Explanation:
p = mv
26 kg m/s = (6.5 kg) v
v = 4 m/s
An organ pipe of length L has one end closed but the other end open. What is the wavelength of the fundamental node emitted?
a. Slightly smaller than 4 L
b. Slightly larger than 4 L c. Roughly equal to 3/2
d. Slightly larger than 2 L
Answer:analize a afirmacao a seguir e tudo que envolve o gerenciamento da marca e que ultrapassa as acoes com objetivos economicos e refere se a cultura principios e valores
Explanation:
A 2kg ball is swinging on a 1m string attached to the ceiling. At the bottom of the arc, its speed is 3m/s.What is the tension in the string at this point?
Answer:
37.6 N
Explanation:
We can represent the situation with the following
Then, the net force is equal to:
\(\begin{gathered} F_{net}=T-mg=ma_c \\ \Rightarrow T-mg=m\frac{v^2}{r} \end{gathered}\)Where T is the tension, mg is the weight, m is the mass, v is the speed, and r is the radius of the circular motion of the ball. Solving for T, we get:
\(T=m\frac{v^2}{r}+mg\)Now, we can replacing m = 2 kg, v = 3 m/s, r = 1 m, and g = 9.8 m/s²
\(\begin{gathered} T=2(\frac{3^2}{1})+2(9.8) \\ T=2(9)+19.6 \\ T=18+19.6 \\ T=37.6 \end{gathered}\)Therefore, the tension in the string at this point is 37.6 N
what is the acceleration of a 10 kg mass pushed by a 5 N force
Answer:
The formula is a = F m so in this case a = 5 10 = 0.5 m s 2
Explanation:
The first P-wave of an earthquake travels 5600 kilometers from the epicenter and arrives at a seismic station at 10:05 a.m. At what time did this earthquake occur?
Ahhhhhh I have a Regent's test in 2 hours and I don't know how to solve this type of question! Any help would be appreciated.
Anyone know what the steps to do this are? I dont even need an answer, just how to get to it. Thank you!
The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.
The p-waves travel with a constant velocity of 7 km/s
The time can be calculated by using the formula
t = d / v
where
T1 = 10:05 a.m
d is the distance they take to travel from the epicenter
v is the speed of the p-waves
On average, the speed of p-waves is
v = 7 km/s
d = 5600 km (given)
Substituting the values in the formula;
t = d / v
t = 5600 ÷ 7
t = 800 seconds
Converting into minutes,
t = 800 ÷ 60
t = 13.3
≈ 13 mins
T1 - 13 mins = T2
10:05 - 13 mins = 9.52 am
It means the earthquake occurred prior 13 minutes, that is at 9.52 am.
Therefore, the earthquake occurred at 9.52 am.
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** State the reason why heat transfer by radiation is faster than heat transfer by conduction
Heat transfer by radiation is faster than heat transfer by conduction because radiation can occur through a vacuum, while conduction requires the presence of a medium, such as a solid, liquid, or gas. Radiation is the transfer of energy through electromagnetic waves and does not require any medium to propagate, which means that radiation can occur even in a vacuum or through transparent materials.
On the other hand, conduction requires particles to transfer heat energy from one object to another. In a solid, this occurs through the transfer of kinetic energy from one molecule to another through direct contact, while in a liquid or gas, conduction occurs through collisions between molecules. This process of molecule-to-molecule transfer of heat energy is much slower than radiation and is limited by the physical properties of the medium, such as its thermal conductivity.
Therefore, heat transfer by radiation is faster than heat transfer by conduction because radiation can occur through a vacuum, and is not limited by the physical properties of a medium, while conduction is limited by the thermal conductivity of the medium and requires direct contact between molecules.
Which law of thermodynamics does each of the following scenarios violate (if any)?
A machine that can turn 1000J of heat directly into 1000J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
Answer: The scenario violates the second law of thermodynamics.
Explanation: The second law states that heat cannot be converted into work without some loss of usable energy, and that the amount of usable energy in a closed system will always decrease over time. Therefore, the machine described in the scenario cannot exist because it would violate the second law by converting all of the heat into electricity without any loss of usable energy.
what is the force when ur pulling heavy furniture that wont budge
Answer:
Gravity? is it multiple choice?
A 1.0-kg cart and a 0.50-kg cart sit at different positions on a low-friction track. You push on the 1.0-kg cart with a constant 4.0-N force for 0.20 m. You then remove your hand, and the cart slides 0.35 m and strikes the 0.50-kg cart. What is the work done by you on the two-cart system? How far does the system's center of mass move while you are pushing the 1.0-kg cart? By what amount does your force change the kinetic energy of the system's center of mass?
Answer:
a)\(W=0.8J\)
b) \(d_t=0.20m\)
c) \(\triangle K.E=0.267J\)
Explanation:
From the question we are told that:
Mass of cart 1 \(M_1=1.0kg\)
Mass of cart 1 \(M_2=0.05kg\)
Force on cart 1 \(F_1=4.0N\)
Push Distance of cart 1 \(d_1=0.20m\)
Slide Distance of cart 1 \(d_1'=0.35m\)
a)
Generally the equation for work-done is mathematically given by
\(W=f*d\\W=4*0.20\\W=0.8J \\\)
b)
The systems center of mass moved a net totally of (while being pushed)
Mass 1 =0.20m
Mass 2=0
Therefore
\(d_t=d_1+d_2\)
\(d_t=0.20+0\)
\(d_t=0.20m\)
c)
Since work-done is equal to K.E energy of cart 1
Therefore
\(W=1/2mv^2\)
\(V_1=\sqrt{\frac{W}{1/2m}}\)
\(V_1=\sqrt{\frac{0.8}{1/2(1)}}\)
\(V_1=1.264\)
Therefore Kinetic energy before collision is
\(K.E_1=1/2mv^2\)
\(K.E_1=1/2*1*1.264^2\)
\(K.E_1=0.768\)
Generally from the equation for conservation of momentum the Velocity of cart 2 is mathematically given by
\(v_2=\frac{m_1V_1}{m_1+m_2}\)
\(v_2=\frac{1*1.264}{1+0.5}\)
\(V_2=0.842m/s\)
Therefore the final K.E is mathematically given by
\(K.E_2=(1/2)(m_1+m_2)V_2^2\)
\(K.E_2=1/2*(1.5)(0.842)^2\)
\(K.E_2=0.531J\)
Generally the Change in K.E is mathematically given by
\(\triangle K.E=K.E_1-K.E_2\)
\(\triangle K.E=0.798-0.531\)
\(\triangle K.E=0.267J\)
Therefore the will force change the kinetic energy of the system's center of mass by
\(\triangle K.E=0.267J\)
(a) The work done by you when you push the cart at a constant force is 0.8 J.
(b) The distance moved by the center mass of the two cart system is 0.23 m.
(c) The change in kinetic energy of the system center of mass is 0.271 J.
Work done by you
The work done by you when you push the cart at a constant force is calculated as follows;
W = Fd
W = 4 x 0.2
W = 0.8 J
Distance moved by the center mass of the two cart systemlet the 0.5 kg mass be the reference mass at zero (0).Xcm = (m₁x₁ + m₂x₂)/(m₁ + m₂)
Xcm = (0.5(0) + 1(0.35)) / (1 + 0.5)
Xcm = (0.35)/(1.5)
Xcm = 0.23 m
Initial velocity of the 1.0 kg massF = ma
a = F/m
a = (4)/1 = 4 m/s²
v² = u² + 2as
v² = 0 + 2(4)(0.2)
v² = 1.6
v = √1.6
v = 1.265 m/s
Final velocity of the massesm₁u₁ + m₂u₂ = v(m₁ + m₂)
1(1.265) + 0 = v(1 + 0.5)
1.265 = 1.5v
v = 0.84 m/s
Change in kinetic energyK.E(initial) = ¹/₂m₁u₁² + ¹/₂m₂u₂²
K.E(initial) = ¹/₂(1)(1.265)² + ¹/₂(0.5)(0) = 0.8 J
K.E(final) = ¹/₂(m₁ + m₂)v²
K.E(final) = ¹/₂(1 + 0.5)(0.84)² = 0.529 J
Δ K.E = 0.8 J - 0.529 J = 0.271 J
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How to solve conservation of momentum
Answer:
Step 1: List the mass and velocity of the object. Step 2: Convert any values into SI units (kg, m, s). Step 3: Multiply the mass and velocity of the object together to get the momentum of the object.
3) A fahrenheit thermometer shaded from the sun on a hot day reads 101⁰ what is the temperature on the centigrade scale?
Answer:
38.33°C
Explanation:
Applying,
180/100 = (F-32)/C............. Equation 1
Where F = Temperature of the hot day in fehrenheit, C = Temperature of the hot day in centigrade.
make C the subject of the equation
C = 100(F-32)/180.............. Equation 2
From the question,
Given: F = 101°F
Substitute into equation 2
C = 100(101-32)/180
C = 38.33°C
1. A girl drops a ball off the roof of her house. It takes the ball 2 seconds to hit the ground. How tall
is the house?
If the acceleration constant..
you can use the formula s = ut + 1/2at²
Known that :
s = ?
u = 0
t = 2s
a = 10ms-²
Then you can apply the formula
s = ut + 1/2at²
s = 0 + 1/2(10)(2)²
s = 5 × 4
s = 20m
Answer : 20m
Explanation :
The gravity can be 9,8 or 10. Also im not sure how people teach you but in my school, if the ball goes down the gravity is positive and not negative thats why i put 10ms-² and not -10ms-²
s = displacement/distance
u = initial speed
a = acceleration
t = time
sorry if im wrong
A rigid, 26-L steam cooker is arranged with a pressure relief valve set to release vapor and maintain the pressure once the pressure inside the cooker reaches 150 kPa. Initially, this cooker is filled with water at 175 kPa with a quality of 10 percent. determine the exergy.
The minimum entropy change of the heat-supplying source is -0.87 kJ/K.
Initial entropy of the systemIn this case, given the initial conditions, we first use the 10-% quality to compute the initial entropy.
at initial pressure of 175 kPaS₁ = 1.485 + (0.1)(5.6865) = 2.0537 kJ/kg K
Final entropyThe entropy at the final state given the new 40-% quality:
pressure inside the cooker = 150 kPa
S₂ = 1.4337 + (0.4)(5.7894) = 3.7495 kJ/kg K
Mass of the steam at specific volumem₁ = 0.026/(0.001057 + 0.1 x 1.002643) = 0.257 kg
m₂ = 0.026/(0.001053 + 0.4 x 1.158347) = 0.056 kg
minimum entropy change of the heat-supplying sourceΔS + S₁ - S₂ + S₂m₂ - S₁m₁ - sfg(m₂ - m₁) > 0
ΔS + 2.0537 - 3.7495 + (3.7495 x 0.056) - (2.0537 x 0.257) - 5.6865( 0.056 - 0.257) > 0
ΔS > -0.87 kJ/K
Thus, the minimum entropy change of the heat-supplying source is -0.87 kJ/K.
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The complete question is below:
A rigid, 26-L steam cooker is arranged with a pressure relief valve set to release vapor and maintain the pressure once the pressure inside the cooker reaches 150 kPa. Initially, this cooker is filled with water at 175 kPa with a quality of 10 percent. determine the exergy.
Heat is now added until the quality inside the cooker is 40 percent. The water is stirred at the same time that it is being heated. Determine the minimum entropy change of the heat-supplying source if 100 kJ of work is done on the water as it is being heated. Use steam tables
r the following questions: a. why should the glassware be dry for this experiment? why might water contamination be a problem when using the reagent acetic anhydride; what byproduct might form due to moisture?
The glassware should be dry for the experiment because of following reasons
a. Glassware should be dry for this experiment because the reagent acetic anhydride reacts with water, producing acetic acid and heat. If the glassware is wet, it can lead to the premature reaction of the acetic anhydride, which can affect the accuracy of the results. Additionally, if water is present in the reaction mixture, it can hydrolyze the acetic anhydride, forming acetic acid and causing the reaction to fail.
b. Water contamination can be a problem when using acetic anhydride because it reacts with water to form acetic acid and heat. This reaction can cause the acetic anhydride to decompose prematurely, leading to inaccurate results. Additionally, water contamination can lead to the formation of byproducts such as acetic acid and acetic acid anhydride.
c. The byproduct that might form due to moisture is acetic acid. In the presence of water, acetic anhydride reacts to form acetic acid and heat. This reaction can lead to premature decomposition of the acetic anhydride and affect the accuracy of the experiment.
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Please provide an explanation.
Thank you!!
Answer:
(a) 22 kN
(b) 36 kN, 29 kN
(c) left will decrease, right will increase
(d) 43 kN
Explanation:
(a) When the truck is off the bridge, there are 3 forces on the bridge.
Reaction force F₁ pushing up at the first support,
reaction force F₂ pushing up at the second support,
and weight force Mg pulling down at the middle of the bridge.
Sum the torques about the second support. (Remember that the magnitude of torque is force times the perpendicular distance. Take counterclockwise to be positive.)
∑τ = Iα
(Mg) (0.3 L) − F₁ (0.6 L) = 0
F₁ (0.6 L) = (Mg) (0.3 L)
F₁ = ½ Mg
F₁ = ½ (44.0 kN)
F₁ = 22.0 kN
(b) This time, we have the added force of the truck's weight.
Using the same logic as part (a), we sum the torques about the second support:
∑τ = Iα
(Mg) (0.3 L) + (mg) (0.4 L) − F₁ (0.6 L) = 0
F₁ (0.6 L) = (Mg) (0.3 L) + (mg) (0.4 L)
F₁ = ½ Mg + ⅔ mg
F₁ = ½ (44.0 kN) + ⅔ (21.0 kN)
F₁ = 36.0 kN
Now sum the torques about the first support:
∑τ = Iα
-(Mg) (0.3 L) − (mg) (0.2 L) + F₂ (0.6 L) = 0
F₂ (0.6 L) = (Mg) (0.3 L) + (mg) (0.2 L)
F₂ = ½ Mg + ⅓ mg
F₂ = ½ (44.0 kN) + ⅓ (21.0 kN)
F₂ = 29.0 kN
Alternatively, sum the forces in the y direction.
∑F = ma
F₁ + F₂ − Mg − mg = 0
F₂ = Mg + mg − F₁
F₂ = 44.0 kN + 21.0 kN − 36.0 kN
F₂ = 29.0 kN
(c) If we say x is the distance between the truck and the first support, then using our equations from part (b):
F₁ (0.6 L) = (Mg) (0.3 L) + (mg) (0.6 L − x)
F₂ (0.6 L) = (Mg) (0.3 L) + (mg) (x)
As x increases, F₁ decreases and F₂ increases.
(d) Using our equation from part (c), when x = 0.6 L, F₂ is:
F₂ (0.6 L) = (Mg) (0.3 L) + (mg) (0.6 L)
F₂ = ½ Mg + mg
F₂ = ½ (44.0 kN) + 21.0 kN
F₂ = 43.0 kN
Answer:
a. Left support = Right support = 22 kNb. Left support = 36 kN Right support = 29 kNc. Left support force will decrease Right support force will increase.d. Right support = 43 kNExplanation:
given:
weight of bridge = 44 kN
weight of truck = 21 kN
a) truck is off the bridge
since the bridge is symmetrical, left support is equal to right support.
Left support = Right support = 44/2
Left support = Right support = 22 kN
b) truck is positioned as shown.
to get the reaction at left support, take moment from right support = 0
∑M at Right support = 0
Left support (0.6) - weight of bridge (0.3) - weight of truck (0.4) = 0
Left support = 44 (0.3) + 21 (0.4)
0.6
Left support = 36 kN
Right support = weight of bridge + weight of truck - Left support
Right support = 44 + 21 - 36
Right support = 29 kN
c)
as the truck continues to drive to the right, Left support will decrease
as the truck get closer to the right support, Right support will increase.
d) truck is directly under the right support, find reaction at Right support?
∑M at Left support = 0
Right support (0.6) - weight of bridge (0.3) - weight of truck (0.6) = 0
Right support = 44 (0.3) + 21 (0.6)
0.6
Right support = 43 kN
Help me please I have other ones like this too on my page please help!
A Bugatti Veyron went from 0 to 60 mph in 2.5 seconds. What is
the mass of the vehicle if the force used to move the car was
10,000 N?
Is the acceleration change or constnt?
lab manual and Ch. 2.7) Suppose you hold a ball at a height of 10.0 m and drop it from rest. It takes 1.40 seconds to hit the ground. What is your measured value of g? Use correct units and show all work.
Answer: ch2.7 × 10.0m = 2.10 ÷ 1.40 sec
= ch.10.23.
Explanation:
The measured value of gravity 'g' can be found by plugging the given height and time into the formula h = 0.5*g*t^2. Solving for 'g' gives us a measured value of approximately 10.20 m/s^2.
Explanation:You can calculate the measured value of gravity 'g' using the formula for motion under gravity, which is: h = 0.5*g*t^2. Here 'h' stands for height, 'g' for gravitational acceleration and 't' for time.
Given in the problem is h = 10.0 m, t = 1.40 s. Substituting these values in the formula, we get 10.0 = 0.5*g*(1.40)^2.
Solving for 'g', we find g ~ 10.204 m/s^2. Hence your measured value of 'g' is approximately 10.20 m/s^2.
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How does the orientation of the bar magnet affect the measured magnetic field strength?
When two magnets are close to each other, the magnets experience a repulsive or attractive force. The magnetic field strength is affected by the orientation of the magnet.
The direction in which the bar magnet obtains its maximum magnetic property is called the orientation of the magnet. The magnetic field strength depends on the orientation of the magnet.
The magnetic field lines emerge from the north pole and end in the south pole. When the two bar magnets of opposite poles face each other, an attractive force will be produced and magnetic field strength increases.
When the bar magnet of the same poles faces each other, repulsive force will produce and magnetic field strength decreases. Hence from the orientation of the bar magnet, the magnetic field strength gets affected.
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Which vector is the sum of vectors à and b?
The vectors addition permits locating the perfect result for the sum of the two vectors in option B). See attached and the vector is directed to the right and up.
Vector addition is the operation of adding or extra vectors together into a vector sum. The so-known as parallelogram regulation gives the rule for vector addition of or greater vectors. for two vectors and, the vector sum is received via placing them head to tail and drawing the vector from the loose tail to the unfastened head.
A vector is an amount or phenomenon that has impartial residences: importance and direction. The time period also denotes the mathematical or geometrical representation of the sort of quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.
Vectors are used in technological know-how to describe something that has a direction and a magnitude. they're commonly drawn as pointed arrows, the length of which represents the vector's importance
Disclaimer: your question is incomplete, please see below for the complete question.
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Which vector is the sum of vectors à and b?
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Conservation of energy says the kinetic energy and the potential energy for each trial should be equal. true or false answer fast
Answer:
true
Explanation:
this is because potienal energy is energy that is stored, and kinetic is energy being used, as kinetic is used, potential is also being used.
A cup of coffee cools from 120-115°f in 0.5 minutes in a room of 65°f. how long will it take to cool from 105°f _90°f in the same room use newton's law of Cooling
HELLPPPP PLZZZ
10. Identify Which gas law
does this graph represent.
what is true about ocean water that is more dense?
1. It is generally warmer water.
2. It sinks to the bottom.
3. It has a lower salinity than less dense water.
4. It rises to the surface.
Answer:
Ocean water is more dense because of the salt in it. ... Temperature has a greater effect on the density of water than salinity does. So a layer of water with higher salinity can actual float on top of water with lower salinity if the layer with higher salinity is quite a bit warmer than the lower salinity layer.
A 387.02 N trunk is pulled at a constant speed up an incline with an angle of 5.88degrees. The coefficient of static friction is 0.28. What is the force required to keep it constant? Hint* using Absolute value solve for the two forces and add
The given problem can be exemplified in the following diagram:
To determine the value of the force "F" we need to add the forces in the direction of the inclined plane. Since we want the velocity to stay constant then the acceleration must be zero and therefore, the sum of the forces must add up to zero, therefore, we have:
\(F-F_f-mg_x=0\)Where:
\(\begin{gathered} F=\text{ force} \\ F_f=\text{ force of friction} \\ mg_x=\text{ component of the weight in the direction of the incline} \end{gathered}\)Now we solve for the Force "F" by adding the force of friction and the component of the weight in both sides of the equation:
\(F=F_f+mg_x\)To determine the force of friction we will use the following equation:
\(F_f=\mu N\)Where:
\(\begin{gathered} \mu=\text{ coefficient of friction} \\ N=\text{ normal force} \end{gathered}\)The normal force can be determined by adding the forces in the perpendicular direction of the incline, we get:
\(N-mg_y=0\)Where:
\(mg_y=\text{ perpendicular component of the weight.}\)Now we need to determine the components of the weight. To do that we will use the following triangle:
Using the trigonometric function cosine we get:
\(\cos 5.88=\frac{mg_y}{mg}\)Now we multiply both sides by "mg":
\(mg\cos 5.88=mg_y\)Replacing the values we get:
\(387.02\cos 5.88=mg_y\)Solving the operations:
\(356N=mg_y\)Now we use the trigonometric function sine:
\(\sin 5.88=\frac{mg_x}{mg}\)Now we multiply both sides by "mg":
\(mg\sin 5.88=mg_x\)Replacing the values:
\(387.02\sin 5.88=mg_x\)Solving the operations:
\(39.65N=mg_x\)Now we replace the perpendicular component in the formula for the normal:
\(N-356N=0\)Therefore, the normal force is:
\(N=356N\)Now we replace the value of the normal force in the formula for the force of friction:
\(F_f=(0.28)(356N)\)Solving the operation we get:
\(F_f=99.68N\)Now we replace in the formula for the force "F":
\(F=F_f+mg_x\)Replacing the values:
\(F=99.68N+39.65N\)Solving the operations
\(F=139.33N\)Therefore, the required force is 139.33 Newtons.
A basketball with a mass of 20 kg is accelerated with a force of 10 N. If resisting forces are ignored, what is the acceleration of the basketball?
Two point charges are a small distance apart.
a. Sketch the electric field lines for the two if one has a charge four times that of the other and both charges are positive.
b. Repeat for the case in which both charges are negative.
Explanation:
We know that, like charges repel and unlike charges attract each other.
IF one of the charge is four times that of the other and both charges are positive, the field lines is shown in figure (1).
Two negative charges attract each other, the field lines is shown in figure (2).
The net force between charges is given by :
\(F=\dfrac{kq_1q_2}{r^2}\)
Whre
k is the electrostatic constant
r is the distance between charges
PIUDICITIS CONSECulvely and Circle your aliswers. Lilyo
proper significant digits.
53. When you turn on your CD player, the turntable accelerates from zero to 41.8 rad/s in
3.0 s. What is the angular acceleration?
or
Answer:
The angular acceleration of CD player is \(13.93\ rad/s^2\).
Explanation:
Initial angular speed of a CD player is 0 and final angular speed is 41.8 rad/s. Time to change the angular speed is 3 s.
It is required to find the angular acceleration. The change in angular speed of the CD player divided by time taken is called its angular acceleration. It can be given by :
\(a=\dfrac{\omega_f-\omega_i}{t}\\\\a=\dfrac{41.8-0}{3}\\\\a=13.94\ rad/s^2\)
So, the angular acceleration of CD player is \(13.93\ rad/s^2\).
Two charged point-like objects are located on the x-axis. The point-like object with charge q1 = 4.60 µC is located at x1 = 1.25 cm and the point-like object with charge q2 = −2.14 µC is located at x2 = −1.80 cm.
A) Determine the total electric potential (in V) at the origin.
B) Determine the total electric potential (in V) at the point with coordinates (0, 1.50 cm).
Answer:
a) the total electric potential is 2282000 V
b) the total electric potential (in V) at the point with coordinates (0, 1.50 cm) is 1330769.23 V
Explanation:
Given the data in the question and as illustrated in the image below;
a) Determine the total electric potential (in V) at the origin.
We know that; electric potential due to multiple charges is equal to sum of electric potentials due to individual charges
so
Electric potential at p in the diagram 1 below is;
Vp = V1 + V2
Vp = kq1/r1 + kq2/r2
we know that; Coulomb constant, k = 9 × 10⁹ C
q1 = 4.60 uC = 4.60 × 10⁻⁶ C
r1 = 1.25 cm = 0.0125 m
q2 = -2.06 uC = -2.06 × 10⁻⁶ C
location x2 = −1.80 cm; so r2 = 1.80 cm = 0.018 m
so we substitute
Vp = ( 9 × 10⁹ × 4.60 × 10⁻⁶/ 0.0125 ) + ( 9 × 10⁹ × -2.06 × 10⁻⁶ / 0.018 )
Vp = (3312000) + ( -1030000 )
Vp = 3312000 -1030000
Vp = 2282000 V
Therefore, the total electric potential is 2282000 V
b)
the total electric potential (in V) at the point with coordinates (0, 1.50 cm).
As illustrated in the second image;
r1² = 0.015² + 0.0125²
r1 = √[ 0.015² + 0.0125² ]
r1 = √0.00038125
r1 = 0.0195
Also
r2² = 0.015² + 0.018²
r2 = √[ 0.015² + 0.018² ]
r2 = √0.000549
r2 = 0.0234
Now, Electric Potential at P in the second image below will be;
Vp = V1 + V2
Vp = kq1/r1 + kq2/r2
we substitute
Vp = ( 9 × 10⁹ × 4.60 × 10⁻⁶/ 0.0195 ) + ( 9 × 10⁹ × -2.06 × 10⁻⁶ / 0.0234 )
Vp = 2123076.923 + ( -762962.962 )
Vp = 2123076.923 -792307.692
Vp = 1330769.23 V
Therefore, the total electric potential (in V) at the point with coordinates (0, 1.50 cm) is 1330769.23 V
a) The total electric potential is 2282000 V
b) The total electric potential (in V) at the point with coordinates (0, 1.50 cm) is 1330769.23 V
What is electric potential?The electric potential is defined as the amount of work energy needed to move a unit of electric charge from a reference point to a specific point in an electric field.
Given the data in the question and as illustrated in the image below;
a) Determine the total electric potential (in V) at the origin.
We know that; electric potential due to multiple charges is equal to sum of electric potentials due to individual charges
Electric potential at p in diagram 1 below is;
\(V_P=V_1+V_2\)
\(Vp = \dfrac{kq_1}{r_1} + \dfrac{kq_2}{r_2}\)
we know that; the Coulomb constant, k = 9 × 10⁹ C
q1 = 4.60 uC = 4.60 × 10⁻⁶ C
r1 = 1.25 cm = 0.0125 m
q2 = -2.06 uC = -2.06 × 10⁻⁶ C
location x2 = −1.80 cm; so r2 = 1.80 cm = 0.018 m
so we substitute
Vp = ( 9 × 10⁹ × 4.60 × 10⁻⁶/ 0.0125 ) + ( 9 × 10⁹ × -2.06 × 10⁻⁶ / 0.018 )
Vp = (3312000) + ( -1030000 )
Vp = 3312000 -1030000
Vp = 2282000 V
Therefore, the total electric potential is 2282000 V
b)The total electric potential (in V) at the point with coordinates (0, 1.50 cm).
As illustrated in the second image;
\(r_1^2=0.015^2+0.0125^2\)
\(r_1 = \sqrt{[ 0.015^2 + 0.0125^2 ]\)
\(r_1 = \sqrt{0.00038125}\)
\(r_1 = 0.0195\)
Also
\(r_2^2 = 0.015^2 + 0.018^2\)
\(r_2 = \sqrt{0.015^2 + 0.018^2}\)
\(r_2 = \sqrt{0.000549\)
\(r_2 = 0.0234\)
Now, Electric Potential at P in the second image below will be;
Vp = V1 + V2
\(Vp = \dfrac{kq_1}{r_1} + \dfrac{kq_2}{r_2}\)
we substitute
Vp = ( 9 × 10⁹ × 4.60 × 10⁻⁶/ 0.0195 ) + ( 9 × 10⁹ × -2.06 × 10⁻⁶ / 0.0234 )
Vp = 2123076.923 + ( -762962.962 )
Vp = 2123076.923 -792307.692
Vp = 1330769.23 V
Therefore, the total electric potential (in V) at the point with coordinates (0, 1.50 cm) is 1330769.23 V
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A rigid body is rotating with constant angular speed 3 radians per second about a fixed axis through the points A. (4, 1, 1), B. (2, -1; 0), distances being measured in centimeters. The rotation is in the left-handed sense relative to the direction AB
1, Determine the unit vector pointing in the direction BA.
2, What is the angular velocity () of the of the body?
3, Write the position vector of point P: P .
Find the instantaneous velocity of particle P [hint v = w×r)
4, What is meant by left-handed rotation (left-handed coordinate system)?
5, Write the position vectors of points A and B The rotation axis AB has direction BA. Write the direction BA in terms of the components given above.
1.Unit vector in the direction BA: BA/|BA| = (2/3, 2/3, 1/3)
2.The angular velocity (ω) of the body is given as 3 radians per second.
3.Without the position of point P given, it is not possible to write the position vector of P.
4.Left-handed rotation refers to the direction of rotation where the rotation follows the left-hand rule.
5.Position vector of point A: (4, 1, 1)
Position vector of point B: (2, -1, 0)
The direction vector BA = (-2, -2, -1)
1.To determine the unit vector pointing in the direction BA, we subtract the coordinates of point B from the coordinates of point A and normalize the resulting vector.
The direction vector BA is given by:
BA = (4 - 2, 1 - (-1), 1 - 0) = (2, 2, 1)
To obtain the unit vector in the direction of BA, we divide the direction vector by its magnitude:
|BA| = √(2^2 + 2^2 + 1^2) = √(4 + 4 + 1) = √9 = 3
Unit vector in the direction BA: BA/|BA| = (2/3, 2/3, 1/3)
2.The angular velocity (ω) of the body is given as 3 radians per second.
3.Without the position of point P given, it is not possible to write the position vector of P. Please provide the position of point P to proceed with the calculation.
4.Left-handed rotation refers to the direction of rotation where the rotation follows the left-hand rule. In a left-handed coordinate system, if you curl the fingers of your left hand in the direction of rotation, your thumb will point in the direction of the rotation axis. It is the opposite direction to a right-handed rotation.
5.The position vectors of points A and B are:
Position vector of point A: (4, 1, 1)
Position vector of point B: (2, -1, 0)
The direction vector BA can be obtained by subtracting the coordinates of point A from the coordinates of point B:
BA = (2 - 4, -1 - 1, 0 - 1) = (-2, -2, -1)
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