If all you know is the mass and velocity of an object, you cannot determine its potential energy.
The potential energy of an object depends on its position in a gravitational or electric field, and this information is not given by the object's mass and velocity alone. To calculate potential energy, we need to know the height of the object above some reference point or the distance between charged particles.
However, using the given information of mass and velocity, we can calculate the speed, kinetic energy, and momentum of the object. The speed is simply the magnitude of the velocity vector, the kinetic energy is given by 1/2 * m * v^2, and the momentum is given by p = m*v, where m is the mass of the object and v is its velocity.
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given constraints: x 0, y 0, 2x 2y 4, x y 8 explain the steps for maximizing the objective function p
To maximize the objective function p with the given constraints, we use linear programming by identifying the feasible region.
Finding corner points, evaluating p at each point, and selecting the point with the maximum value of p.In this case, the given constraints are x = 0, y = 0, 2x + 2y = 4, and x + y = 8. To maximize the objective function p, we follow these steps:Identify the feasible region by graphing the constraints on a coordinate plane.
The corner points, which represent the vertices of the feasible region.Evaluate the objective function p at each corner point.Select the point with the maximum value of p as the optimal solution that maximizes p while satisfying the given constraints.
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While on the surface of the earth a student has a weight of 450n if she is moved twice as far from the center of the earth then how does the new weight compare to her old?
Based on the fact that the student is moved twice as far from the center of the earth, her new weight will be 112.5 N.
What is her new weight?When the student was moved by the same distance from the center of the earth, her weight was halved.
When she was then moved twice as far, her weight was halved again.
This means that her new weight is:
= 450 x 1/2 x 1/2
= 450 x 1/4
= 112.5 N.
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Please design the differential amplifier shown in Fig. P3 to meet the following specifications: (1) Two NMOS transistors are matched: unCox = 400 UA/V2, Vtn = 0.8 V, n = 0.02 V-!, Wn = 4.Wp, L = 0.2 um. Please short the BODY to the SOURCE. (2) Two PMOS transistors are matched: up Cox = 200 UA/V², Vtp = -0.8 V, p = 0.04 V?, Wp = TBD, L = 0.2 um. Please short the BODY to the SOURCE. (3) Iss = 2 mA. (4) Vs = 0.3 V. (5) The DC voltages of both VOP and VON 3.5 V. (6) The small-signal gain Av = (vop – Von) (Vip - Vin) 10. (7) The differential AC sinusoidal signal, vi = (Vip - Vin), has 100 mV amplitude and 1 kHz frequency (8) VDD = 5 V. Design procedure: (a) Design Wp, W. (=4.Wp), VB, and Rp by hand-calculations. Please round the resolution of Wp and Wn to 0.1 um. (Hint: 2n and 2p could be zero for your hand-calculations.)
For the designing of differential amplifier following were found out :
the small-signal gain is zero.
the transconductance (gm) and output resistance (ro) of the NMOS transistors are -640 * (W/L) μA/V and 1 / (8 * (W/L)) kΩ respectively.
the transconductance (gm) and output resistance (ro) of the PMOS transistors are -320 * (W/L) μA/V and respectively.
NMOS transistor: Wn = 0.03 μm, L = 0.2 μm
PMOS transistor: Wp = 0.0075 μm, L = 0.2 μm
Bias current: Itail = 1 mA
Resistance: R = 0.3 kΩ
To design the differential amplifier according to the given specifications, we will follow these steps:
Step 1: Calculate the small-signal gain (Av)
Step 2: Determine the transconductance (gm) and output resistance (ro) of the NMOS transistors
Step 3: Determine the transconductance (gm) and output resistance (ro) of the PMOS transistors
Step 4: Calculate the tail current (Itail) based on the specified Iss
Step 5: Determine the resistance (R) value
Step 6: Calculate the width (Wp) of the PMOS transistor
Step 7: Calculate the width (Wn) of the NMOS transistors
Now let's go through each step in detail.
Step 1: Calculate the small-signal gain (Av)
Given: Av = 10, VOP = VON = 3.5V
Av = (vop - von) / (vip - vin)
10 = (3.5 - 3.5) / (0.1)
10 = 0 / 0.1
Since the numerator is zero, the small-signal gain is zero.
Step 2: Determine the transconductance (gm) and output resistance (ro) of the NMOS transistors
Given: unCox = 400 μA/V², Vtn = 0.8V, n = 0.02 V^(-1), L = 0.2 μm
gm = 2 * unCox * (W/L) * (Vgs - Vtn)
ro = 1 / (lambda * unCox * (W/L))
We need to design the amplifier for DC operation (Vin = Vbias), where the differential voltage (vgs = Vin - Vbias) should be zero to operate the transistors in the saturation region.
For the NMOS transistors:
Vgs = 0 (since Vin = Vbias)
gm = 2 * unCox * (W/L) * (Vgs - Vtn)
= 2 * 400 μA/V² * (W/L) * (0 - 0.8)
= -640 * (W/L) μA/V
ro = 1 / (lambda * unCox * (W/L))
= 1 / (0.02 V^(-1) * 400 μA/V² * (W/L))
= 1 / (8 * (W/L)) kΩ
Step 3: Determine the transconductance (gm) and output resistance (ro) of the PMOS transistors
Given: upCox = 200 μA/V², Vtp = -0.8V, p = 0.04 V^(-1), L = 0.2 μm
Similarly, for the PMOS transistors, we need to design the amplifier for DC operation (Vin = Vbias), where the differential voltage (vsg = Vbias - Vin) should be zero to operate the transistors in the saturation region.
For the PMOS transistors:
Vsg = 0 (since Vin = Vbias)
gm = 2 * upCox * (W/L) * (Vtp - Vsg)
= 2 * 200 μA/V² * (W/L) * (-0.8 - 0)
= -320 * (W/L) μA/V
ro = 1 / (lambda * upCox * (W/L))
= 1 / (0.04 V^(-1) * 200 μA/V² *
= 1 / (5 * (W/L)) kΩ
Step 4: Calculate the tail current (Itail) based on the specified Iss
Given: Iss = 2 mA
Itail = Iss / 2
= 2 mA / 2
= 1 mA
Step 5: Determine the resistance (R) value
Given: Vs = 0.3 V, VDD = 5 V
We can calculate the resistance (R) value using Ohm's Law:
Vs = Itail * R
0.3 V = 1 mA * R
R = 0.3 kΩ
Step 6: Calculate the width (Wp) of the PMOS transistor
To calculate Wp, we'll use the equation for the tail current:
Itail = 2 * upCox * (Wp/L) * (VDD - Vtp)^2
1 mA = 2 * 200 μA/V² * (Wp/0.2 μm) * (5 V + 0.8 V)^2
1 mA = 2 * 200 μA/V² * (Wp/0.2 μm) * (5.8 V)^2
Solving for Wp:
Wp = (1 mA * 0.2 μm) / (2 * 200 μA/V² * (5.8 V)^2)
Wp = 0.01 μm / (2 * 200 μA/V² * 33.64 V^2)
Wp ≈ 0.0075 μm
Step 7: Calculate the width (Wn) of the NMOS transistors
Given: Wn = 4 * Wp
Wn = 4 * 0.0075 μm
Wn = 0.03 μm
So, the design parameters for the differential amplifier are as follows:
the small-signal gain is zero.
the transconductance (gm) and output resistance (ro) of the NMOS transistors are -640 * (W/L) μA/V and 1 / (8 * (W/L)) kΩ respectively.
the transconductance (gm) and output resistance (ro) of the PMOS transistors are -320 * (W/L) μA/V and respectively.
NMOS transistor: Wn = 0.03 μm, L = 0.2 μm
PMOS transistor: Wp = 0.0075 μm, L = 0.2 μm
Bias current: Itail = 1 mA
Resistance: R = 0.3 kΩ
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Two 20 v batteries are in series, connected positive pole to negative pole. They each have internal resistance of 5 Ω. What power is dissipated in one of the batteries? 1). 80 watts. 2). 200 watts 3). 150 watts 4). 50 watts
The power dissipated in one of the batteries is 80 watts (option 1).
To find the power dissipated in one of the 20 V batteries with an internal resistance of 5 Ω connected in series, we will follow these steps:
1. Calculate the total voltage (Vt) provided by the two batteries connected in series:
Vt = V1 + V2 = 20 V + 20 V = 40 V
2. Calculate the total internal resistance (Rt) of the two batteries connected in series:
Rt = R1 + R2 = 5 Ω + 5 Ω = 10 Ω
3. Calculate the current (I) flowing through the circuit using Ohm's Law:
I = Vt / Rt = 40 V / 10 Ω = 4 A
4. Calculate the power (P) dissipated in one battery (we can use any battery since they have the same internal resistance) using the formula P = I² * R: P = (4 A)² * 5 Ω = 16 A² * 5 Ω = 80 W
So, the power dissipated in one of the batteries is 80 watts (option 1).
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A student lifts
an apple to a height of 1 m.
The apple weighs 1 N. How
much work does the student
do on the apple?
Use the work formula:
W = Fd
Replacing we have:
W = 1 N * 1 m
Resolving operation:
W = 1 J
The work efectuated is 1 Joule.
in exercises 33–36, determine the direction in which has maximum rate of increase from , and give the rate of change in that direction. f(x,y) = x e^-y, P =(2,0)
The rate of change in the direction of maximum rate of increase is \(-3/\sqrt{5}\)at the point P = (2,0).
To find the direction of maximum rate of increase of the function f(x,y) = x e^-y at the point P = (2,0), we need to calculate the gradient of the function at that point and then find the direction in which the gradient has the maximum magnitude.
Gradient of the function f(x,y):
∇f(x,y) =\((∂f/∂x, ∂f/∂y) = (e^-y, -x e^-y)\)
At the point P = (2,0), gradient is:
∇f(2,0) = \((e^0, -2e^0) = (1, -2)\)
Magnitude of gradient at point is:
\(|∇f(2,0)| = \sqrt{(1^2 + (-2)^2) = \sqrt{5} }\)
To find the direction of maximum rate of increase, we need to find a unit vector in the direction of the gradient. The unit vector in the direction of the gradient is given by:
\(u = (∇f(2,0)) / |∇f(2,0)| = (1/\sqrt{5} , -2/\sqrt{5} )\)
The direction of maximum rate of increase of the function f(x,y) at the point P = (2,0) is in the direction of the vector\(u = (1/\sqrt{5} , -2/\sqrt{5} )\). The rate of change in this direction is given by the dot product of the gradient and the unit vector:
\(Duf(2,0) = ∇f(2,0) · u = (1, -2) · (1/\sqrt{5} , -2/\sqrt{5} = -3/\sqrt{5}\)
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Which wave measure is changing by the greatest amount in the image?
A. amplitude
B. wavelength
C. speed
D. frequency
Answer: frequency
Explanation:
amplitude is the max height at which the wave reaches
wavelength distance b/w two waves
the speed at which the wave is oscillating
frequency is no. of oscillations of a wave per unit length
What is the net force on an object that is pulled with forces of 80 newtons to the right and 80 newtons to the left?.
The net force on an object is zero that is pulled with forces of 80 newtons to the right and 80 newtons to the left.
Net force is equal to sum of all the force acting on a body.
The formula for net force if n force are acting on it:
\(F_{net}=F_{1}+ F_{2}+F_{3}.....F_{n}\)
In this case the two forces are equal but opposite in direction.
Putting the values in the formula
\(F_{net} = 80+(-80)\) (since forces are equal but opposite)
\(F_{net}= 0\)
So the net force acting on the object is zero because the forces are equal and opposite.
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The net force on an object that is pulled with forces of 80 newtons to the right and 80 newtons to the left is: 0 newtons
To solve this problem the formula of net force and the procedure that we have to use is:
Fr = ∑F
Where:
Fr = resultant force∑Fr = F1 + F2 + FnInformation about the problem:
F1 = 80 newtonsF2 = - 80 newtonsFr = ?Applying the resultant force formula we get:
Fr = ∑F
Fr = F1 + F2
Fr = 80 newtons - 80 newtons
Fr= 0 newtons
What is resultant force?
We can say that the resultant force is the algebraic sum of all the forces acting on a body.
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Suggest any five activities where application of relation between pressure and area in day to day activities is used.
Five activities that will see the application of relation between pressure and area include:
Using a bicycle pump to inflate a tireAdjusting the water pressure in a showerheadOperating a hydraulic car liftOperating a hydraulic jackUsing a blood pressure cuffWhat are some examples that show pressure and area in real life ?When the handle of a pump is squeezed, the pressure inside the tire increases, causing the tire to inflate. By adjusting the size of the opening in the showerhead, the water pressure can be increased or decreased.
When a car is placed on a hydraulic lift, the pressure in the lift's cylinder is increased, causing the lift to raise the car off the ground. When a hydraulic jack is used to lift a heavy object, the pressure in the jack's cylinder is increased, causing the jack to lift the object.
A blood pressure cuff uses pressure to measure the blood pressure in a person's artery. The pressure in the cuff is increased until it is high enough to stop the flow of blood, and then the pressure is slowly released. The pressure readings at various points during this process can be used to determine a person's blood pressure.
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Does earths gravitational force field act on objects that aren’t touching earths surface?
( Explanation needed ASAP NEEDED
Answer:
no the earth gravitational force field
Answer:
yes, it acts on everything within the earth
Explanation:
In order to maximize the resolution in the visible range of a circular aperture such as a telescope, it is best to
A. apply a violet filter and use the telescope with the largest aperture possible
B. apply a red filter and use the telescope with the smallest aperture possible
C. apply a violet filter and use the telescope with the smallest aperture possible
D. apply a red filter and use the telescope with the largest aperture possible
A red filter with a large aperture telescope offers the best solution for maximizing resolution.
How does the choice of a red filter affect the resolution in a telescope?To maximize resolution in the visible range of a circular aperture, it is best to choose option D: apply a red filter and use the telescope with the largest aperture possible.
Resolution is determined by the size of the aperture, with larger apertures allowing more light to enter and providing higher resolution.
The red filter is chosen because longer wavelengths of light (such as red) are less affected by atmospheric turbulence, resulting in better image quality.
This combination enables the telescope to capture more light and reduce the blurring effects caused by atmospheric conditions, leading to enhanced resolution in the visible range.
A red filter with a large aperture telescope offers the best solution for maximizing resolution.
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A car driver measures a tire pressure of 320 kPa. What is the absolute pressure in the tire?(A) 0 kPa (B) 219 kPa (C) 101 kPa (D) 421 kPa (E) 320 kPa
Answer:
(D) 421 kPa
Explanation:
The absolute pressure of the tire is equal to the pressure measured plus the atmospheric pressure of 101 kPa. Then, the absolute pressure is
P = 320 kPa + 101 kPa
P = 421 kPa
So, the answer is
(D) 421 kPa
describing light interactions with curved mirrors match the descriptions to the feature
In addition, many predictions based on the idea have led to additional observations that support it. Which best describes this idea of the origin of the universe?
hypothesis
theory
law
fact
a 62-kg sprinter starts a race with an acceleration of 4.8 m/s2. what is the net external force on him?
The net external force of the sprinter is 297.6 N
The parameters given in the question are;
mass= 62 kg
acceleration= 4.8 m/s2
The formula that can be used to calculate the net force is;
= mass × acceleration
= 62 × 4.8
= 297.6 N
An external force is a physical influence that originates from outside a system and affects its behavior. In physics, a system is defined as a collection of objects or particles that are being studied or analyzed, and external forces are any forces that are not part of the system itself. These forces can come from a variety of sources, such as other objects, fields of energy, or the environment.
External forces can have a significant impact on a system's motion and behavior, and are often used in physics to model real-world phenomena. For example, the force of gravity acting on an object is an external force, as it is caused by the Earth's mass and affects the object's motion. Similarly, the force of air resistance acting on a moving object is an external force that can slow it down.
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PLEASE HELP!!!! i will give brainliest to the first person...
Answer: Fossil fuels power the machine that shakes the tree so the apples fall to the ground
Explanation: most machines are powered by fossil fuels
A cylindrical shape iron object of radius 400000 micro-meters and length 2 m initially at 30°C is placed in hot water at 60 °C. The heat energy received by the iron ball will be (Given: Specific Heat of iron = 452J/kg.°c, Density of iron = 7.874 g/cm) A. 42 KJ B. 87KJ C. 107 KJ D. None of the above
The heat energy received by the cylindrical iron object is 107338.3589 kJ. The correct answer is option D.
To find the heat energy received by the iron object, we'll need to follow these steps:
1: Calculate the volume of the iron object.
Volume = π × (radius)^2 × length
Radius = 400000 micrometers = 40 cm (1 cm = 10000 micrometers)
Volume = π × (40 cm)^2 × 200 cm = 1005309.64 cm³
2: Convert the volume to mass using the density of iron.
mass = density × volume
mass = 7.874 g/cm³ × 1005309.64 cm³ = 7915808.177 g = 7915.808 kg (1 kg = 1000 g)
3: Calculate the temperature change.
ΔT = T_final - T_initial = 60°C - 30°C = 30°C
4: Use the specific heat formula to find the heat energy received.
Q = m × c × ΔT
Q = 7915.808 kg × 452 J/kg°C × 30°C = 107338358.9 J = 107338.3589 kJ
Therefore, the correct answer is D. None of the above, as the heat energy received by the iron object is 107338.3589 kJ.
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How does Boyle's laws describe the relationship between gas pressure and volume?
Answer:
For a fixed mass of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional. Or Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant.
Marlene loves astronomy and has enrolled in an online course to learn more about space. The course gives Marlene access to a digital classroom.
What does this enable her to do? Check all that apply.
discuss the solar system with others in the class
attend a field trip to a planetarium at a local college
upload an amateur video of a shooting star
make a presentation about her favorite planet
take notes, tests, and quizzes
watch instructional videos made by a teacher
Answer:
A E and F are the correct answers
Explanation:
Answer:
A E F are correct
Explanation:
When you drop a 0.43 kg apple, Earth ex erts a force on it that accelerates it at 9.8m / (s ^ 2) toward the earth's surface. According to New ton's third law, the apple must exert an equal but opposite force on Earth. If the mass of the earth 5.98 * 10 ^ 24 * kg what is the magnitude of the earth's acceleration toward the apple?
Answer in units of m / (s ^ 2)
Answer:
The answer to the question is highlighted in the box
draw a figure of a simple pendulum explain its amplitude and effective length ?
Answer:
Explanation:
A simple pendulum consists of a mass (usually represented as a small object or bob) attached to a string or rod of negligible mass. The mass is free to swing back and forth under the influence of gravity.
In the figure, the point of suspension is denoted by "O," and the mass (bob) is represented by the small circle. The string or rod is represented by the vertical line connecting the point of suspension to the bob.
Amplitude:
The amplitude of a pendulum refers to the maximum displacement or swing of the bob from its equilibrium position. In the figure, the amplitude can be represented by the angle formed between the vertical position and the position of the bob when it swings to its maximum distance on one side. It is usually denoted by the symbol "A."
Effective Length:
The effective length of a pendulum refers to the distance from the point of suspension to the center of mass of the bob. It represents the distance over which the mass swings back and forth. In the figure, the effective length can be measured as the length of the string or rod from the point of suspension to the center of the bob. It is usually denoted by the symbol "L."
It is important to note that the amplitude and effective length of a simple pendulum affect its period of oscillation (the time taken for one complete swing). The relationship between these parameters and the period can be described by mathematical formulas.
Overall, the simple pendulum is a fundamental concept in physics and provides a simplified model for understanding oscillatory motion and the principles of periodic motion.
What two types of motion are the same in which they both are under the influence of gravity?
Answer:
Orbit and Gravity
Explanation:
May I have brainliest please I would appreciate it! Have a great day!
hand pushes on table with force of 35 N forward. whats the reaction force
Answer:
i think it is newtons third law of motion but i'm not sure sorry.i just really need point i don't know the answer.
Explanation:
Spirit of Australia, a hydroplane boat, made speed records by traveling 239 miles at a speed of 318.8 mi. How long did this trip take? if you could respond to this I would really appreciate it.
Answer:
Explanation:
I'm assuming we're measuring speed in mph, so here we go:
The boat travelled 239 miles in 0.75 of an hour. So how far did it travel in a full hour?
239
0.75
=
318.7 ≅ 319 m p h
The gravitational contraction of an interstellar cloud is primarily the result of its (a) mass (b) composition (c) diameter (d) pressure
The mass of the interstellar cloud is the primary factor that causes its gravitational contraction. The cloud gains mass and increases its gravity as it shrinks, eventually leading to the formation of a protostar.The correct option is a.
The gravitational contraction of an interstellar cloud is primarily the result of its mass. When an interstellar cloud, which is a vast collection of gas, dust, and other matter present in space, starts to shrink due to gravitational attraction, the resulting phenomenon is referred to as gravitational contraction.
The gravitational collapse of an interstellar cloud is caused by its own gravity as it pulls in the gas and dust. The cloud's mass is crucial because it produces a gravitational force that is required for its contraction. As the cloud shrinks, it gains mass, allowing it to increase its gravity and attract more matter from its surroundings until it forms a protostar.
:Gravitational contraction is primarily caused by the mass of an interstellar cloud. The cloud's mass creates a gravitational force that attracts gas and dust towards its center, causing it to collapse. As the cloud shrinks, it gains mass, causing its gravity to increase and draw more matter from its surroundings. This process continues until a protostar forms. Therefore, the mass of the cloud is the most important factor in its gravitational contraction.The correct option is b.
In summary, the mass of the interstellar cloud is the primary factor that causes its gravitational contraction. The cloud gains mass and increases its gravity as it shrinks, eventually leading to the formation of a protostar.
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4 (JAMB) The diagram below shows a light see-saw, which is balanced horizontally by the weights W₁, W2, W3, W4 in the positions shown: d a W₁ Fig. 4.44 W₂ b W3 WA Which of the following equations correctly represents the principle of the lever balance? A W₁ + W₂ = W3 + W4 B W₁-W₁ = W4 - W3 C W₁a+W₂b = W3c+Wad D (W₂-W₁)a= (W4 - W3)c E (W₁ + W₂ )ab = (W3+ W4)cd (SCIGCE) 4 ( JAMB ) The diagram below shows a light see - saw , which is balanced horizontally by the weights W₁ , W2 , W3 , W4 in the positions shown : d a W₁ Fig . 4.44 W₂ b W3 WA Which of the following equations correctly represents the principle of the lever balance ? A W₁ + W₂ = W3 + W4 B W₁ - W₁ = W4 - W3 C W₁a + W₂b = W3c + Wad D ( W₂ - W₁ ) a = ( W4 - W3 ) c E ( W₁ + W₂ ) ab = ( W3 + W4 ) cd ( SCIGCE )
The equation that represents the principle of the lever balance is:
W₁ + W₂ = W3 + W4; option A.What is the principle of moments?The principle of moments states when a body is in equilibrium, the sum of the clockwise moment about a point equals the sum of anticlockwise moment about that point.
A see-saw represents a balanced system of moments.
The sum of clockwise moment = The sum of anticlockwise moments.
Assuming W1 and W2 are clockwise moments and W3 and W4 are anticlockwise moments.
The equation will b: W₁ + W₂ = W3 + W4
In conclusion, a balanced see-saw illustrates the principle of the lever balance.
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In each of three trials of an investigation, a single force is applied to a mobile. Each time, the mobile acquires a different acceleration. The table
shows the relationship between the acceleration and the acting force.
Acceleration (m/s²)
Force (N)
1.2
0.7
1.6
4.8
2.8
6.4
Which phrase best describes a graph that would represent the relationship shown in the table? (1 point)
an upward-sloping line drawn on a graph with acceleration shown on the x-axis and force shown on the y-axis
a downward-sloping line drawn on a graph with acceleration shown on the y-axis and force shown on the x-axis
a downward-sloping line drawn on a graph with acceleration shown on the x-axis and force shown on the y-axis
an upward-sloping line drawn on a graph with acceleration shown on the y-axis and force shown on the x-axis
Answer: an upward-sloping line drawn on a graph with acceleration shown on the y-axis and force shown on the X-axis
just took the test
an upward-sloping line drawn on a graph with acceleration shown on the y-axis and force shown on the X-axis best describes a graph that would represent the relationship shown in the table
What are the features of graph ?A graph is represented as pictorial form the of data or numeric values in an organized manner which enables user to represent large amount of data in visual form.
There are 2 types of questions and the features of graphs are interpretation of given graphs or selecting a graph based on a verbal description.
The bar graphs are the most common type of graph, other graphs are dot plots, histograms, line graphs and scatterplots.
A Bar Graph is represented as the graphical display of data using rectangular bars of different parameters like heights, The structure can be represented in the y axis contains values, and the x axis contains categories or time periods.
A dot plot is a simple graphical representation which shows the frequency with which items appears in a data set and present data on the x axis.
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A particle moves in the xy-plane with coordinates given by
x = A cosωt and y = A sin ωt,
where A = 1. 5 m and ω = 2. 0 rad/s.
What is the magnitude of the particle's acceleration?
a. Zero
b. 1. 3 m/s2
c. 3. 0 m/s2
d. 4. 5 m/s2
e. 6. 0 m/s2
Answer:
The position of the particle in the xy-plane is given by:
x = A cos(ωt)
y = A sin(ωt)
Differentiating the position equation twice with respect to time gives the acceleration equation:
a = -Aω^2cos(ωt) - Aω^2sin(ωt)
The magnitude of the acceleration is:
|a| = sqrt[(Aω^2cos(ωt))^2 + (Aω^2sin(ωt))^2]
Since the maximum value of sin and cos functions is 1, the maximum magnitude of acceleration is:
|a|max = sqrt[(Aω^2)^2 + (Aω^2)^2] = sqrt[2(Aω^2)^2] = sqrt[2]Aω^2
Substituting the given values gives:
|a|max = sqrt[2](1.5 m)(2.0 rad/s)^2 = 6.0 m/s^2
Therefore, the magnitude of the particle's acceleration is 6.0 m/s2, option (e).
Explanation:
find the ratio of turns on the primary coil to turns on the secondary coil in a transformer that will stop the 110v household voltage down to 4.1 v .
Ratio of turns on the primary coil is 26
Briefing
So to solve for this problem this is computed by the following steps
Vp/Vs (=Np/Ns)
Briefing
Where;
Vp = Voltage primary
Vs = Voltage Secondary
Np =Turn ratio primary
Ns = Turn ratio Secondary
So plugging in our Valves
110/4.1 =Np/Ns
Np/Ns= 26.82
So the answer is 26 Coils
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How many of our solar system's large moons orbit their planets in the same direction as their planet rotates?
most
very few
about half
Most of our solar system's large moons orbit their planets in the same direction as their planet rotates.
There is a long answer to this question because it depends on what is considered a "large" moon and which planets are being considered. However, in general, most of the large moons in our solar system do orbit their planets in the same direction as their planet rotates. For example, Earth's moon orbits in the same direction that Earth rotates. Similarly, Jupiter's largest moons (such as Io, Europa, and Ganymede) also orbit in the same direction as Jupiter's rotation.
However, there are some exceptions. For example, Neptune's largest moon, Triton, orbits in the opposite direction of Neptune's rotation. Overall, it can be said that about two-thirds of the large moons in our solar system orbit their planets in the same direction as their planet rotates, while about one-third orbit in the opposite direction.
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