The magnitude of the normal acceleration is inversely proportional to the radius of curvature. This is choice 1b.
Normal Acceleration: Also known as radial acceleration or centripetal acceleration, normal acceleration a(n) = v^2/r, where v is the tangential velocity. It is responsible to change the direction of velocity and thus keeping particle in circular motion.
The tangential acceleration is a measure of the rate of change in the magnitude of the velocity vector, i.e. speed, and the normal acceleration are a measure of the rate of change of the direction of the velocity vector.
When the radius of the circular path goes down, the centripetal acceleration goes up.
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--The complete question is, The magnitude of the normal acceleration is,
a. proportional to radius of curvature.
b. inversely proportional to radius of curvature.
c. inversely proportional to diameter of curvature.
d. zero when velocity is constant.--
What system is the coffee cup calorimeter?
We can presume that all of the heat from the metal was transmitted to the water because the walls of the coffee-cup calorimeter are thought to be entirely adiabatic.
A calorimeter is a what kind of system?An instrument called a calorimeter measures the amount of heat produced during a chemical or physical process. For instance, when an exothermic reaction takes place in solution in a calorimeter, the solution absorbs the heat created by the process, raising its temperature.
The closed nature of a coffee cup calorimeter is why?Coffee calorimeters are isolated (but only if they have a lid that prevents gas from leaving) - they maintain constant pressure and, in a perfect world, allow no heat exchange (adiabatic); but, depending on the setup, gases (or matter) can exchange.
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a force of 30.0 n accelerates a 2.0 kg object from rest for a distance of 3.0 m along a level, frictionless surface; the force then changes to 15 n and acts for an additional 2.0 m. a) what is the final kinetic energy of the object? b) how fast is it moving?
The force acts in same direction for a further 2.0 m before decreasing to 15 N. the body's total kinetic energy is given by bodya = Fnet / m.
Describe kinetic energy?An object's amount of kinetic energy it has as a result of motion. Applying force is necessary if we wish to accelerate an object. We have to put in work to apply a force.
Energy – what is it?Energy, according to scientists, is the capacity for work. The ability to transform converted one object to another and use it to perform tasks is what makes modern civilization possible.
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you are going to an outdoor concert, and you'll be standing near a speaker that emits 51 w of acoustic power as a spherical wave. what minimum distance should you be from the speaker to keep the sound intensity level below 94 db ?
The minimum distance from the speaker to keep the sound intensity level below [tex]94 dB is 3.7 m.[/tex]
What is the intensity ?.Intensity is the amount of energy or force associated with a particular phenomenon or activity. It is usually measured in terms of power, amplitude, or strength. Intensity can be seen in many forms, including sound, light, heat, electricity, and magnetism. In terms of sound, for example, intensity is measured in decibels and is related to the loudness of a sound.
The intensity of a sound wave decreases with distance. Intensity is measured in decibels (dB) and is related to the sound pressure level (SPL) of the wave.
The formula for calculating the intensity of a sound wave at a given distance from its source is as follows:
[tex]I = I_o/r^2[/tex]
where [tex]I_o[/tex] is the initial intensity of the wave (in dB) and r is the distance from the source (in meters).
In this case, the initial intensity of the wave is 51 W as a spherical wave, so[tex]I_o = 51 W.[/tex]
We want to find the minimum distance r such that the intensity of the sound wave is 94 dB, so we can rearrange the equation to solve for r:
[tex]r^2 = I_o/Ir = sqrt(I_o/I)r = sqrt(51 W/94 dB)r = 3.7 m[/tex]
Therefore, the minimum distance from the speaker to keep the sound intensity level below 94 dB is 3.7 m.
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the two plates of a capacitor hold and of charge, respectively, when the potential difference is 960 v. what is the capacitance?
When there is a potential difference of 960 volts, the capacitance of a capacitor's two plates is 2.6 F.
What is the difference in potential between two capacitor plates?
V = E d, or the electric field intensity times the distance between the plates, is used to express the electrical potential difference between the two plates. The final units in this expression are Joules/coulomb, which are obtained by multiplying Newtons/coulomb by meters.
What does a capacitor's two plates contain?
The capacitor has two plates: one with a positive charge Q and the other with a negative charge -Q. The potential difference V between the two plates is proportional to the charge Q on the plates. Q = CV, where C is the proportional constant.
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if the heating value of coal (heat that is realeased when 1 kg of coal is burned) is 30 mj/kg , determine the rate of consumption of coal in tons(us)/day . assume that 100 % of heat released goes to the cycle.
The rate of consumption of coal is approximately 0.102 tons per day.
The heating value of coal, which is the amount of heat released when 1 kilogram of coal is burned, is 30 megajoules per kilogram. If 100% of this heat is used in a cycle, the rate of consumption of coal in tons per day can be determined by multiplying the heating value by the number of kilograms of coal burned in a day and converting the result to tons. To convert megajoules to tons, you can divide the result by the energy equivalent of 1 ton of coal, which is approximately 29.3 gigajoules. The calculation would be as follows: (30 MJ/kg) × (kg of coal burned in a day) / (29.3 GJ/ton) = tons of coal burned per day.
Let's assume that the rate of consumption of coal is 10,000 kilograms per day.
The calculation to determine the rate of consumption in tons per day would be as follows:
(30 MJ/kg) × (10,000 kg/day) / (29.3 GJ/ton) = (30 × [tex]10^{6}[/tex] J/kg) × (10,000 kg/day) / (29.3 × [tex]10^{9}[/tex] J/ton) = 0.102 tons/day.
So, the rate of consumption of coal is approximately 0.102 tons per day when 10,000 kilograms of coal are burned per day and 100% of the heat is used in the cycle.
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determine the velocity of car a if point p on the cable has a speed of 4 m>s when the motor m winds the cable in.
When the motor m winds the wire in at a speed of 1 m/s, the point p on the cable moves at a speed of 4 m>s.
Is speed also referred to as velocity?Quickness of motion or activity is known as velocity. Speed is a shorter term and a synonym for celerity. The term "velocity" in physics especially refers to the measurement of an object's rate and direction of positional change. It is a vector quantity that describes a body's motion in terms of both speed and direction.
(La - Lp) + La + 2(La - C) = L
La - Lp + La + 2La - 2C = L
4La - Lp -2C = L
4Va - Vp = 0
4Va = Vp
4Va = 4
Va = 1m/s
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a block of metal which weighs 60 newtons in air and 40 newtons under water has a density, in kilograms per meter cubed, of:
Answer:
B = buoyant force of water = (60 - 40) N = 20 N
S (specific gravity) = Weight object / Weight of water
S (water) = 1 gm/cc = 1000 kg/m^3
S (block) = 60 N / 20 N * 1000 kg/m^3 = 3000 kg/m^3
when you bring a small object close to a charged tape you find that there is an attraction between them. considering all the evidence you have seen, what can you conclude about the charge of the small object?
Option d is Correct. B or C might be accurate. A charged tape will draw both neutrally charged objects and those with the opposite charge to the tape.
The tape has a negative charge because it has additional electrons. Electrons in your skin are rejected and migrate away when you move your finger close to the tape. Your finger tip's skin develops a tiny positive charge as a result of this. The tape goes toward your finger because positive and negative things draw each other.
Charged objects have an imbalanced charge, either more positive protons or electrons than electrons. Additionally, neutral objects have an equal quantity of protons and electrons, balancing their charge. The same idea that applies to atoms also applies to objects.
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Correct Question:
When you bring a small object close to a charged tape you find that there is an attraction between them. Considering all the evidence you saw in early in this unit, what can you conclude about the charge of the small object?
a. It has the same charge as the tape.
b. It is uncharged.
c. It has the opposite charge to the tape.
d. Either B or C could be true.
On the way to work in the morning, a man drives five miles east to a gas station before heading another ten miles north to his office. Assuming he travels directly from work at the end of the day, what is the magnitude of the resultant displacement ‘C’?
The separation between two places of the an object in motion is known as displacement.Therefore, it depends on both the starting position and the ending position.Displacement is also the shortest distance between the initial and ultimate places.
How can the length traveled from position function be determined?We may determine the overall distance traveled from t = a to t = b by a body with location function s (t) when it moves along a coordinates line without changing direction.To get the overall distance traveled if the body changes course more than once throughout the journey, we must integrate the body's velocity |v (t)|.
10 meters: What does that mean?Greek prefixes are applied to units bigger than meters:A dekameter was 10 meters; the prefix deka- indicates "ten."Hectometers measure distances in units of 100 meters.A km is 1,000 meters, and the prefix kilo- denotes 1,000.
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if i double the length, and halve the diameter of a copper wire, what is the value of its new resistance? original resistance was r0
The new resistance of the wire will be 4 times the original resistance (r0).
This is because the resistance of a wire is proportional to its length and inversely proportional to its cross-sectional area. Doubling the length of the wire will double its resistance. Halving the diameter of the wire will result in a reduction of its cross-sectional area by a factor of 4, which will result in an increase in its resistance by a factor of 4. The net effect is that the resistance of the wire will be 4 times the original resistance.
To be more precise, the resistance R of a wire is given by the equation
R = ρL / A
where ρ is the resistivity of the material, L is the length of the wire, and A is its cross-sectional area. So, if we double the length and halve the diameter, the new resistance will be given by
R = ρ(2L) / (A/4) = 4ρL / A = 4R0.
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what average force is required to stop a 990 kg car in 7.2 s if the car is traveling at 83 km/h ? express your answer to two significant figures and include the appropriate units.
The average force required to stop a car, we need to calculate the change in momentum of the car. The formula for the change in momentum is given by: Δp = m * vf - vi is 32 kN.
where Δp is the change in momentum, m is the mass of the car,
vf is the final velocity, and
vi is the initial velocity.
Since the car is stopping,
the final velocity is zero.
Next, we can use the equation for force,
which is:
Force = Δp / Δt
where Δt is the time taken to stop the car.
So, we can substitute the change in momentum equation into the force equation to get:
Force = (m * vi) / Δt
Now, we can substitute the known values into this equation:
Force = (990 kg * 83 km/h) / 7.2 s
First, we need to convert the initial velocity from km/h to m/s:
83 km/h = 83 * 1000 / 3600 m/s
= 23.06 m/s
So, the equation becomes:
Force = (990 kg * 23.06 m/s) / 7.2 s
Force = 32,400 N
So, the average force required to stop a 990 kg car traveling at 83 km/h in 7.2 seconds is approximately 32,400 N. To two significant figures, this is 32 kN.
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rigid rod of negligible mass lying along the y axis connects three particles as shown: should the total rotational kinetic energy from (c) be the same as the total kinetic energy of the system you calculated from (e)? why or why not?
Total rotational kinetic energy & the total kinetic energy (KE_tot) are not necessarily same as one is associated with rotational motion and other with total energy.
The total rotational kinetic energy (KE_rot) and the total kinetic energy (KE_tot) of a system are not necessarily the same, as they represent different types of energy. KE_rot represents the energy associated with rotational motion, while KE_tot represents the total energy of the system, including both translational motion and rotational motion.
In the case of the rigid rod connecting three particles, if the system is in rotational motion, the particles will have both translational and rotational motion. The translational motion of the particles contributes to the total kinetic energy of the system, while the rotational motion contributes to the rotational kinetic energy of the system.
In general, it can be said that KE_rot and KE_tot are related, but their values will depend on the specific details of the system, such as the masses of the particles, their distances from the axis of rotation, and the speed and direction of their motion.
It is not necessarily the case that the total rotational kinetic energy from (c) should be the same as the total kinetic energy of the system you calculated from (e), as the two represent different aspects of the energy of the system. However, in some specific cases, if the system is in pure rotational motion, the total rotational kinetic energy and the total kinetic energy of the system will be the same.
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if the object is moving horizontally and at the same constant speed of 0.1 m/s, a force must be exerted on it to maintain that motion. that means someone is doing work! calculate the work required to maintain the motion for 16 seconds.
The work required to maintain the motion for 16 seconds is 0.16 J.
work = force x distance
In this case, the distance is constant and equal to the horizontal distance covered in 16 seconds, which is 0.1 m/s x 16 s = 1.6 m.
The force required to maintain the horizontal motion at a constant speed is known as the frictional force, which is equal to the force of friction times the normal force. In this case, let's assume the frictional force is 0.1 N.
So the work done in maintaining the horizontal motion for 16 seconds would be:
work = force x distance = 0.1 N x 1.6 m = 0.16 J (joules)
Therefore, the work required to maintain the motion for 16 seconds is 0.16 J.
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assume the driver has a mass of 72.1 kg . what horizontal force does the seat exert on the driver? answer in units of n.
The horizontal force that the seat exerts on the driver is 72.1 times the acceleration of the car, expressed in Newtons (N), the unit of force.
What is the force ?
Force is a type of physical phenomenon that can cause an object to move, stop, accelerate, deform, or otherwise change its state of motion. A force is a vector, which means it has both magnitude and direction. Force is one of the fundamental building blocks of physics, and is an important concept to understand when studying the behavior of physical systems
The horizontal force that the seat exerts on the driver depends on the acceleration of the car. If the car is not accelerating, then the seat exerts no horizontal force on the driver (only a vertical force due to the weight of the driver).
However, if the car is accelerating, then the seat will exert a horizontal force on the driver to accelerate the driver along with the car. The magnitude of this force can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Let's assume that the car is accelerating with an acceleration of a m/s^2, and that the driver has a mass of 72.1 kg.
The horizontal force that the seat exerts on the driver can be calculated as follows:
Net force = mass x acceleration
F_seat - friction_force = m_driver x a
where F_seat is the force that the seat exerts on the driver, and friction_force is the force of friction between the driver and the seat.
If we assume that the friction force is negligible (for example, if the driver is wearing a seatbelt that prevents them from sliding on the seat), then we can simplify the equation to:
F_seat = m_driver x a
Substituting the values, we get:
F_seat = 72.1 kg x a
So the horizontal force that the seat exerts on the driver is 72.1 times the acceleration of the car, expressed in Newtons (N), the unit of force.
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Identifying Forces
For the following situations:
1) Draw a picture describing each situation
2) Write all of the forces acting on the underlined object (and include the direction that the force is acting in).
3) Draw an FBD for the underlined object.
A) Doughnut resting on a coffee table.
B) Football as it travels through the air (it's already been tossed).
C) A box sliding across concrete
D) A cat sitting on a rug
The free body diagram shows the forces that act on the object.
What is a free body diagram?We know that force is a vector quantity as such the direction of the force can also be seen to be very important and this is what have given rise to the idea of the free body diagram because it would show all the forces that have acted on the objects.
In effect, what we have been asked to do here is to draw the free body diagram of the system that is under study here. In this diagram all of the forces that is acting on each of the objects must be balanced.
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at least two forces are acting on you right now. what are these forces? describe the relationship between the size and direction of these two forces
According to Newton's third law of motion, For every action, there is an equal and opposite reaction.
If a body is pressed against another body with some force, the second body also presses the first body with an equal and opposite force. The force with which the first body presses the second is called the action force, while the force exerted by the second body on the first one is called the reaction force. Action and reaction forces always occur in pairs.
While sitting the forces acting on us are;
The force of gravity W=m g
The normal force $N$ applied by the chair.
The force 'mg' acts downward on the chair due to us, while the normal force '{N} ' applied by chair acts upward on us.
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what is social peace.
Answer:
Social peace is achieved when people have a strong two-way relationship with the state and other community groups, and they trust that decisions by the state are made fairly, even if they do not benefit from them directly.
Answer:
Social peace is a state of society in which there is no significant conflict or violence.
Explanation:
Social peace is a state of society in which there is no significant conflict or violence. It is characterized by a high degree of social harmony and cooperation, and by a lack of social unrest or instability.
Social peace is important for a number of reasons. It allows people to live and work together without fear of violence or intimidation. It also facilitates economic development and social progress. In addition, social peace can help to prevent the outbreak of war or other forms of large-scale violence.
There are a number of factors that can contribute to social peace. These include:
Good governance:There are a number of things that individuals can do to promote social peace. These include:
Be kind and respectful to others, regardless of their differences.Get involved in your community and work to solve problems together.Speak out against violence and injustice.Vote for leaders who promote peace and social justice.Social peace is not something that happens overnight. It takes time, effort, and commitment from everyone in society. However, it is an essential goal for any society that wants to live in peace and harmony.
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so how can we infer some of the properties of the solar system by the orderly motions? what about sizes?
Naturally, a falling gas cloud tends to heat it up, spin more quickly, and flat out as it gets smaller. Consequently, our solar system started as a rotating disc of gas.
What size is it?The dimensions are described by size. Example: Consider a box that is shaped like a cube. Its proportions, including length, width, and height, determine its size. Are length and height equivalent.
What is the duration?The measured distance between the two ends.
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the motorcycle is traveling at a constant speed of 60 km>h. determine the magnitude of its acceleration when it is at point a.
The magnitude of its acceleration when it is at point a. is 0.763 [tex]m/s^2[/tex]
Acceleration is the rate at which the speed and direction of a moving object change over time.Something is said to be accelerating when it starts to move faster or slower.Motion on a circle accelerates even while the speed is constant because the direction is always changing.These collisions lead to an acceleration of all other motion types.Another vector quantity is velocity. The change in velocity vector over a time interval divided by the time interval is the definition of acceleration.
[tex]y=\sqrt2 x^{\frac{1}{2} }[/tex]
[tex]\frac{dy}{dx} =\frac{1}{2} \sqrt2x^{\frac{-1}{2} }[/tex]
[tex]\frac{d^2y}{dx^2} =\frac{-1}{4} \sqrt2x^{\frac{-3}{2} }[/tex]
[tex]p=\frac{[1+\frac{dy}{dx}^2]^{\frac{3}{2} } }{\frac{d^2y}{dx^2}} =\frac{[1+\frac{1}{2} \sqrt2x^{\frac{-1}{2} }]^{\frac{3}{2} } }{\frac{-1}{4} \sqrt2x^{\frac{-3}{2} }} \\:[/tex] at x= 25m
p=364.21 m
acceleration: the speed of motorcycle at a is
v = [tex](60) \frac{km}{h}(\frac{1000 m}{1Km})(\frac{1h}{3600s})[/tex]= 16.67 m/s
[tex]a_n=\frac{v^2}{p}=\frac{16.67^2}{364.21}=0.7627 \: m/s^2[/tex]
since the motorcycle travels with the constant speed a=0 the magnitude of acceleration of motorcycle at a is
a=[tex]\sqrt{a_r^2+a_n^2}=\sqrt{0^2+0.7627^2}=0.763\: m/s^2[/tex]
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you rub a balloon on your head, and the balloon gains a charge of 50 nc n c . how many electrons were transferred during this process?
Number of electrons transferred in this process are given by = 3.125 x 10^11 electrons
What is electron?The smallest elemental component of an atom, the electron has a negative charge. In a neutral atom, there are an equal number of electrons and protons. One electron but one proton are all that the hydrogen atom has. On the other hand hand, the uranium atom includes 92 protons, this means 92 electrons.
Given:
q = magnitude of charge gained by balloon = 50 nC = 50 x 10^-9 C
e = magnitude of charge on electron = 1.60 x 10^-19 C
When you rub balloon on your head, the electrons from your head migrate to balloon. As a result balloon becomes negatively charged and your head becomes positively charged.
We can compute the number of electrons transferred in the process as follows:
Let N = number of electrons transferred in this process = q / e
N = q / e = (50 x 10^-9 C) / (1.60 x 10^-19 C) = 3.125 x 10^11 electrons
N = 3.125 x 10^11 electrons [answer]
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in coming to a stop, a car leaves skid marks 85 m long on the highway. assuming a deceleration of 3.50 m/s2 m / s 2 , estimate the speed of the car just before braking.
The speed of the car just before applying the brakes is 24.39 m/s.
Given details in he question are:
Deceleration is 3.50 m/s2
Skid marks by the kid - 85 m
The formula to be used in the question is:
[tex]V^{2}=u^{2}+2as\\[/tex]
[tex]v^{2}=0+ 2 (3.50)(85)\\[/tex]
[tex]v^{2}= 595\\v=24.39 m/s[/tex]
The speed of the car just before applying the brakes is 24.39 m/s.
The average speed can be explained as the displacement of a particle divided into a time in which the displacement occurs. Instantaneous speed is calculated to be the limit of the average speed as the time interval approaches zero. Speed denotes distance traveled divided by time on the contrary instantaneous speed measures how quickly and in which direction does it move.
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he ship based on this hull design is to have a cruising speed of 24 mph. to ensure dynamic similarity for a 1:32 scale model, at what velocity should the model be tested?
The velocity with which the model should be tested is calculated to be 768 mph.
When the length, time, and force scale ratios of the model and prototype are the same, dynamic similarity exists.
Dynamic similarity enables scaling of model test outcomes to forecast matching outcomes for the full-scale prototype.
The dynamic similarity of a ship is given to have a scale 1:32.
The cruising speed of the first ship is given as, 24 mph.
So, the velocity of the model is calculated as,
⇒ 24 × 32 = 768 mph
Thus, the velocity of the model should be tested at 768 mph.
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-.The Scablands in Washington are large
areas of erosion due to immense flooding. A
student claims the flooding of the Scablands
is due to erosion and melting of glaciers
which increased the amount of water until
it overwhelmed the dams. Using the claim
and map shown, create a claim-evidence-
reasoning model.
Water flo
Answer:
Here is a claim-evidence-reasoning (CER) model for the student's claim about the flooding of the Scablands:
Claim: The flooding of the Scablands is due to erosion and melting of glaciers which increased the amount of water until it overwhelmed the dams.
Evidence:
Erosion patterns in the Scablands that suggest a large amount of water was present in the region.
The presence of glacial deposits in the area.
The location of the Scablands near glacial formations that would have melted and contributed to the increase in water.
Reasoning: The evidence supports the idea that melting glaciers and erosion caused a significant increase in water in the region, which then overwhelmed the dams and caused flooding in the Scablands. The presence of glacial deposits and the proximity to active glacial formations suggest that a large amount of water was released into the area, causing the observed erosion patterns and the flooding.
Explanation:
when the ciliary body changes the size and shape of the lens by contracting or relaxing, this refractory adjustment is known as:
The zonular fibers, a group of minuscule fibrous strands, hold the ciliary body to the lens. This add-on is essential
What exactly minuscule is tiny?
The definition of tiny. (Page 1 of 2) lowercase letter 1 2a: one of a number of cursive writing types that emerged in the ancient and medieval periods and included small, simpler forms. B: This kind of a letter.
Is our understanding of the effects of any occurrence minimal?
Or possibly tiny, like the daydreams we think and pray will keep us safe. It should be clear that compared to the full range of repercussions leading till the of history, our understanding of the impact of any given event is extremely limited.
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a carpinter is pounding a nail into the wall the reaction force to the force of a hammer hitting a nail is
Newton's third law of movement expresses that the response power to the power of a hammer striking a nail is equivalent and inverse.
As indicated by this, there is an inverse and equivalent reaction to each activity. At the point when the hammer strikes the nail, the nail hits back with equivalent and inverse power.
The power that drives the nail into the wall is alluded to as the reaction force. The reaction power's course is the specific inverse of the applied power's heading.
As an outcome, the powers are adjusted and energy is moved from the hammer to the nail.
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two telephone poles are separated by 40 m and connected by a massless wire. a bird of mass 0.5 kg lands on the wire midway between the poles, causing the wire to sag 2.0 m below horizontal. what is the tension in the wire?
According to the static equilibrium, the tension in the wire would be 24.62 N
Since all parts of the system are at rest (Ftotal = Ttotal = 0), we will be using static equilibrium. An object is said to be in a state of static equilibrium when all of the forces acting on it are in equilibrium with one another and the object is not moving in regard to the relative plane.
Thus, the tension in the wire would be:
2Fy = m × g
Fy = (m × g) ÷ 2
Fy = (0.5 × 9.8) ÷ 2
Fy = 2.45 N
Sinθ = 2 ÷ √(4+400)
F = Fy ÷ Sinθ
F = 2.45 ÷ 0.0995
F = 24.62 N
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a karate master is about to split a piece of wood with his hand. in order to deliver the maximum force to split the wood, she will:
With as much force as she can muster, strike it wood perpendicular towards its surface. Then, as swiftly as she can, snap her hand back.
Which four fundamental forces are there?Any of the four fundamental forces in physics—gravitational, magnetic, strong, & weak—that control how things or particles interact as well as how some particles decay—is referred to as a fundamental force, also known as a fundamental interaction. It is possible to link these fundamental forces to all known natural forces.
What are the two terms that best sum up a force?
A force can be adequately described by two concepts: push and pull. The push or pull that causes a mass item to change velocity in physics is known as force.
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for springs connected in series, how does the effective spring constant compare to the individual spring constants? determine a simple mathematical relationship.
For springs connected in series, the effective spring constant can be compared to the individual spring constants mathematically by k1 + k2 + k3 +... + kn = keff
The effective spring constant, also known as the equivalent spring constant, is equal to the sum of the individual spring constants for springs connected in series.
where Keff represents the effective spring constant and ki represents the spring constant of the ith spring in the series.
It is vital to notice that springs in a series connection experience the same amount of displacement and hence the same amount of force. Each spring's displacement is proportional to its spring constant, and the overall displacement of the system is equal to the sum of each spring's displacements. This indicates that the system's equivalent spring constant will be the total of the separate spring constants indicated above.
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if a pendulum-driven clock gains 5.20 s/day, what fractional change in pendulum length must be made for it to keep perfect time? (your answer should be negative if the length is decreased.)
The fractional change in pendulum length must be -0.0026, meaning the pendulum length should be decreased by 0.0026 of its original length.
To keep a pendulum-driven clock accurate, the fractional change in pendulum length must be negative since a decrease in length will cause the pendulum to go faster.
To find the exact fractional change required, you must use the equation for simple harmonic motion, which states that the period of the pendulum is proportional to the square root of the length.
If the clock is gaining 5.20 s/day, then the fractional change in pendulum length must be -0.0026, meaning the pendulum length should be decreased by 0.0026 of its original length.
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80 POINTS!! Please show your though process. Picture is attached. Thank you!
The final kinetic energy of the block depends on the height of the ramp and mass of the block, also, final speed and mass of the block.
option B and D.
What is the final kinetic energy of the ball?
The final kinetic energy of the ball is determined by applying the principle of conservation of energy.
Neglecting friction and air drag, the initial potential energy of the block at the maximum height must be equal to the final kinetic energy of the block at the lowest point.
P.E = K.E
mgh = ¹/₂mv²
v = √ 2gh
where;
h is the height of the rampg is acceleration due to gravityKinetic energy depends on mass and velocity, since the mass is constant, the final velocity will depend on the height of the ramp.
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