex]
[tex]Ek_2 \approx 1.27 \times Ek_1[/tex]
[tex]\texttt{ }[/tex]
Conclusion:The average kinetic energy of the gas will increase by a factor of 1.27 if the temperature of a gas is raised from 100°C to 200°C.
[tex]\texttt{ }[/tex]
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Answer detailsGrade: High School
Subject: Physics
Chapter: Pressure