At t = 10.0 s, the rocket is 135 m above the surface of the earth.
What is acceleration? What is its SI equivalent?In physics, acceleration is the rate at which the velocity of an object changes in relation to time. According to Newton's Second Law, the sum of all forces acting on an item results in its acceleration. Meter per second squared (m s2) is the unit of acceleration used in the SI system.
We can utilise the equations of motion with constant acceleration to resolve this issue. The formula we require is:
[tex]y = yo + vot + 1/2at^2[/tex]
where:
y is the final position of the rocket above the surface of the earth
yo is the initial position, which is 0 m
vo is the initial velocity, which is 0 m/s
a is the acceleration of the rocket, which is given by ay = [tex](2.70 m/s^3)t[/tex]
t is the time elapsed, which is 10.0 s
Plugging in the values, we get:
[tex]y = 0 + 0(10.0) + 1/2(2.70)(10.0)^2[/tex]
y = 135 m
[tex]v^2 = vo^2 + 2a(y - yo)[/tex]
where:
v is the final velocity of the rocket
vo is the initial velocity, which is 0 m/s
(B) A is the acceleration of the rocket, which is given by ay =[tex](2.70 m/s^3)t[/tex]
y is the final position of the rocket, which is 275 m
yo is the initial position, which is 0 m
Plugging in the values, we get:
[tex]v^2 = 0^2 + 2(2.70)(275 - 0)[/tex]
[tex]v^2 = 1485v = sqrt(1485)v = 38.5 m/s[/tex]
The speed of the rocket when it is 275 m above the surface of the earth is 38.5 m/s.
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If a graded receptor potential made the resting membrane potential of the axon more negative (for example, -70 mV changes to 75 m), you would expect A. it to be easier for this axon to reach the threshold voltage. B. subsequent action potentials to be shorter in duration C. no change in the ability of this axon to reach threshold voltage. D. it to be more difficult for this axon to reach the threshold voltage.
If a graded receptor potential made the resting membrane potential of the axon more negative (for example, -70 mV changes to 75 m), it would be more difficult for this axon to reach the threshold voltage (option D)
The resting membrane potential will become less negative as the extracellular K+ concentration rises.
Because the negative charge inside the cell exceeds the positive charge outside, the resting membrane potential is negative.
The distinction between the inside and outside of the cell is lessened as a result.
The resting membrane potential would be impacted by a change in Na+ or K+ conductance.
Since the membrane is more permeable to K+, a change in K+ conductance would have a bigger impact on resting membrane potential than a change in Na+ conductance.
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the ______of the hubble space telescope is better for shorter (bluer) wavelengths of light than for longer (redder) wavelengths of light.
the large research observatories on mauna kea use giant ____.
_____separate the various colors of light, allowing astronomers to determine stellar composition and many other stellar properties.
the twin 10-m keck telescopes can work together to obtain better angular resolution through a technique known as ____.
the chandra x-ray observatory focuses x rays with ____mirrors.
a 10-meter telescope has a larger blankthan a 4-meter telescope.
galileo's telescope designs using lenses were examples of _____.
"The angular resolution of the Hubble Space Telescope is better for shorter (bluer) wavelengths of light than for longer (redder) wavelengths of light.
The large research observatories on mauna kea use giant reflecting telescope.
Spectrograph, separate the various colours of light, allowing astronomers to determine stellar composition and many other stellar properties.
The twin 10-m keck telescopes can work together to obtain better angular resolution through a technique known as interferometry.
The Chandra X-ray observatory focuses X rays with grazing incident mirrors.
A 10-meter telescope has a larger light-collecting area than a 4-meter telescope. Galileo's telescope designs using lenses were examples of reflecting telescope."
The tool that is used to display a magnified view of a distant object is a telescope.
There are several telescope kinds that are utilised for various tasks.
The Hubble telescope and its best resolution cameras produce an angular resolution of around 0.04 arc seconds in visible light (at wavelengths close to 500 nm). The human eye can distinguish between objects separated by 40 arc seconds or less.
Astronomers can divide light from space into a spectrum and analyse its spectral lines to determine what substances are released or absorbed using specialised tools like a spectrograph or spectroscope.
By seeing at shorter wavelengths and extending the distance between telescopes, one can acquire a finer angular resolution.
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find the magnitude and direction of the electric field at the location of particle x, and the magnitude and direction of the electric field at the location of particle y. show your work. 6. is there a location at a finite distance from the charges at which the magnitude of the electric field due to both charges is zero? if so, make a sketch to indicate where this occurs (approximately;
A point between two opposite charges is where the net electric field is zero. The electric field due to many charges can be calculated by computing the individual electric fields due to each charge then vector summing them.
I need to be aware of the charges' placements and magnitudes in order to fix this issue. I can't offer a precise answer without this information. I can offer the broad strategy for resolving the issue, though.
We must apply Coulomb's law to determine the electric field where particle x or y is located. The electric field produced by a point charge Q at a distance r is described by Coulomb's law as follows:
E = kQ/r^2
where k equals 8.9910-9 Nm2/C2, the Coulomb constant. In order to determine the electric field due to each charge independently and then add them vectorially, we must first determine the c due to each charge at the location of particle x or y.
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How can a spacecraft reduce its speed during a trip to Mars?
Answer options with 4 options
A.
eliminate all forces acting on the spacecraft
B.
fire rockets to increase force acting in the direction of travel
C.
fire reverse rockets to increase force acting opposite of the direction of travel
D.
open a parachute to increase force acting opposite to the direction of motion of the spacecraft
A spacecraft can reduce its speed during a trip to Mars by firing reverse rockets to increase force acting opposite of the direction of travel.
option C.
How can a spacecraft reduce its speed?To reduce the speed of a spacecraft during a trip to Mars, the most common method is to fire reverse rockets, also known as braking thrusters.
These thrusters are used to generate a force that acts in the opposite direction of the spacecraft's motion, slowing it down. This is called a deceleration burn, and it is an important step in the process of entering into orbit around a planet or landing on its surface.
The reverse thrust slows down the spacecraft, reducing its speed and allowing it to be captured by the planet's gravity. This is crucial for the success of the mission and ensures that the spacecraft can be safely guided into orbit or landed on the surface of the planet.
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As an architect, you are designing a new house. A window has a height between
150 cm and 160 cm and a width between 82 cm and 70 cm .
What is the largest area that the window could be?
What is the smallest area that the window could be?
The largest area that the window could be is when it has the maximum height and width, so
What will be the maximum height of window ?Between the interior jambs on the left and right, measure the distance horizontally with a tape measure. Shut the window and take a similar measurement in the centre of the window from jamb to jamb.
At the top of the window, measure the space between the jambs. Take the shortest reading.
Area = height x width [tex]= 160 cm x 82 cm = 13,120 cm²[/tex]
Additional heights of [tex]18, 52, 54,[/tex]And [tex]62[/tex] Inches can be added to the standard height range of 2 feet to 8 feet.
Rough openings are given in whole numbers, and the actual window size is calculated by subtracting 1/2 inch from each rough opening size.
Area = height x width [tex]= 150 cm x 70 cm = 10,500 cm²[/tex]
Therefore, The smallest area that the window could be is when it has the minimum height and width, so:
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water continues to be removed at the rate until the tank becomes empty let k be the time at which the tank becomes empty write an equation involving an integral expression that can be used to find the value of k
The integral that can be used to find the value of k when the tank becomes empty is [tex]\int\limits^k_{18}[/tex] R(t)dt = 1310
The differential solution is a function that satisfies the intended differential. In this case, it is intended to find the value of R(t).
The solution to the differential equation can be an analytical solution, where the answer to the differential equation can be expressed in terms of basic functions such as eⁿ, sin t, cost t, etc.
Not all differential equations can be solved analytically. Differential payment solutions can also be searched using numerical methods that produce solutions with approximate values.
So, the uniqueness involving the integral expression on the water pumped into the tank is [tex]\int\limits^k_{18}[/tex] R(t)dt = 1310
Your question is incomplete but most probably your full question was:
For t > 18 no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. Let k be the time at which the tank becomes empty. Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
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57. You are driving through town at 12 m/s when suddenly a ball rolls out in front of you. You apply the brakes and begin decelerating at 3.5 m/s2. (a) how far do you travel before stopping? (b) When you have traveled only half the distance in part a, is your speed 6.0 m/s, greater than 6 m/s or less than 6 m/s? Support your answer with calculations.
a) Travelled 20.57 meters before coming to a stop.
b) When travelled half the distance, the speed is 2.6 m/s, which is less than 6 m/s.
What does speed mean?Speed is a measure of how fast an object is moving, without regard to the direction of its motion. It is defined as the distance travelled by an object per unit of time. Speed is a scalar quantity, which means it only has magnitude (i.e., numerical value) and not direction. The standard unit of speed is meters per second (m/s) in the International System of Units (SI), although other units such as kilometres per hour (km/h) and miles per hour (mph) are also commonly used. It can be calculated as the ratio of distance traveled by an object to the time taken to cover that distance.
For example, if a car travels 100 meters in 10 seconds, its speed can be calculated as 100 meters divided by 10 seconds, which equals 10 meters per second. Speed can also be constant, if the object is moving at a constant rate without changing its speed, or variable, if the object's speed changes over time.
(a) To determine how far travelled before stopping, use the kinematic equation:
[tex]v^2 = u^2 + 2as[/tex]
where,
v = final velocity (0 m/s, since you come to a stop)
u = initial velocity (12 m/s)
a = acceleration (-3.5 m/s^2, since decelerating)
s = distance traveled (unknown)
Rearranging the equation to solve for s, we get:
[tex]s = (v^2 - u^2) / (2a)[/tex]
Substituting in the known values, we get:
[tex]s = (0 - (12 m/s)^2) / (2*(-3.5 m/s^2)) = 20.57 m[/tex]
Therefore, travelled 20.57 meters before coming to a stop.
(b) To determine speed, travelled half the distance, use the kinematic equation:
[tex]s = ut + 0.5at^2[/tex]
where,
t = time elapsed (unknown, but use the fact that have travelled half the distance)
s = distance traveled (half of 20.57 m = 10.285 m)
u = initial velocity (12 m/s)
a = acceleration (-3.5 m/s^2)
Substituting the known values,
[tex]10.285 m = (12 m/s)t + 0.5(-3.5 m/s^2)t^2[/tex]
Simplifying and rearranging, a quadratic equation is obtained:
[tex]1.75t^2 - 12t + 10.285 = 0[/tex]
Solving t using the quadratic formula,
t = 2.52 s (rounded to two decimal places)
Now, to find your speed at this point, we can use the kinematic equation:
[tex]v = u + at[/tex]
Substituting the known values,
[tex]v = 12 m/s + (-3.5 m/s^2)(2.52 s) = 2.6 m/s[/tex]
Therefore, when travelled half the distance, the speed is 2.6 m/s, which is less than 6 m/s.
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Which is an example of kinetic energy being used?(1 point)
Answer:
A person walking, a soaring baseball, a crumb falling from a table and a charged particle in an electric field are all examples of kinetic energy at work.
Explanation:
Walking and running. Cycling. In a windmill, when the moving air hits the blades, it causes rotation which ultimately leads to the generation of electricity. In a hydropower plant, when the kinetic energy of the moving water hits the turbine the kinetic energy of the water gets converted to mechanical energy.
A student wants to launch a toy dart toward a target that hangs from a light string: As time t = 0,the dart is launched with an initial speed v at an angle 0 above the horizontal ground: At the instant the dart is launched, the string is cut such that the target begins to fall straight down. The positive horizontal direction is considered to be to the right, and the positive vertical direction is considered to be up.
A student wants to launch a toy dart As time t = 0, release a ball that has been resting near the Earth's surface. Allow a cart to leave rest and move down a 40°40° inclination with regard to the ground.
The graphs which could represent the vertical component of the velocity as a function of time for the dart and the target immediately after the dart is launched and the target begins to fall is Dart: above x-axis, decreasing; Target: below x-axis, decreasing.
Velocity is the directional speed of a moving object as an indicator of the rate at which its position changes as perceived from a given frame of reference and measured by a particular standard of time. The idea of speed is important in kinematics, the part of classical mechanics that explains the motion of things.
Velocity is a physical vector quantity that requires both magnitude and direction to be determined. Velocity is a scalar absolute value of speed, a consistently derived unit whose quantity is measured in SI (metric system) in meters per second.
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The above question is incomplete, the complete question is-
A student wants to launch a toy dart toward a target that hangs from a light string. At time t=0, the dart is launched with an initial speed v0 at an angle θ0 above the horizontal ground. At the instant the dart is launched, the string is cut such that the target begins to fall straight down. The positive horizontal direction is considered to be to the right, and the positive vertical direction is considered to be up.
Which of the following graphs could represent the vertical component of the velocity as a function of time for the dart and the target immediately after the dart is launched and the target begins to fall?
If a 0.4 kg baseball is traveling at 25 m/s straight into the air, how high does the ball go? Use energy to find the answer
The ball will rise to a height of approximately 31.25 meters.
How to determine the height to which the baseball will rise
First we can use the concept of energy conservation. Initially, the baseball has kinetic energy due to its motion, and as it rises, this kinetic energy is converted into potential energy due to its increased height.
The sum of the kinetic and potential energy of the baseball must remain constant, so we can use this principle to determine the maximum height reached by the ball.
The formula for kinetic energy is:
KE = 0.5 x m x v^2
where m is the mass of the ball (0.4 kg) and v is the velocity of the ball (25 m/s).
The formula for potential energy is:
PE = m x g x h
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the ball.
Since the total energy is conserved, we can set the initial kinetic energy equal to the final potential energy and solve for h:
0.5 x m x v^2 = m x g x h
0.5 x 0.4 kg x (25 m/s)^2 = 0.4 kg x 9.8 m/s^2 x h
h = (0.5 x (25 m/s)^2) / (9.8 m/s^2)
h = 31.25 m
Therefore, the ball will rise to a height of approximately 31.25 meters.
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In Part H, you discovered that the luminosity of a light bulb increases if the current increases. The rate at which electric potential energy is converted into heat depends on the current flowing through the bulb and the voltage across the bulb. This energy is supplied by the battery. Mathematically, the luminosity P of the light bulb is given by P=AVI, where AV is the voltage across the bulb and I is the current.What happens to the luminosity of the light bulb if the voltage of the battery is doubled? (Note that the PhET simulation does not display a numerical value for the luminosity, so you should use the relationship between the luminosity, the voltage across the bulb, and the current.)The luminosity does not change. The luminosity doubles. The luminosity increases by a factor of four. The luminosity increases by a factor of eight.
The luminosity doubles if the voltage of the battery is doubled.
Describe luminosity.
Luminosity, which is essentially measured in joules per second or watts in SI units, refers to the total energy produced by various celestial bodies (stars, galaxies) per unit time. A light-emitting object's radiant power, which is measured in absolute terms as luminosity, is the electromagnetic power that it radiates out over time.
The brightness of the bulb increases as the voltage rises. All of the bulbs in a series circuit are turned off when one of the bulbs is unscrewed. The brightness of the bulbs in a series circuit reduces as the number of lamps increases.
P=AVI,
If V is doubled, P also becomes doubled.
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Two piers, A and B, are located on a river: B is 1500 m downstream from A. Two friends must take round trips from pier A to pier B and return. One rows a boat at a constant speed of 4.00 km/h relative the water; the other walks on the shore at a constant speed of 4.00 km/h. The velocity of the river is 2.80 km/h in the direction from A to B. How much times does it take each person to make the round trip? Show all work.
The time will take for each persons to make a round trip will be=2.5 hours for pier A and 0.75 hours for pier B
Let's first find the time it takes for the rower to make the round trip. The rower's velocity relative to the water is 4 km/h, but the water is flowing at 2.8 km/h in the direction from A to B, so the rower's velocity relative to the shore is:
v_r = 4 km/h - 2.8 km/h = 1.2 km/h
The distance the rower travels is 2 * 1500 m = 3000 m, or 3 km. Therefore, the time it takes for the rower to make the round trip is:
t_r = 3 km / 1.2 km/h = 2.5 hours
Now let's find the time it takes for the walker to make the round trip. The walker's velocity is 4 km/h, so the time it takes for them to walk 1500 m from A to B is:
t_w = 1500 m / 4 km/h = 0.375 hours
The walker then turns around and walks 1500 m back to A, which takes another 0.375 hours. Therefore, the total time it takes for the walker to make the round trip is:
t_w = 2 * 0.375 hours = 0.75 hours
So the rower takes 2.5 hours and the walker takes 0.75 hours to make the round trip from pier A to pier B and back.
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Calculate the height to which water at 4°C will rise in a capillary tube of 0.5 × 10^-3 m diameter. (Given g=9.8 m/s^2; angle of contact 0°; surface tension= 0.072 N/m.
Step-by-step Explanation
Given: Diameter (D) of the capillary tube = m
Surface Tension (T) =
The angle of contact () =
Acceleration due to gravity (g) =
The temperature of water =
To Find: The height (h) of rising of water in the capillary tube
Solution:
Formula to find the height of the rise
The following expression is used to find the height (h) of rising of water in the capillary tube;
Where, is the density of water, and is the radius of the capillary tube.
Calculating the height of the rise in the capillary tube
Since the diameter of the capillary tube is , the radius of the tube will be;
And, at , the density of water is
Substituting all the required values in the above formula, we get;
Hence, the water will rise in a capillary tube to a height of
If the intensity level of a siren is 80dB at a distance of 10m from a fire truck, what is the intensity level at a distance of 100m?
The intensity level of the siren at a distance of 100m from the fire truck is 60 dB.
What is the intensity level?The decibel scale used to quantify a sound wave's energy or strength is known as the intensity level (dB). The sound pressure level is measured using a logarithmic scale in comparison to a reference sound level. The sound gets louder as the intensity level rises. The human ear can hear noises between the threshold of hearing (0 dB) to 120 dB. (threshold of pain). Maintaining safe noise levels is crucial because prolonged exposure to loud noises can cause hearing loss or injury. In order to assure the correct design and maintenance of structures, machinery, and equipment, understanding the intensity level is crucial in disciplines like engineering, acoustics, and environmental health and safety.
The intensity level of a sound wave decreases with distance from the source according to the inverse-square law, which states that the intensity is inversely proportional to the square of the distance. Therefore, if the distance from the source is increased by a factor of 10 (from 10m to 100m), the intensity level will decrease by a factor of 10² = 100. To calculate the intensity level at a distance of 100m, we can use the following formula:
IL2 = IL1 - 20 log (d2/d1)
where IL1 is the initial intensity level (80 dB), d1 is the initial distance (10 m), d2 is the new distance (100 m), and IL2 is the new intensity level.
Now,
IL2 = 80 dB - 20 log (100/10)
IL2 = 80 dB - 20 log (10)
IL2 = 80 dB - 20 x 1
IL2 = 60 dB
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Which of the following actions will increase the electric field strength at the position of the dot? - Make the rod longer without changing the charge. - Make the rod shorter without changing the charge. - Make the rod fatter without changing the charge.- Make the rod narrower without changing the charge. - Remove charge from the rod
E: "Removing charge from the rod" will increase the electric field strength at the position of the dot.
The electric field strength at the position of the dot depends on the charge and the distance from the charge. Therefore, any change that affects the charge or the distance will also affect the electric field strength.
A and B - Changing the length of the rod without changing the charge does not affect the charge density, and thus does not affect the electric field strength at the position of the dot. Therefore, options A and B are not correct.C and D - Changing the cross-sectional area of the rod without changing the charge does affect the charge density, and therefore can affect the electric field strength at the position of the dot. However, it is not clear how changing the rod's shape will affect the charge density, and so it is not possible to determine whether option C or D will increase or decrease the electric field strength. Therefore, options C and D are not correct.E - Removing charge from the rod will decrease the charge, and therefore decrease the electric field strength at the position of the dot. Therefore, option E is correct.You can learn more about electric field strength at
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How can static friction be harmful
Static friction is a force which keeps an object at rest. Static friction can be harmful as it releases energy in the form of heat due to rubbing of two bodies.
What is Static friction?Static friction is a force which keeps an object at the state of rest. Static friction can be defined as the friction which is experienced when the individuals try to move a stationary object on a smooth surface, without actually triggering any relative motion between the two objects or body and the surface on which it is moving.
In static friction, the frictional force resists the force which is applied to an object in motion, and the object which remains at the state of rest until the force of static friction is overcome. In the kinetic friction, the frictional force resists the motion of an object. This produces heat energy.
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Learning Goal: To understand the meaning of the variables that appear in the equations for one-dimensional kinematics with constant acceleration.Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or threwn) objects and cars starting and stopping approximate this type of motion It is also the type of motion most frequently involved in introductory kinematics problems The kinematic equations for such motion can be written as z(t) = x + vt + at^2 v(t) = 1+ at where the symbols are defined as follows .A. X(t) is the position of the particle is the initial position of the particle . B. x(i) is the velocity of the particleC. v(t) is the initial velocity of the particle D. Vi is the acceleration of the particle
The variables in the kinematic equations for motion in one dimension with constant acceleration are time, initial position, initial velocity, initial acceleration, velocity, and position.
The following are accurate definitions for the variables in the kinematic equations for motion in one dimension with constant acceleration:
A. x(t) represents the particle's position at time t as determined by its initial position x. (0).
B. v(t) represents the particle's speed at time t as determined by its initial speed v. (0).
C. The particle's starting position, or the position at time t=0, is represented by the number x(0).
D. The initial velocity of the particle, or its speed at time t=0, is known as v(0).
E. an is the particle's constant acceleration.
It's vital to remember that the x and v subscripts denote the time at which the location or velocity is being measured. As an illustration, x(0) is the particle's position at time.
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FILL IN THE BLANK. the ___ of the kinetic energy in a crash is what caused vehicles to be damaged or destroyed and the occupants injured or killed.
The release of the kinetic energy in a crash is what caused vehicles to be damaged or destroyed and the occupants injured or killed.
The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
We deduct the initial energy from the end energy to get the change in kinetic energy.
When a particle with mass m starts moving in a straight line, the rate of change of kinetic energy is equal to n times (n is a constant with the proper dimension).
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A GPS satellite orbits at an altitude of 20,200 km above the surface of the earth. What is the speed of the satellite? Recall that RE= 6.37 x 10^6 m
The speed of the GPS satellite can be calculated using the following formula:
How to calculate GPS satellite ?v = √(GM/r)
where G is the gravitational constant, M is the mass of the Earth, r is the distance between the center of the Earth and the satellite, and v is the speed of the satellite.The distance between the satellite and the center of the Earth can be found by adding the radius of the Earth to the altitude of the satellite:r = RE + h = 6.37 x 10^6 m + 20,200,000 m = 2.06 x 10^7 m
The mass of the Earth is M = 5.97 x 10^24 kg, and the gravitational constant is G = 6.67 x 10^-11 Nm^2/kg^2. Substituting these values into the formula, we get:v = √(GM/r) = √((6.67 x 10^-11 Nm^2/kg^2)(5.97 x 10^24 kg)/(2.06 x 10^7 m)) ≈ 3,870 m/s
Therefore, the speed of the GPS satellite is approximately 3,870 m/s.
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in a frictionless setup, two block of different masses are laying on two incline planes with different slopes and joined together by a pulley (see figure). find the acceleration of each block and the tension in the rope. also write the criteria (or equation) needed to be satisfied for block 2 to be moving down its incline plane.
Answer:
Explanation:
The problem you're describing involves two blocks connected by a rope over a pulley, with each block resting on a separate incline plane. The acceleration of each block and the tension in the rope can be determined using the principles of dynamics and conservation of energy.
Let's call the masses of the two blocks m1 and m2, the incline angles of the two planes θ1 and θ2, and the acceleration of each block a1 and a2.
The net force on each block is given by the sum of the gravitational force, the normal force, and the tension in the rope.
For block 1:
m1 * g * sin(θ1) - m1 * a1 = T
For block 2:
m2 * g * sin(θ2) - m2 * a2 = -T
where g is the acceleration due to gravity and T is the tension in the rope.
From these equations, we can see that the tension in the rope is equal in magnitude but opposite in direction for each block. The acceleration of each block can be found by rearranging the equations and solving for a1 and a2.
The condition for block 2 to be moving down its incline plane is that the net force on the block must be in the direction of motion, which means that the tension in the rope must be less than the gravitational force acting on the block. This can be expressed as:
T < m2 * g * sin(θ2)
Here is a definition of each variable in the problem:
m1: mass of block 1
m2: mass of block 2
θ1: incline angle of the first plane
θ2: incline angle of the second plane
a1: acceleration of block 1
a2: acceleration of block 2
g: acceleration due to gravity
T: tension in the rope
I hope this helps! Let me know if you have any other questions or if you need further clarification.
A bowling ball of mass 7 kg and radius 10.9 cm is rolled down a lane at a bowling alley with a velocity of 6 m/s. a) Find the rotational kinetic energy of the bowling ball, assuming it does not slip. b) What is the TOTAL kinetic energy of the ball? (you must now include the KE of translational, linear motion).
The bowling ball has a rotating kinetic energy of 8.573 J and a total velocity of 134.573 J.
What exactly is kinetic energy?A particle or an item that is in motion has a sort of energy called kinetic energy. An item accumulates kinetic energy when work, which involves the energy transfer, is done on it by exerting a net force. The word "kinetic" derives from the Greek "kinesis," which means motion. Any direction can be used to move it. As can be seen, kinetic energy rises with increasing mass and/or speed, and it stays unchanged if an object slows down or accelerates up.
To calculate rotational kinetic energy:
Rotational kinetic energy = (1/2) * I * ω^2
where I is the intertia of solid
I = (2/5) * m * r^2, m is the mass and r is radius
Substituting the given values, we get:
I = (2/5) * 7 kg * (0.109 m)^2
I = 0.00265 kg * m^2
The angular velocity of the ball ω = v / r
let v is the linear velocity of the ball.
Substituting the given values, we get:
ω = 6 m/s / 0.109 m
ω = 55.046 rad/s
by substituting this values into formulae we get
Rotational KE= (1/2) * 0.00265 kg * m^2 * (55.046 rad/s)^2
Rotational KE = 8.573 J
Therefore, the rotational kinetic energy of the bowling ball is 8.573 J.
The translational kinetic energy can be calculated as:
Translational kinetic energy = (1/2) * m * v^2
Substituting the given values, we get:
Translational KE= (1/2) * 7 kg * (6 m/s)^2
Translational KE = 126 J
Therefore, the total KE of the ball is:
Total kinetic energy = Rotational kinetic energy + Translational kinetic energy
Total KE = 8.573 J + 126 J
Total kinetic energy = 134.573 J
Therefore, the total kinetic energy of the ball is 134.57
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Find the marginal cost functions for each of the following average cost functions. a) AC= 1.5Q + 4 + 460 b) AC = 160 +5+3Q+2Q²
(a) The marginal cost function is MC = 3Q + 464.
(b) The marginal cost function is MC = 160 + 5 + 6Q + 6Q^2.
What is the marginal cost function?The marginal cost (MC) of a product is the change in the total cost of producing an additional unit of the product.
(a) AC = 1.5Q + 4 + 460
The total cost (TC) of producing Q units is given by:
TC = AC * Q
TC = (1.5Q + 4 + 460) * Q
TC = 1.5Q^2 + 4Q + 460Q
TC = 1.5Q^2 + 464Q + 460
The marginal cost function is given by the derivative of the total cost function with respect to Q:
MC = dTC/dQ
MC = d/dQ (1.5Q^2 + 464Q + 460)
MC = 3Q + 464
b) AC = 160 + 5 + 3Q + 2Q²
The total cost of producing Q units is given by:
TC = AC * Q
TC = (160 + 5 + 3Q + 2Q^2) * Q
TC = 160Q + 5Q + 3Q^2 + 2Q^3
The marginal cost function is given by the derivative of the total cost function with respect to Q:
MC = dTC/dQ
MC = d/dQ (160Q + 5Q + 3Q^2 + 2Q^3)
MC = 160 + 5 + 6Q + 6Q^2.
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a researcher raises the temperature from 92.2 to 105 o c and finds that the rate of the reaction doubles. what was the activation energy (in kj) for this reaction? (R = 8.3145 J/molK)
The activation energy of this reaction is approximately 94.6 kJ/mol.
To determine the activation energy of a reaction, we can use the Arrhenius equation:
[tex]k = A * e^(-Ea/RT)[/tex]
where k is the rate constant of the reaction, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, T is the temperature in Kelvin.
Let's assume that the pre-exponential factor A is constant, and the temperature is increased from T1 = 92.2°C to T2 = 105°C, such that the rate constant doubles (i.e., k2 = 2 * k1). We can use these two sets of data to find the activation energy Ea:
[tex]k2/k1 = e^(-Ea/R * (1/T2 - 1/T1))[/tex]
[tex]2 = e^(-Ea/R * (1/(105+273.15) - 1/(92.2+273.15)))2 = e^(-Ea/8.3145 * (-0.0039))ln(2) = -Ea/8.3145 * (-0.0039)Ea = -ln(2) * 8.3145 / (-0.0039) = 94.6 kJ/mol[/tex]
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If a machine does work faster, what does that mean about the power rating?
If a machine does some kind of work faster, then this mean that the power rating of the machine is higher. Power rating is directly proportional to the work done.
What is Power rating?The power rating of an equipment is the highest power input which is allowed to flow through a particular equipment. According to the particular discipline, the power may be referred to as the electrical or mechanical power.
Work is proportional to the energy, and higher power means higher energy present in an object. If a machine does work at a faster rate, this means that it has high power rating.
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A thick, spherical shell of inner radius a and outer radius b carries a uniform volume charge density rho.
Find an expression for the electric field strength in the region a
Express your answer in terms of r, a, b, rho, ϵ0.
Answer:
Explanation:
Here is the definition of each variable used in the expression for the electric field strength:
• r: radial distance from the center of the shell to the point where the electric field strength is being calculated
• a: radius of the shell
• b: thickness of the shell
• ρ_0: charge density in the shell
• ε_0: permittivity of free space, a constant that relates the electric flux density to the electric field strength. Its value is approximately 8.854 x 10^(-12) C^2/Nm^2.
• E: electric field strength, a vector quantity that describes the force experienced by a unit positive test charge placed at a particular point in an electric field.
• ∇: the gradient operator, a vector differential operator that describes the rate of change of a scalar field with respect to position.
• ∫: the definite integral symbol, denoting the sum of an infinite number of infinitesimal quantities over a specified range.
• dr': infinitesimal element of the radial distance used in the integration over the shell.
The electric field strength in a region is given by the gradient of the electric potential, V, in that region. The electric potential is related to the charge distribution, ρ, by the Poisson equation:
∇^2V = -(1/ε_0) * ρ
where ε_0 is the permittivity of free space.
If we assume the charge distribution is spherically symmetric, such that ρ = ρ(r), we can express the electric potential as:
V(r) = (1/4πε_0) * ∫(ρ(r')/|r-r'|) dV'
We can simplify this expression by assuming that the charge distribution is confined to a thin shell of radius a and thickness 2b, so that ρ(r) = ρ_0 for a-b <= r <= a+b and ρ(r) = 0 elsewhere. The electric potential in the region a can then be calculated by integrating over the shell:
V(r) = (1/4πε_0) * ρ_0 * ∫_{a-b}^{a+b} (1/|r-r'|) * dr'
To find the electric field strength, we need to take the gradient of the electric potential:
E = -∇V
Substituting in the expression for the electric potential, we get:
E = -∇[(1/4πε_0) * ρ_0 * ∫_{a-b}^{a+b} (1/|r-r'|) * dr']
So, the electric field strength in the region a is proportional to the gradient of the integral of the charge distribution over the shell, and is expressed in terms of the radius, a, the thickness, b, the charge density, ρ_0, and the permittivity of free space, ε_0.
The figure below shows four charges located at the corners of a square. The a origin of the coordinate system shown is at the center of the square. Also shown are the points A (located at the origin), B (a point on the x-axis), and C (a point on the y-axis). Which of the following statements are true? 9 -9 А B х C -9 9 = O Ex = 0 at points A and B, and Ey = 0 at points A and C. = O Ex = 0 at points A and B, Ey = 0 at A, B, and C. = O Ex = 0) at point A, and Ey = 0 at point B. = O Ex = 0 at points A and C, and Ey = 0 at points A and B
The statement Ex = 0 at points A and B, and Ey = 0 at points A and C
is true for the coordinate system.
What is the coordinate system?A mathematical tool called a coordinate system is used to find and quantify points in space. It offers a means of expressing how objects or points are situated and facing in either two- or three-dimensional space. Each point in a coordinate system is designated by its position in relation to a set of axes. The coordinate axes, often known as the axes, are typically depicted by two or three lines that intersect at the origin. These axes are used to measure coordinates, which pinpoint a point's exact location. The two most used coordinate systems are the polar coordinate system and the cartesian coordinate system, which both use two or three perpendicular axes to indicate a point's location.
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Calculate whether the kinetic energy of the particle increase, decrease or remain the same if the particle`s velocity changes (a) from -3 m/s to -2 m/s and (b) from -2 m/s to 2 m/s if the particle moves along x axis.? (c) In each situation, is the work done on the particle positive, negative or zero?
Answer:
(a) The kinetic energy of the particle will decrease if the particle's velocity changes from -3 m/s to -2 m/s.
(b) The kinetic energy of the particle will increase if the particle's velocity changes from -2 m/s to 2 m/s.
(c) The work done on the particle in both situations is positive. This is because work is the energy transferred to or from a system and the kinetic energy of the particle increases in both cases, indicating energy was transferred to the particle.
Select all the following situations that are similar to Copernicus's explanation for retrograde motion.A runner on an inner track lapping a slower runner on an outer track.
A fire truck overtaking and passing other vehicles on the road.
The following situations are similar to Copernicus's explanation for the retrograde motion:
A runner on an inner track lapping a slower runner on an outer track.
A fire truck overtaking and passing other vehicles on the road.
What is retrograde motion?When a planet appears to be moving backward in its orbit when viewed from Earth, this is known as retrograde motion. It happens when Earth crosses in front of a slower-moving outer planet or when an inner planet catches up to and passes Earth. As it moves in contrast to the background stars, the planet appears to move in a loop or zigzag pattern. Ancient astronomers initially noticed retrograde motion and thought the planets were moving haphazardly or in the opposite direction. However, it is now known that this phenomenon is an optical illusion brought on by the planet's orbit differing from Earth's orbit in both speed and direction. Astronomers use the notion of retrograde motion to better comprehend the dynamics of our solar system.
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a - ladder leans against the side of a house. the bottom of the ladder is from the side of the house. how high is the top of the ladder from the ground? if necessary, round your answer to the nearest tenth.
The top of the 12 ft ladder that leans against the house, and the bottom of the ladder is 9 ft from the side of the house = 7.9 ft
The triangle formed by the ladder must be a right angle with a hypotenuse (Side opposite to right angle) of 12 feet since the side of the house must be vertical to the ground to form a right angle.
Let x represent how high the ladder's top is above the ground.
We have the following using the Pythagoras theorem of right triangles:
c² = a² + b²
12² = 9² + x²
x² = 144 - 81
= 63
Hence,
x = √63
= 7.9 ft
The question is incomplete, it should be:
A 12 - ft ladder leans against the side of a house. the bottom of the ladder is 9 ft from the side of the house. how high is the top of the ladder from the ground? if necessary, round your answer to the nearest tenth.
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20° An 80 kg acrobat rests at top of a frictionless cannon angled at 20 degrees above the horizontal. A 20 kg cannonball is fired as shown. Upon reaching the acrobat, the ball is moving at 50 m/s just before colliding. The ball and acrobat stick together and soar through the air landing on a trampoline at the same height that the projectiles left the cannon at. Determine the following: a) The time in the air b) The range from when the objects leave the cannon c) The maximum height measured from where the projectiles leaves the cannon m m
The maximum height reached is approximately 101 meters above the ground.
Using this equation, we can solve for the time in the air, which turns out to be approximately 4.06 seconds. To find the range of the objects, we can use the horizontal component of the velocity of the cannonball, which is given by :
[tex]v = v 0 cos(theta),[/tex]
where v0 is the initial velocity of the cannonball and theta is the angle of elevation. We can use the equation of motion for the vertical component of the motion, which is given by:
[tex]height = v0y * t + (1/2) * g * t^2,[/tex]
where v0y is the initial vertical velocity and g is the acceleration due to gravity.
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