Which of the following scenarios is possible for the resultant velocity of an airplane in a strong wind to be 150 m/s?
A. The wind is blowing at 10 m/s. The airplane is flying against the wind at 140 m/s.
B. The wind is blowing at 20 m/s. The airplane is flying with the wind at 130 m/s.
C. The wind is blowing at 200 m/s. The airplane is flying with the wind at 50 m/s.
D. The wind is blowing at 50 m/s. The airplane is flying against the wind at 100 m/s.
Answers
Answer:
B. The wind is blowing at 20 m/s. The airplane is flying with the wind at 130 m/s.
Explanation:
From Physics we get that resultant velocity of an airplane is the sum of an absolute velocity and a relative velocity, that is:
\(\vec v_{A} = \vec v_{W}+\vec v_{A/W}\) (Eq. 1)
Where:
\(\vec v_{W}\) - Wind velocity, measured in meters per second.
\(\vec v_{A/W}\) - Airplance velocity relative to wind, measured in meters per second.
\(\vec v_{A}\) - Airplane velocity, measured in meters per second.
If we assume that \(\vec v_{W} = 20\,\hat{i}\,\,\,\left[\frac{m}{s} \right]\) (The airplane flies with the wind), \(\vec v_{A/W} = 130\,\hat{i}\,\,\,\left[\frac{m}{s} \right]\), then the resultant velocity of the airplane is:
\(\vec v_{A} = 20\,\hat{i}+130\,\hat{i}\,\,\,\left[\frac{m}{s} \right]\)
\(\vec v_{A} = 150\,\hat{i}\,\,\,\left[\frac{m}{s} \right]\)
Therefore, correct answer is B.
Answer:
B. The wind is blowing at 20 m/s. The airplane is flying with the wind at 130 m/s.
Explanation:
Related Questions
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The Euler buckling load of a 160-cm-long column will be _____ times the Euler buckling load of an equivalent 120-cm-long column.
1.78
0.56
0.75
2.37
1.33
0.42
Answers
Answer:
Length in times = 0.75 times
Explanation:
Given:
Length of Euler buckling load = 160 cm
Equivalent load length = 120 cm
Find:
Length in times
Computation:
Length in times = Equivalent load length / Length of Euler buckling load
Length in times = 120 / 160
Length in times = 12 / 16
Length in times = 3 / 4
Length in times = 0.75 times
Describe where radio waves are found on the ems compared to the other six forms of radiation.
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The far left side of the spectrum is where the waves with lower energy are located, while the far right side is where the waves with higher energy are located.
What is radio waves ?
A radio wave is the fundamental component of radio communications. A radio wave is made up of recurring peaks and valleys, similar to the waves on a pond. Before a wave repeats again, its full pattern is referred to be a cycle. The distance a wave travels in one cycle is known as its wavelength. Frequency is the measure of how many times a wave repeats itself in a second. The hertz (Hz) unit of measurement for frequency refers to the quantity of cycles per second. One hertz equals one kilohertz (kHz), one million hertz equals one megahertz (MHz), and one billion hertz equals one gigahertz.A transmitter produces a radio wave, which a receiver then picks up. A radio transmitter and receiver can both transmit and receive energy into and from space using an antenna.Learn more about Radio wave refer to :
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What is the total surface charge qintqintq_int on the interior surface of the conductor (i.e., on the wall of the cavity)
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The total surface charge on the interior surface of the conductor (wall of the cavity) is zero.
When a conductor is in electrostatic equilibrium, the electric field inside the conductor is zero. This means that any excess charge on the conductor will distribute itself in such a way that there is no electric field inside. In the case of a cavity within the conductor, any excess charge on the interior surface will induce an equal and opposite charge on the outer surface of the conductor. This redistribution of charges ensures that the net electric field inside the conductor is zero. Therefore, the total surface charge on the interior surface of the conductor is zero, as the excess charge is effectively canceled out by the induced charges on the outer surface.
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The total surface charge on the interior surface of the conductor (wall of the cavity) is zero.
When a conductor is in electrostatic equilibrium, the electric field inside the conductor is zero. This means that any excess charge on the conductor will distribute itself in such a way that there is no electric field inside. In the case of a cavity within the conductor, any excess charge on the interior surface will induce an equal and opposite charge on the outer surface of the conductor. This redistribution of charges ensures that the net electric field inside the conductor is zero. Therefore, the total surface charge on the interior surface of the conductor is zero, as the excess charge is effectively cancelled out by the induced charges on the outer surface.
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When managers establish accurate measuring and monitoring systems to evaluate how well the organization has achieved its goals, they are engaging in the essential task of _______.
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Managers do the crucial duty of controlling when they create precise measuring and monitoring methods to assess how well the firm has achieved its goals.
What do you understand by monitoring systems?Software that assists system administrators in monitoring their infrastructure is known as a monitoring system. These tools keep an eye on the hardware, software, and traffic of the system and raise the alarm in the event of errors or disturbances. There are several monitoring systems available, ranging from commercial software to freeware.
The monitoring system broadcasts a signal and logs information about the signal, including whether it was received, how long it took the host to receive it, whether any signal data was lost, and other details.
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Can you freeze sound waves
Answers
Answer:
I believe it's not possible
Explanation:
there's really no way I currently know of that we can do that so I suppose no.
que 2. Why do we keep frequency constant instead of keeping vibrating length constam second law of vibrating string?
Answers
Answer:
The second law of a vibrating string states that for a transverse vibration in a stretched string, the frequency is directly proportional to the square root of the string's tension, when the vibrating string's mass per unit length and the vibrating length are kept constant
The law can be expressed mathematically as follows;
\(f = \dfrac{1}{2\cdot l} \cdot \sqrt{\dfrac{T}{m} }\)
The second law of the vibrating string can be verified directly, however, the third law of the vibrating string states that frequency is inversely proportional to the square root of the mass per unit length cannot be directly verified due to the lack of continuous variation in both the frequency, 'f', and the mass, 'm', simultaneously
Therefore, the law is verified indirectly, by rearranging the above equation as follows;
\(m = \dfrac{1}{ l^2} \cdot \dfrac{T}{4\cdot f^2} }\)
From which it can be shown that the following relation holds with the limits of error in the experiment
m₁·l₁² = m₂·l₂² = m₃·l₃² = m₄·l₄² = m₅·l₅²
Explanation:
Explain how the design of a racing car makes it less likely to turn over.
Answers
The principles which allow aircraft to fly are also applicable in car racing. The only difference being the wing or airfoil shape is mounted upside down producing downforce instead of lift. The Bernoulli Effect means that: if a fluid (gas or liquid) flows around an object at different speeds, the slower moving fluid will exert more pressure than the faster moving fluid on the object. The object will then be forced toward the faster moving fluid. The wing of an airplane is shaped so that the air moving over the top of the wing moves faster than the air beneath it. Since the air pressure under the wing is greater than that above the wing, lift is produced. The shape of the Indy car exhibits the same principle. The shape of the chasis is similar to an upside down airfoil. The air moving under the car moves faster than that above it, creating downforce or negative lift on the car. Airfoils or wings are also used in the front and rear of the car in an effort to generate more downforce. Downforce is necessary in maintaining high speeds through the corners and forces the car to the track. Light planes can take off at slower speeds than a ground effects race car can generate on the track. An Indy ground effect race car can reach speeds in excess of 230 mph using downforce. In addition the shape of the underbody (an inverted wing) creates an area of low pressure between the bottom of the car and the racing surface. This sucks the car to road which results in higher cornering speeds.
The total aerodynamic package of the race car is emphasized now more than ever before. Teams that plan on staying competitive use track testing and wind tunnels to develop the most efficient aerodynamic design. The focus of their efforts is on the aerodynamic forces of negative lift or downforce and drag. The relationship between drag and downforce is especially important. Aerodynamic improvements in wings are directed at generating downforce on the race car with a minimum of drag. Downforce is necessary for maintaining speed through the corners. Unwanted drag which accompanies downforce will slow the car. The efficient design of a chassis is based on a downforce/drag compromise. In addition the specific race circuit will place a different demand on the aerodynamic setup of the car.
A road course with low speed corners, requires a car setup with a high downforce package. A high downforce package is necessary to maintain speeds in the corners and to reduce wear on the brakes. This setup includes large front and rear wings. The front wings have additional flaps which are adjustable. The rear wing is made up of three sections that maximize downforce.
The speedway setup looks much different. The front and rear wings are almost flat and are used as stabilizers. The major downforce is found in the shape of the body and underbody. Drag reduction is more critical on the speedway than on other circuits. Since the drag force is proportional to the square of the speed, minimizing drag is a primary concern in the speedway setup. Lap speeds can average over 228 mph and top speeds can exceed 240 mph on a speedway circuit. Effective use of downforce is especially pronounced in highspeed corners. A race car traveling at 200 mph. can generate downforce that is approximately twice its own weight.
Generating the necessary downforce is concentrated in three specific areas of the car. The ongoing challenge for team engineers is to fine tune the airflow around these areas.
What is the mechanical advantage of a pulley? 0.5 1.0 1.5 2.0
Answers
The mechanical advantage of a pulley is the ratio of the output force to the input force.
For example, if a pulley is used to lift a weight of 100 pounds, and the input force is 10 pounds, then the mechanical advantage is 10:1 (100/10).
This means that for every 10 pounds of input force, the pulley can lift 100 pounds of weight. The mechanical advantage of a pulley is determined by the number of strands of rope that are used in the pulley system. The more strands of rope, the higher the mechanical advantage will be.
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This type of severe weather only develops when a group of storms meet over warm tropical waters what type of storm is this
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Christopher, who weighs 240 N, and Thomas, who weighs 185 N, are sitting on opposite ends of a balanced seesaw. If Thomas is sitting 1.2 m from the balance point, how far is Christopher sitting from the balance point
Answers
Answer:
0.925 m
Explanation:
As the seesaw is balanced, the torque ( = Fd)of both should be the same
So, 240 * d = 185 * 1.2
(Assuming d is the distance from Christopher to the balance point)
Solving for d, we get d = 0.925 m
How to derive the formula for centripetal acceleration.
Answers
Because r is given, we can use the second expression in the equation ac=v2r;ac=rω2 a c = v 2 r ; a c = r ω 2 to calculate the centripetal acceleration. Solution.
i) Show that total energy of the body at points A, B and C during the fall is same. ii) Find the distance from A to B and final velocity of the ball just reach before C. mass =5 kg, total height (h)= 100m
Answers
The total energy of the body at evevry point is remained same due to the law of conservation of energy. Distance from A to B and final velocity of the ball just reach before C is 44.3 m/s.
d (distance) from A to B is = √2gh
In this case given are, g = 9.8 m/s² and h = 100m,
so here d = √(2⋅9.8⋅100) = 44.3m.
Final velocity ,v = √2gh
Here given are , v is the velocity, g is the acceleration due to gravity, and h is the height. In this case,
g = 9.8 m/s² ,h = 100m,
v = √(2⋅9.8⋅100)
= 44.3 m/s (final velocity)
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A box with mass of 2 kg is pushed directly horizontally over a horizontal surface (with friction) at a constant speed of 10 m/s. The force of the push is 60 N. How much thermal energy is generated pushing the box a distance of 15 m
Answers
Answer:
E= 600 W
Explanation:
Given that
m = 2 kg
Speed , v= 10 m/s
Force , F= 60 N
Given that box is moving with constant velocity, it means that friction force will be 60 N.
f = 60 N
Therefore total energy generated
E= f x v
E= 60 x 10 = 600 W
E= 600 W
Thus the answer will be 600 W.
The statement “the scientific process is open-ended “means
Answers
We have that the statement "The scientific process is open-ended" means that the process is continues in summary,
From the Question we are told that
The scientific process is open-ended
It is important to note that"The scientific process is open-ended" simply refers to a process can go in different Patterns. Means that questions can have many Reconciliations. experiments are continues and other scientists can added there concepts.
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. A rock is dropped from a height of 4 m. How fast is it going when it hits the ground? The rock has a mass of 2 kg. (Hint: MEi = MEf)
Answers
Hello!
When the rock is dropped, it only contains Gravitational Potential Energy, and when it hits the ground, it contains Kinetic Energy.
So:
PE = KE
\(\large\boxed{mgh = \frac{1}{2}mv^2}\)
We can rearrange to solve for velocity. Cancel out mass and solve.
\(gh = \frac{1}{2}v^2\\\\2gh = v^2\\\\v = \sqrt{2gh}\)
Plug in the givens:
\(v = \sqrt{2(9.8)(4)} = \boxed{8.85 \frac{m}{s}}\)
Answer:
8.85 m/s
Explanation:
a satellite, placed into the earth's orbit to investigate the ionosphere, had the following orbit parameters: perigee, 477 km; apogee, 2271 km (both distances above the earth's surface); period, 112.7 min. find the ratio vp/va of the speed at perigee to that at apogee.
Answers
The ratio of the speed at perigee to that at apogee is 0.935.
The speed of a satellite at perigee and apogee can be calculated using the formula for the velocity of an object in an elliptical orbit, which is given by:
v = sqrt(μ * (2/r - 1/a))
Where v is the velocity, r is the distance from the center of the Earth, a is the semi-major axis, and μ is the gravitational parameter of the Earth (approximately 3.986 x 10^14 m^3/s^2).
The semi-major axis of an elliptical orbit is given by:
a = (r_perigee + r_apogee) / 2
Given, perigee = 477 km = 477000 m; apogee = 2271 km = 2271000 m; period = 112.7 min = 6763 sec
We can find the semi-major axis first:
a = (477000 + 2271000) / 2 = 1274000 m
Then we can find the period:
T = 2 * π * sqrt(a^3/μ)
We can substitute the value of the semi-major axis and the period in the formula, to find the value of the gravitational parameter of the Earth
μ = (4π^2 * a^3) / T^2
Now we have the value of μ and the value of r (perigee and apogee), we can find the speed at perigee and apogee, respectively
v_perigee = sqrt(μ * (2/r_perigee - 1/a))
v_apogee = sqrt(μ * (2/r_apogee - 1/a))
We can use these values to find the ratio of the speed at perigee to that at apogee:
vp/va = v_perigee / v_apogee
By substituting the given values and solving the equations we get:
vp/va = 0.935
The ratio of the speed at perigee to that at apogee is 0.935.
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A large boulder has been perched on the side of a mountain for many years. What change would cause it to suddenly roll down the mountain?
Answers
Answer:
he weight vector approaches the point within the mass, the equilibrium becomes unstable
any change in the conditions of the environment can cause the rock to slide
Explanation:
In general, a rock in a mountain is in stable equilibrium with the help of the force of gravity that causes its weight to be within the center of mass, that is, the weight vector is first and then it is electing the center of mass.
When for some reason the weight vector approaches the point within the mass, the equilibrium becomes unstable, and any change in the conditions of the environment can cause the rock to slide, for example a rain that reduces the friction force.
It may happen that the weight vector is after the center of the hubs, in this case there is an unstable balance and the stone is held in place by the force of friction with the environment that surrounds it, if this friction decreases the rock will slide .
Two friends watch a jogger complete a 400 m lap in 100s .One of the friends states, "The jogger's velocity was 4 m/s during this lap." The second friend objects, saying, "No, the jogger's speed was 4 m/s ." Who is correct?
Answers
The jogger's speed was indeed 4 m/s, as speed is the distance traveled divided by time (400m / 100s = 4 m/s).
However, velocity is a vector quantity that includes both magnitude and direction. Since the jogger completed a lap and returned to the starting point, their overall displacement is zero, resulting in a velocity of 0 m/s. So, the first friend is incorrect in stating that the velocity was 4 m/s.
The second friend is correct. Velocity is a vector quantity that includes both speed and direction, whereas speed is a scalar quantity that only indicates how fast something is moving. Since the question does not provide any information about the direction of the jogger's movement, it is not possible to determine their velocity. However, based on the given information, the jogger's speed can be calculated as distance divided by time, which is 4 m/s (400 m divided by 100 s).
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Azimuth refers to ________________. Group of answer choices the angular displacement westward from the autumnal equinox the angular displacement eastward from the vernal equinox the angular displacement westward from north the angular displacement eastward from north
Answers
Azimuth is referred to as the angular displacement eastward from north
making it an horizontal angle.
What is Displacement?This is defined as the distance or change in position of an object or body.
It can be classified as a vector quantity.
Azimuth is an angular measurement in a spherical system. The
displacement occurs eastwards along the northern or southern plain
which makes option D the most appropriate choice.
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what is a hydraulic system
Answers
Explanation:
Hydraulic systems use the pump to push hydraulic fluid through the system to create fluid power. The fluid passes through the valves and flows to the cylinder where the hydraulic energy converts back into mechanical energy. The valves help to direct the flow of the liquid and relieve pressure when needed
A plane is flying horizontally with speed 171 m/s at a height 6520 m above the ground, when a package is dropped from the plane. The acceleration of gravity is 9.8 m/s 2 . Neglecting air resistance, when the package hits the ground, the plane will be 1. directly above the package. 2. ahead of the package. 3. behind the package.
Answers
Answer:
2. Ahead of the package
Explanation:
The plane is going straight without stopping while the package is going straight down.
.What do all waves transmit?
energy
mass
matter
radiation
Answers
Answer:
Energy I guess can be the answer
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Duff is a breakdancer whose signature move is spinning around on his head while his body is upside down. Which axis is Duff rotating? sagittal transverse axis vertical axis anteroposterior axis frontal horizontal axis
Answers
Answer:
vertical axis
Explanation:
Duff is a breakdancer whose signature move is spinning around on his head while his body is upside down. It means that the center of axis lies at the center of head. it means that Duff is rotating at vertical axis.
Hence, the correct option is (b) "vertical axis"
Answer:
verticalaxis
Explanation:
radiation of a certain wavelength causes electrons with a maximum kinetic energy of 0.60 ev to be ejected from a metal whose work function is 2.90 v. what will be the maximum kinetic energy with which this same radiation ejects electrons from another metal whose work function is 2.19 ev?
Answers
The maximum kinetic energy with which the same radiation ejects electrons from another metal with a work function of 2.19 eV is 1.31 eV.
When radiation of a certain wavelength falls on a metal surface, it can eject electrons from the surface if the energy of the radiation is greater than the work function of the metal. The work function is the minimum energy required to remove an electron from the metal surface. The maximum kinetic energy of the ejected electrons depends on the difference between the energy of the radiation and the work function of the metal. If the maximum kinetic energy of the ejected electrons is 0.60 eV for one metal with a work function of 2.90 eV, then the energy of the radiation can be calculated as 3.50 eV. Using this same radiation, the maximum kinetic energy of the ejected electrons for another metal with a work function of 2.19 eV can be calculated as 1.31 eV. This is because the difference between the energy of the radiation and the work function of the second metal is 3.50 eV - 2.19 eV = 1.31 eV.
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Correctly label the following parts of a motor unit. neuromuscular junction spinal cord skeletal muscle fibers neuromuscular junction skeletal muscle fibers spinal cord
Answers
The correct labeling for the parts of a motor unit is neuromuscular junction, spinal cord, and skeletal muscle fibers.
A motor unit refers to a group of muscle fibers or cells that are controlled by a single motor neuron. Motor units are essential for the functionality of the neuromuscular system as they permit the muscle to produce force and movement. A motor unit is composed of three main parts: neuromuscular junction, spinal cord, and skeletal muscle fibers.
Neuromuscular junction refers to the site where a motor neuron meets and connects with the muscle fiber. This junction is critical for the transfer of impulses and activation of muscle fibers. Spinal cord plays a significant role in the functionality of motor units. It contains motor neurons that control the movement of the skeletal muscle fibers.
The spinal cord receives signals from the brain, which it then translates into a motor response to control the contraction of the muscle fibers. Skeletal muscle fibers refer to the individual muscle fibers that make up a muscle. They are attached to the bones of the skeleton and play an essential role in locomotion and body movements.
Skeletal muscle fibers are activated by the motor neuron, which initiates the release of calcium ions to stimulate the contraction of the muscle fibers.
In conclusion, the correct labeling for the parts of a motor unit is neuromuscular junction, spinal cord, and skeletal muscle fibers.
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The neuromuscular junction is where neurons connect to muscle fibers to transmit muscle contraction signals. Skeletal muscle fibers are the cells within a muscle that contract in response to these signals. These contraction signals originate from motor neurons located in the spinal cord.
Explanation:The neuromuscular junction serves as the connection point between neurons and skeletal muscle fibers that allows signals to pass and trigger contractions. An axon terminal of a motor neuron connects with a muscle fiber at the neuromuscular junction and it uses acetylcholine to propagate signals. Skeletal muscle fibers are individual cells within a skeletal muscle and respond to these signals by contracting, facilitated by the neuromuscular junction. The spinal cord is involved as it houses motor neurons originating from the brainstem and these neurons are responsible for transmitting the signals that cause a skeletal muscle to contract via the neuromuscular junctions.
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What is the weight of a 100 slug box? use acceleration of gravity, g = 32 or g =9.8.
Answers
the weight of a 100 slug box is either 3200 pounds or 9800 newtons, depending on the unit of measurement choose. The weight of a 100 slug box can be calculated using the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity.
In this case, we can use the value of g as 32 ft/s^2 or 9.8 m/s^2, depending on the unit of measurement you prefer.
To calculate the weight of the box using g = 32 ft/s^2:
W = mg = 100 slugs * 32 ft/s^2 = 3200 pounds.
To calculate the weight of the box using g = 9.8 m/s^2:
W = mg = 100 slugs * 9.8 m/s^2 = 9800 newtons.
So, the weight of a 100 slug box is either 3200 pounds or 9800 newtons, depending on the unit of measurement choose.
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the major factor in the development of a constitution is
Answers
Answer:
Below are some of the important dates that led to the creation of the Constitution: 1775 — The Revolutionary War between the Colonies and Britain begins. ... 1781 — The last battle of the Revolutionary War takes place; the 13 states set up a federal government under laws called the Articles of Confederation.
Explanation:
please give me a heart
Q.7. For a system with a transfer function of G(s)=- co² s² +2a+w² if the natural frequency is 0.5 and the damping ratio is 1.3, which of the following statements is correct regarding the unit step response of the system?
O A) Damped
O B) Undamped
O C) Underdamped
O D) Crittically Damped
O E) Overdamped
Answers
The system described by the transfer function G(s) = -co² s² + 2a + w², with a damping ratio of 1.3 and a natural frequency of 0.5, has an overdamped unit step response. So, the correct option is (E)
The transfer function of the system is given as G(s) = -co² s² + 2a + w², where co represents the damping ratio, a represents an arbitrary constant, and w represents the natural frequency of the system. We are given that the natural frequency is 0.5 and the damping ratio is 1.3.
To determine the type of unit step response, we need to analyze the damping ratio (co) in relation to the critical damping value (co_critical).
The critical damping ratio (co_critical) is defined as the value where the system is on the threshold between being overdamped and underdamped. It is given by the formula co_critical = 2 * sqrt(a * w²).
In our case, the natural frequency (w) is 0.5, so we can calculate co_critical as follows: co_critical = 2 * sqrt(a * 0.5²).
Since the damping ratio (co) is given as 1.3, we can compare it with co_critical to determine the type of unit step response.
If co > co_critical, the system is considered overdamped (Option E).
If co = co_critical, the system is considered critically damped (Option D).
If co < co_critical, the system is considered underdamped (Option C).
Based on the given values, we can determine that the system is overdamped (Option E) because the damping ratio (1.3) is greater than the critical damping ratio.
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a crane does 3.00 x 10^4 J of work on a crate in order to lift it 20.0 meter to the roof of a construction site. What is the PE of the crate with respect to the ground? 2. what is the mass of the crate
Answers
The potential energy of the crate with respect to the ground is 3×10⁴ J, and the mass of the crate is 153.1 kg.
What is potential energy?This is the energy of a body by virtue of it position in the gravitationla field.
The potential energy of the crate with respect to the ground is the same as the amount of work needed to lift the crate to a height of 20m.
From the question,
Work done to lift the crate = Potential energy of the crate = 3×10⁴ JAlso,
To caluclate the mass of the crate, we use the formula below.
Formula:
m = P.E/gh.............. Equation 1Where:
m = Mass of the crateP.E = Potential energy of the crateh = height of the crateg = Acceleration due to gravity of the crateFrom the question,
Given:
P.E = 3.00×10⁴ Jg = 9.8 m/s²h = 20 mSUbstitute these values into equation 1
m = 3.00×10⁴/(9.8×20)m = 153.1 kg.Hence, the Potential energy and the mass of the crate is 3×10⁴ J
and 153.1 kg respectively.
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a block is attached to a horizontal spring. it takes 1.0 n to pull the block 11 cm back from its equilibrium position. when the block is released, it oscillates with a frequency of 1.1 hz. what is the mass of the block? answer in kg.
Answers
The mass of the block is approximately 0.23 kg of it oscillates with a frequency of 1.1hz.
We can use the equations for simple harmonic motion to solve this problem. The period of oscillation (T) is the inverse of the frequency (f):
T = 1/f = 1/1.1 Hz = 0.9091 s
The spring constant (k) can be calculated from the force (F) and displacement (x):
F = kx
k = F/x = 1.0 N / 0.11 m = 9.09 N/m
The angular frequency (ω) of the oscillation is:
ω = 2π/T = 6.91 rad/s
The mass (m) of the block can be found from the angular frequency and the spring constant:
ω =
\( \sqrt{ (k/m)}\)
m = 9.09 N/m / (6.91 rad/s) ≈ 0.23 kg
The problem involves a block attached to a horizontal spring, which is pulled back from its equilibrium position by a force of 1.0 N, causing it to oscillate with a frequency of 1.1 Hz. To find the mass of the block, we use the equations for simple harmonic motion, which relate the period (T), angular frequency (ω), mass (m), spring constant (k), force (F), and displacement (x).
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