The work done on the object moving in the xy-plane that is subjected to the given applied force is determined as (2ab²i + 3b²j) J.
Magnitude of the force on the objectThe magnitude of the force on the object is calculated as follows;
f = (2xyi + 3yj)
when;
x = a, and y = b
f = (2abi + 3bj)
Work done by the forceThe work done the applied force is the product of force and displacement of the object.
W = fΔs
where;
Δs is displacement of the objectΔx = a - a = 0
Δy = 0 - b = -b
Δs = √(Δx² + Δy²)
Δs = √(-b)²
Δs = b
W = (2abi + 3bj) x b
W = (2ab²i + 3b²j) J
Thus, the work done by the applied force on the object is (2ab²i + 3b²j) J.
The complete question is below;
An object moving in the xy-plane is subjected to the force f = (2xyi + 3yj), where x and y are in m. The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis. How much work does the force do?
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The work done on an item moving in the xy-plane that is subjected to a particular force is found as (2ab²i + 3b²j) J.
What is work done?Work done is defined as the product of applied force and the distance through which the body is displaced on which the force is applied.
Work may be zero, positive, and negative.it depends on the direction of the body displaced. if the body is displaced in the same direction of the force, it will be positive.
The given data in the problem is;
F is the force applied; f⃗ = (2xyi + 3yj)
Work done is found as the product of force and the body displacement;
[tex]\rm W = F \triangle S[/tex]
As the object is moving in the xy- plane. Displacement in the x direction;
[tex]\rm \triangle x = a-a \\\\ \triangle x =0[/tex]
Displacement in the y direction;
[tex]\rm \triangle y = 0-b \\\\ \rm \triangle y = -b \\\\[/tex]
The net displacement in the xy plane is;
[tex]\rm \triangle s= \sqrt{(\triangle x)^2+(\triangle y)^2 } \\\\\ \rm \triangle s= \sqrt{(0)^2+(-b)^2 } \\\\\ \triangle s= \sqrt{b^2} \\\\ \triangle s=b[/tex]
The work done is found as;
[tex]\rm W= F \triangle S \\\\ W=( 2 ab \vec i+3b \vec j) \triangle S\\\\ W= W=( 2 ab \vec i+3b \vec j) b \\\\\ W=(2ab^2 \vec i + 3b^2 \vec j)\ J[/tex]
Hence, the work done on an item moving in the xy-plane will be,[tex]\rm W=(2ab^2 \vec i + 3b^2 \vec j)\ J[/tex]
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11. Which of the following gives the correct relation between the acceleration due to gravity and period of a pendulum?
g = 2πLT2
g = 4π2LT2
g = 2πLT
g = 2π2LT
Please show all of your algebra.
[tex]\\ \rm\rightarrowtail T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
Derive g[tex]\\ \rm\rightarrowtail T^2=4\pi^2\dfrac{l}{g}[/tex]
[tex]\\ \rm\rightarrowtail g=\dfrac{4\pi ^2\ell}{T^2}[/tex]
[tex]\\ \rm\rightarrowtail g=\left(\dfrac{2\pi\sqrt{l}}{T}\right)^2[/tex]
A car with a mass of 1,500 kg accelerates at a rate of 3.0
/s2 forward. What is the force acting on the car? Show work.
Answer:
4500 N
Explanation:
F = ma
= 1500 kg * 3 m/s^2 = 4500 N
edited to correct units !
According to Newton's second law for rotational motion, an object's angular
acceleration equals the
(A) net torque multiplied by the moment of inertia.
(B) net moment of inertia divided by the net torque.
(C) net torque divided by the moment of inertia.
(D) net torque added to the moment of inertia.
Answer:
C: Net Torque divided by Moment of Inertia
Explanation:
Torque = Moment of Inertia x Angular Acceleration.
According to Newton's second law for rotational motion, an object's angular acceleration equals the net torque multiplied by the moment of inertia, not divided by it. The correct answer is (A)
Mathematically, it can be expressed as:
Angular acceleration (α) = (Net torque (τ) / Moment of inertia (I))
Where:
α = angular acceleration (measured in rad/s²)
τ = net torque (measured in Nm or kgm²/s²)
I = moment of inertia (measured in kgm²)
This equation shows that the angular acceleration of an object is equal to the net torque applied to it divided by its moment of inertia. So, the correct answer is (A) net torque multiplied by the moment of inertia.
To summarize, Newton's second law for rotational motion states that the angular acceleration of an object is directly proportional to the net torque applied to it and inversely proportional to its moment of inertia. The moment of inertia represents an object's resistance to changes in its rotational motion, while the net torque represents the total rotational force acting on the object.
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1. Which of the following represents the distance (how much ground the particle covers) moved by a particle in a simple harmonic motion in one time period? (Here, A represents the amplitude of the oscillation.)
0 cm
A cm
2A cm
4A cm
Please show all of your work.
What's the relationship
[tex]\\ \rm\Rrightarrow T=2\pi \sqrt{\dfrac{l}{g}}[/tex]
[tex]\\ \rm\Rrightarrow T^2g=4\pi ^2\ell[/tex]
[tex]\\ \rm\Rrightarrow\ell=\dfrac{T^2g}{4\pi^2}[/tex]
4A can be correct
The correct option is: 2A cm
What is simple harmonic motion?In a simple harmonic motion, the particle moves back and forth around a mean position. The distance covered by the particle in one time period depends on the amplitude of the oscillation.
The time period (T) of a simple harmonic motion can be expressed in terms of the frequency (f) as:
T = 1/f
The frequency (f) of a simple harmonic motion can be related to the angular frequency (ω) as:
ω = 2πf
Therefore, the time period (T) can also be expressed in terms of the angular frequency (ω) as:
T = 2π/ω
The displacement of the particle at any time (t) during the simple harmonic motion can be expressed as:
x = A cos(ωt)
where x is the displacement, A is the amplitude, and cos(ωt) is the cosine function.
The particle moves from its initial position to its maximum displacement (+A), then back to its initial position, and finally to its maximum displacement in the opposite direction (-A), before returning to its initial position again. Therefore, the distance covered by the particle in one time period is twice the amplitude (2A).
Therefore, the correct option is:
2A cm
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What is the electric potential energy of a charge that experiences a force of 3. 6 × 10–4 N when it is 9. 8 × 10–5 m from the source of the electric field? 3. 5 × 10–8 J 4. 6 × 10–4 J 2. 7 × 10–1 J 3. 7 × 100 J.
The electric potential energy of the charge will be =3.5*10^8 J
What is Electric potential energy?Electric potential energy is the energy that is needed to move a charge against an electric field.
F=Force experienced by the charge = 3.6*10^-4 N
q1 = magnitude of charge producing the electric field
q2 = magnitude of charge experiencing the electric force
r1 = distance between the two charges
Electric force experienced by the charge is given using coulomb's law as
[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]
[tex]3.6\times 10^{-4}=\dfrac{9\times 10^9 q_1q_2}{(9.8\times 10^{-5})^2}[/tex]
[tex]q_1q_2=3.84\times 10^{-22}[/tex]
Electric potential energy of the charge can be given as
[tex]U=\dfrac{kq_1q_2}{r}[/tex]
[tex]U=\dfrac{(9\times 10^9)q_1q_2}{(9.8\times 10^{-5})^2}[/tex]
[tex]U=3.5\times 10^{-8}\ J[/tex]
Thus Electric potential energy of the charge can be given as [tex]U=3.5\times 10^{-8}\ J[/tex]
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A microwave has a period 0.000015 s has a wavelenth of ?
(Round your answer to the nearest hundreth. Add a zero to the begining of the number if necessary.)
Answer:
30 cm to 1 mm
Explanation:
30 cm to 1 mm
A coin has a mass of 7.0g. It is made of a metal alloy of density 5.6g/cm3. Calculate the volume of the coin.
[tex]\text{Density,}\\\\~~~~~~~~\rho = \dfrac mV\\\\\\\implies V = \dfrac m{\rho}\\\\\\\implies V = \dfrac{7 \times 10^{-3}~ \text{kg}}{\tfrac{5.6 \times 10^{-3}~ \text{kg}}{ 10^{-6} ~\text{m}^3} }\\\\ \\\implies V = \dfrac{7 \times 10^{-3}~ \text{kg}}{5.6 \times 10^{-3} \times 10^6~~ \text{kg}~ \text{m}^{-3}}\\\\\\ \implies V = 1.25 \times 10^{-6}~ \text m^3\\\\\\\implies V =0.00000125~ \text m^3\\\\\text{Hence the volume of the coin is 0.00000125}~ \text m^3[/tex]
9. Graph the following data on the graph, then use the graph to determine the half life of this
isotope.
The half life is the time taken for half the number of radioactive atoms originally present to remain. This is the time that corresponds to exactly half of the original number of radioactive isotopes remaining in the system.
What is half life?The half life is the time taken for half the number of radioactive atoms originally present to remain. We can plot the number of atoms against the time taken in a graph.
We can obtain the half life of the radioactive isotope from the graph by noting the time that corresponds to exactly half of the original number of radioactive isotopes remaining in the system.
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hey guys can y’all help quickly?
how to induce a positive temporary charge on the right side of a metal ball
Answer:
Temporary? You have two options
If you have a positively charged object, bring it close to the LEFT side of the ball (not touching it!).
If you have a negatively charged object, bring it close to the RIGHT side of the ball (again, not in contact).
Either way, the electron cloud will migrate towards the right side of the of your sphere.
Another option is to have a capacitor large enough to house the sphere inside it, and polarize it by attaching it to a DC source making sure that the negative plate of it is to the right of the sphere.
While on an ice-fishing trip, you find yourself holding a 10 kg fish but stuck in the middle of
the lake. The ice is perfectly smooth and you cannot walk or shuffle your feet towards the
shore. But because you understand Newton's Laws, you are still able to make it back to shore. A
Briefly explain what did you did. Why did it worked? (Please include directional words such as
up/down, towards/away from shore, left/right, etc.)
The forward force you exert on the fish and your backward action will allow you to reach the shore.
Newton's third law of motionNewton's third law of motion states that for every action, there is an equal and opposite reaction.
Fa = -Fb
Let's assume the fish is held in the hook, this will give you the opportunity to throw the fish forward while still holding it.
When the the fish is thrown forward, you will move backwards with an equal force based on Newton's third law. Your backward momentum towards the shore will help to maintain equal linear momentum between you and the fish.
Thus, this forward force of the fish and your backward action will allow you to reach the shore.
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What are radio isotopes??
Give one example of a radio isotope State one use too..
Don't spam..
Answer:
An isotope is one of two or more species of atoms of a chemical element with the same atomic number and position in the periodic table and nearly identical chemical behavior but with different atomic masses and physical properties. In medicine, for example, cobalt-60 is extensively employed as a radiation source to arrest the development of cancer. Other radioactive isotopes are used as tracers for diagnostic purposes as well as in research on metabolic processes.
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
Those isotopes which are unstable due to the presence of extra neutrons in their nuclei and emit various types of radiations are called radioactive isotopes. The radiations emitted are in the form of alpha particles, beta particles and gamma rays.
For eg :- carbon,hydrogen and chlorine.
Hope it helps you!!Hello~
Which of the following produces least friction?
(a) Sliding friction
(b) Rolling friction
(c) Composite friction
(d) Static friction
Answer:
Rolling friction
Explanation:
When a object rolls down the all sides of object comes contact to under surface for very low timeFor which the friction decreases .Option B is correct
3 Select the correct answer.
Which of the following statements is TRUE? А. Children in the US are generally given the opportunity to play sports in school starting at a young age.
B. The US is one of the few countries to integrate sports into their school systems.
C. Most high schools and colleges in the US have various sport teams.
D. All of the above
Answer:
A,B,C
Explanation:
because that is true
according to this passage when making healthcare decisions, how should a person approach the decision making process
Answer:
What is your name?
Explanation:
no bro I don't know I am New of this app so I don't know
What is current of 12 ohm? help me pleasee
Answer:
Current for 12 ohms = 2.5
Explanation:
Ohm's Law:
Voltage = IR
Current = V/R
Resistance = V/I
Therefore, current = 30V/12 Ohms
30/12 = 2.5
So current for 12 ohms = 2.5
I hope this helps :>
Which characteristic is the same for every color of light in a vacuum?.
In a vacuum all colors of light travel with same speed and this is the reason a white ray travels through the vacuum without going through any dispersion..
What is speed?Speed of light is the distance per time light waves propagate through different materials. The value for the speed of light in a vacuum is now defined as exactly 299,792,458 metres per second.
Therefore, In a vacuum all colors of light travel with same speed and this is the reason a white ray travels through the vacuum without going through any dispersion
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The electric field is measured for points at distances r from the center of a uniformly charged insulating sphere that has volume charge densi
For the electric field is measured for points at distances r,Electric field is mathematically given as
E=19.9*10^{-5}c/m^3
What is the Electric field?Generally, the equation for the electric field uniform charged is mathematically given as
[tex]E=\frac{lr}{3e0}[/tex]
Therefore
E=lr/3E0=3Ee0/r
Therefore
E=3*6*10^4*8.85*10^{-12}
E=19.9*10^{-5}c/m^3
In conclusion, E=19.9*10^{-5}c/m^3
E=19.9*10^{-5}c/m^3
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CQ
Complete question attached below
a 600kg wrecking ball is swinging from a crane as shown. When the wrecking ball reached the bottom of the path, the wrecking ball is moving 10m/s
Answer:
Explanation:
The picture is cut off so the wrecking ball and its path are not shown. It would be better if the whole picture is available.
Based on the written info, at the bottom of the path, the wrecking ball is moving at 10m/s.
The centripetal acceleration = velocity^2 / radius
= 10^2 / 25
= 100 / 25
= 4m/s^2
The centripetal force = mass * centripetal acceleration
= 600*4
= 2400N
As the ball is moving horizontally at the bottom, net vertical force is zero.
So Tension force in cable = Wrecking ball weight + Centripetal force
= 600*g + 2400
= 6000 + 2400; assuming g is 10m/s^2
= 8400N
Un motor eléctrico consume 10A de corriente de un circuito de 120v. Calcular la potencia y el trabajo que suministra al motor durante 5hrs de funcionamiento:
A) P=0.9 kw, T=6 kwh
B) P=0.85 kw, T=4 kwh
C) P=1.2 kw, T=3 kwh
D) P=1.2 kw, T=6 kwh
Answer:
D. P=1.2 kw, T=6kwh
Explanation:
P = A × V
P = 120×10
= 1200 watts or 1.2 kw
T = Watts × hr
1000
= 1200 × 5
1000
= 6 kwh
Which is the destructive interference formula for diffraction grating problems? dsin = dcos = dcos = n dsin = n.
The destructive interference formula for diffraction grating problems is [tex]d sin \theta = (n+\frac{1}{2})\lambda[/tex].
What is the definition of destructive interference?Destructive interference happens when the maxima of two waves are 180° out of phase a positive displacement of one wave is canceled exactly by a negative displacement of the other wave.
The formula for brighter patches resulting from constructive interference and darker patches resulting from destructive interference in a diffraction grating is:
[tex]\rm d sin \theta = n \lambda[/tex]
The grating spacing is denoted by d, the angle of light is denoted by a the fringe order is denoted by n, and the wavelength is denoted by [tex]\rm \lambda[/tex].
The destructive interference formula is now based on the fact that destructive interference occurs between the fringes.
Hence the destructive interference formula for diffraction grating problems is [tex]d sin \theta = (n+\frac{1}{2})\lambda[/tex].
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Answer:
A. dsin =
Explanation:
A 1000 kg rocket carrying 25 kg of fuel and oxygen rises at a velocity of 305 m/s. If all the mass of fuel and oxygen is burned to form gases of combustion, what is the downward velocity of these gases?
If all the mass of fuel and oxygen is burned to form gases of combustion, the downward velocity of these gases would be 12,505 m/s.
Conservation of linear momentumThe principle of conservation of linear momentum states that, the total momentum of an isolated system is constant.
The downward velocity of thes gases is calculated as follows;
v1(m1 + m2) = v2(m2)
305(1000 + 25) = v2(25)
312,625 = 25v2
v2 = 312,625/25
v2 = 12,505 m/s
Thus, If all the mass of fuel and oxygen is burned to form gases of combustion, the downward velocity of these gases would be 12,505 m/s.
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Which property of the sound wave changes when the volume is increased on a radio?.
Answer:
amplitude
Explanation:
When we increase the volume of a sound, the amplitude of the wave is increased. The frequency of a wave is related to its pitch. If the pitch is high, then the frequency of the wave is high. This means that the wave will looked squashed on an oscilloscope trace.
A body of mass 0.1 kg falling freely under gravity takes 10 s to reach the ground. Calculate the kinetic energy and potential energy of the body when it has travelled for first 6 s. Given, g = 9.8 m/ s²
Answer: KE = 172.872 J
PE = 307.328 J
Explanation:
For KE: acceleration = change in velocity / time → 9.8 = final velocity - 0 (because initial velocity is zero) / 6s → final velocity after 6s = 58.8 m/s.
Now, plug this into: KE = 1/2(m)(v^2) → KE = 1/2(.1)(58.8^2) = 172.872 J.
For PE: Find the velocity after 10 s: acceleration = change in velocity / time → 9.8 = final velocity - 0 (because initial velocity is zero) / 10s → final velocity after 10s = 98 m/s.
Now, find the total height: (v final)^2 = (v initial)^2 + 2*a*d → 98^2 = 0^2 + 2*9.8*d → d = total height = 490 m.
Now, find the change in height after 6 s: (v final)^2 = (v initial)^2 + 2*a*d → 58.8^2 = 0^2 + 2*9.8*d → d = change in height after 6 s → 176.4 m
Now, subtract the change in height from the total height to get its height after 6s: 490-176.4=313.6m
PE = m*g*h → Pe=.1*9.8*313.6 = 307.328 J :)
Is the moons diameter about the same as the United States
Answer:
the Moon is smaller in diameter than the United States
however. The United States is 2,545 km / 1,582 mi from north to south, and thus, the Moon is smaller across than the United States is wide.
Answer:
The moon is smaller than the earth.
Explanation:
Moon's Diameter is 2,159.1 mi
Earth's Diameter is 7,917.5 mi
A car of mass 1200kg moving 90km/hr is brought to rest over a distance of 20m. calculate breaking force.
Answer:
-18,750N
Explanation:
90x1000
-------------
3600
u=25m/s
v=0m/s
v^2=u^2+2as
v=0
=625+(2×a×20)
625+40a
-625=40a
a= -15.625 m/s^2
F=ma
=(1200)(-15.625)
= -18,750N
Why a surface that always have a perpendicular is an equipotential
Electromagnets project student guide
y’all i need helppppo
Answer:
I don't know
Explanation:
you need then search here
When a 10-V battery is connected to a resistor, 2 A of current flow in the resistor. What is the resistor's value
Hi there!
We can use Ohm's law to solve:
[tex]V = IR[/tex]
V = Potential Difference (V)
I = Current (A)
R = Resistance (Ω)
We can rearrange the equation to solve for resistance:
[tex]R = \frac{V}{I}[/tex]
Plug in the given values to solve.
[tex]R = \frac{10}{2} = \boxed{5 \Omega}[/tex]
Determine the slope of end a of the cantilevered beam. E = 200 gpa and i = 65. 0(106) mm4
For E = 200 gpa and i = 65. 0(106) mm4, the slope of end a of the cantilevered beam is mathematically given as
A=0.0048rads
What is the slope of end a of the cantilevered beam?Generally, the equation for the is mathematically given as
[tex]A=\frac{PL^2}{2EI}+\frac{ML}{EI}[/tex]
Therefore
A=\frac{10+10^2+3^2}{2*240*10^9*65*10^6}+\frac{10+10^3*3}{240*10^9*65*10^{-6}}
A=0.00288+0.00192=0.0048rads
A=0.0048rads
In conclusion, the slope is
A=0.0048rads
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The value of slope of end a of the cantilevered beam when E = 200 gpa and i = 65. 0(106) mm4 is 0.0048 rads.
How to find the slope at the end of the cantilevered beam?The formula used to find the slope at the end of the cantilevered beam is,
[tex]A=\dfrac{PL^2}{2EI}+\dfrac{ML}{EI}[/tex]
Here, (M) is the momentum, (EI) is flexural rigidity, (P) is concentrated load and (L) is the length of the beam.
Concentrated load is 10 KN and uniform load is 3 kN/m. E = 200 gpa and i = 65. 0(106) mm4.
[tex]A=\dfrac{10+10^2+3^2}{2\times240\times10^9\times65\times10^6}+\dfrac{10+10^3\times3}{240\times10^9\times65\times10^{-6}}\\A=0.00288+0.00192A=0.0048 \rm\; rads[/tex]
Thus, the value of slope of end a of the cantilevered beam when E = 200 gpa and i = 65. 0(106) mm4 is 0.0048 rads.
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How does the maximum value of the current depend on the frequency of the ac voltage source?.
The maximum value of the current depend on the frequency of the ac voltage source because it increases as the frequency increases.
What is peak current of AC source?
The peak current of an ac source is the amplitude current flowing in the ac circuit.
The magnitude of the peak current is calculated as follows;
I₀ = i/(sin ωt)
I₀ = i/(sin 2πft)
where;
I₀ is the peak currenti is the ac currentω is angular speedf is the frequencyt is timemaximum value ac currenti = I₀ x sin 2πft
From the equation above, as the frequency of the of the ac voltage source increases, the value of the ac current (i) increases.
Thus, the maximum value of the current depend on the frequency of the ac voltage source because it increases as the frequency increases.
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