The Coriolis effect describes the deflection pattern experienced by an object that is not firmly anchored to the ground as it travels long distances around the Earth. Many large-scale weather patterns are caused by the Coriolis effect.
The rotation of the Earth is important for the Coriolis effect. In particular, the Earth rotates faster at the equator than at the poles. Because the Earth is wider at the equator, the equatorial region must travel about 1,000 kilometers (1,000 miles) per hour to make one revolution of her in 24 hours. The Earth rotates slowly near the poles at 0.00008 kilometers (0.00005 miles) per hour. If you play catch anywhere in the northern hemisphere, the ball will curve to the right.
Apparent deflection is due to the Coriolis effect.
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A lawn mower that weighs 196 N is pushed along the ground at a constant speed with a force of
240 N applied to the handle, which makes an angle of 40 degrees with the ground. With what force does the ground push upward on the mower?
Answer:(i) The magnitude of the force that is pressing the lawn-mower directly into the ground is 25 N
(ii) The magnitude of the effective force that moves the mower forward is approximately 43.3 N
(iii) Because there are no net downward force acting on the lawn-mower
Explanation:
when the moon is waxing, what side of the moon do we see illuminated?
We see the right side of the moon illuminated when the moon is waxing.
What is waxing?The Moon is in the Waxing Crescent phase when its western edge is bright but the majority of the surface that can be seen from Earth is dark. Waxing refers to the fact that the amount of light visible during this phase increases day by day.
What are the phases of the moon?The Earth's moon cycle has four phases, to start. A new moon, first quarter, third quarter, and full moon are among them.
There are 29.5 days in a lunar cycle. The moon completes one orbit of the Earth in around 27.3 days. Given that the Earth has travelled around 45 million miles during the time it takes the moon to complete one full orbit around the Earth, the 2.2-day delay is effectively the moon "catching up" to the Earth.
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a constant force acts upon an object moving along a straight line from point (9, -7, -10) to point (10, -5, 9). find the work done by the force if the distance is measured in meters, and the magnitude of the force is measured in newtons.
The work done by the force is √7 Newtons. The result is obtained by multiplying the distance by the force.
How to find the work done on an object?The work done on an object can be counted by the equation:
W = F × d
Where
W = Work (Joule or Nm)F = Force (Newton)Find the work done by the force!
We have:
(x₁, y₁, z₁) = (9, -7, -10)(x₂, y₂, z₂) = (10, -5, 9)The distance (straight line) is
[tex]d = \sqrt{(x_{1}- x_{2})^{2} + (y_{1}- y_{2})^{2} + (z_{1}- z_{2})^{2} }[/tex]
[tex]d = \sqrt{(9-19) + (-7 + 5) + ((-10) - (-9)) }[/tex]
[tex]d = \sqrt{(10) -2 + (-1 )[/tex]
d = √7 meters
The force is F.
Hence, the magnitude of the force on the object are √7 F.
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despite emitting the same power as a 100 w incandescent bulb, humans don't shine as brightly. we'll learn in week 4 why that is, but for now, let's compute the first step of the difference: the temperature. a human has a surface area of roughly 1.6 m2, but the filament a surface area of 6e-5 m2, so to emit the same power, it needs a much higher power density, and so needs to be at a higher temperature. what temperature is the lightbulb at (in kelvin)?
According to the problem the temperature of the light bulb is 1 Kelvin.
What is temperature?Temperature is a measure of how hot or cold something is. It is measured using a thermometer or thermocouple and is usually expressed as a number on a scale, such as Celsius or Fahrenheit.
The temperature of a light bulb can be calculated using the Stefan-Boltzmann law. This law states that the power emitted by a blackbody is proportional to the fourth power of its temperature. Therefore, the temperature of the light bulb can be calculated by taking the fourth root of the ratio of the power emitted by the human to the power emitted by the light bulb.
The power emitted by a human is around 100 watts and the power emitted by a 100 watt incandescent bulb is also 100 watts. Therefore, the temperature of the light bulb is the fourth root of 100/100, which is 1.
Therefore, the temperature of the light bulb is 1 Kelvin.
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a nonconducting sphere with center c and radius a has a spherically symmetric electric charge density. the total charge of the object is q > 0. a. determine the magnitude and direction of the electric field at point p, which is a distance r > a to the right of the sphere's center. b. determine
the magnitude and the polarisation of the electric field at point p, with the polarisation of the electric field pointing away from charge B. (to the left). If the sphere has a nonconducting , the magnitude is force*q.
The magnitude of the electric field at point P is 3*10^5 N/C. The electric field strength at point P, which is along the straight line between point P and Q, is parallel to the direction of the charge Q. (since there is a negative charge). The equation E = F Q thus describes the electric field at point p that point charge Q produces. The electric field created by a point charge Q is shown in the accompanying graphic in its direction.
magnitude = force*q for q>0.
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which measurement has the fewest number of significant figures? a. 0.001280 m b. 12.8 m c. 12.80 m d. 12.08 e. 0.1280 m
In the followings set of the numbers given, 12.8 m have the fewest number of significant figures.
Significant figures can be described as the number of digits that is present in a in a value, and made up of the degree of accuracy of the value.
The rules for calculations using significant figures are:
1. All non-zero numbers are included.
2. Leading zeros are not significant.
3. Zeros that is found in between two non-zero digits are included.
4. All trailing zeros to the right of the decimal are significant.
5. Trailing zeros in a whole number with no decimal shown are significant.
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nitrogen is compressed to a density of 4 kg/m3 under an absolute pressure of 400 kpa. determine the temperature in degrees fahrenheit.
The temperature in Fahrenheit is 146.799°F.
The equation of state for a fictitious ideal gas is known as the ideal gas law, sometimes known as the generic gas equation. Although it has some restrictions, it is a good approximation of the behavior of numerous gases under various circumstances. Benoît Paul Émile Clapeyron introduced it for the first time in 1834 as a synthesis of the empirical Boyle's law, Charles' law, Avogadro's law, and Gay's law. Lussac's. The empirical form of the ideal gas law is frequently used which is PV = nRT. The ideal gas constant is R.
Density = ρ = 4 kg/m3
Pressure = P = 400 kPa
As we know the ideal gas equation is PV = nRT
P = ρRT
400 = 4 x 0.2968 x T
T = 336.927 K
The temperature in Fahrenheit is 146.799°F.
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Need this ASAP please because it's for a homework!
Make a time line where you organize the events since the Big Bang in sequence.
After the universe's 13.7 billion year old Big Bang, it has gone through numerous phases or epochs.
What is Big bang theory?It may have experienced more activity and change in the first second than in all the billions of years since because of the harsh environment and violence of its very early beginnings.
We can construct a rough timeline as follows using our current understanding of how the Big Bang might have developed, taking into account notions about inflation, the Grand Unification, etc.
The Planck Epoch (or Planck Era), which spans from 0 to around 10-43 seconds (1 Planck Time), is the closest that modern physics can come to the beginning of time itself.
Therefore, After the universe's 13.7 billion year old Big Bang, it has gone through numerous phases or epochs.
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A billiard ball traveling at 4 m/s has an elastic head-on collision with a billiard ball of equal mass that is initially at rest. The first ball is at rest after the collision. What is the speed of the second ball after the collision?
__m/s
Following the collision, the initial ball is now at rest. 4 m/s is the speed of the second ball after the collision.
This is an elastic collision, which means that both kinetic energy and momentum are conserved.
We can use the conservation of momentum to find the velocity of the second ball after the collision:
momentum initial = momentum final
m1v1 + m2v2 = m10 + m2v'2
where m1 and m2 are the masses of the balls, v1 is the initial velocity of the first ball, and v'2 is the final velocity of the second ball.
Since the mass of the two balls are equal and the first ball is initially moving, and the second ball is initially at rest, we can simplify the equation as:
m1v1 = m2v'2
v'2 = v1*(m1/m2)
Therefore, the final velocity of the second ball is 4 m/s * (m1/m2) = 4 m/s
We can conclude that the final velocity of the second ball is 4 m/s , and the speed of the first ball is 0 m/s after the collision, which confirms that it is an elastic collision and the total kinetic energy is conserved.
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a point charge is placed at the center of an uncharged, spherical, conducting shell of radius r. the electric fields inside and outside the sphere are measured. the point charge is then moved off center a distance r/2 and the fields are measured again. what is the effect on the electric fields? (a) changed neither inside nor outside (b) changed inside but not changed outside (c) not changed inside but changed outside (d) changed inside a
As the charge is relocated because of that charge, the configuration of the field lines inside will alter. The induced surface charge outside the sphere is uniformly dispersed throughout the exterior surface.
Two point charges: what are they?Two point charges A and B are set at a specific distance apart with force F acting between them. They have charges of +Q and -Q, respectively. It is accurate to say that only stationary electric charges are subject to Coulomb's law. This is because, in the case of moving charges, a current exists, which produces a magnetic field, which in turn exerts force on moving charges; as a result, Coulomb's Force is no longer the only force to be taken into account. A charge distribution that has a value solely at one specific place is known as a point charge. A test charge is a point charge that is so little that it has no impact on the charge distribution you are testing.
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where m 0 is the mass of the particle at rest and c is the speed of light. what happens as v goes to c?
As velocity, v of the object approach the speed of light c, the energy of the particles will increase.
From the famous equation of Einstein of mass-energy relationship, that is
E = m₀c²/√(1-v²/c²)
Where E denotes the energy, c is the speed of light, v is the speed of the object.
If mass of the object at rest is m₀, we can see from the above relationship that as we approaches c, the denominator terms goes closer to 0. And when v becomes speed of light c, then the denominator becomes zero. Thus making the Energy infinite. So the energy becomes infinite.
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a ringing alarm clock is put under a glass jar. the air is slowly removed from the space around it. what will happen as the air is removed? (1 point)
As the air is removed from space around a ringing alarm clock that is placed under glass jar, sound of the alarm will become progressively quieter, and the clock's mechanical parts will move more smoothly.
What will happen as the air is removed?As the air is slowly removed from space around a ringing alarm clock that is placed under a glass jar, the sound of alarm will become progressively quieter. This is because sound is a mechanical wave that travels through a medium.
The air particles in jar vibrate as the sound waves pass through them, which allows us to hear the sound. As the air is removed, number of air particles available to vibrate and carry the sound waves decreases, which reduces the intensity of sound. As the air is almost completely removed, there will be very few air particles left to vibrate, then the sound will be almost inaudible.
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An airplane travels down a
runway for 4.0 seconds with an
acceleration of 9.0 m/s2. What
its change in velocity during
this
time?
Someone helpppp!!
Answer:
We can use the equation of motion of an object under constant acceleration to calculate the change in velocity during this time. The equation is:
Δv = at
Where:
Δv = change in velocity (m/s)
a = acceleration (m/s^2)
t = time (s)
Given that the acceleration of the airplane is 9.0 m/s^2 and the time it travels down the runway is 4.0 seconds we can substitute these values into the equation:
Δv = 9.0 m/s^2 * 4.0 s = 36 m/s
Therefore, the change in velocity of the airplane during this time is 36 m/s.
A man is driving through his neighborhood
when a boy on a bike comes out of a driveway.
The driver skids to a stop in an attempt to avoid
hitting the biker, but ends up knocking the boy
off of his bike. The biker has minor injuries and
his parents file a lawsuit against the driver,
claiming that the car was going over the speed
limit at the time. The drag of the road is 0. 75
You might need to slow down because, generally speaking, a bicycle moves more slowly than other vehicles.
What sort of vehicle can a driver encounter on a slow-moving road? You might need to slow down because, generally speaking, a bicycle moves more slowly than other vehicles.Before overtaking a bicycle in a lane that is too small to share, wait until there is a clear section of the road.Before opening your automobile door into a traffic lane or a cycling lane, look out for passing bicycles.I'd like to outline three fundamental ideas that, in my opinion, form the basis of this skill set, despite the fact that defensive and professional driving entail many specific techniques:1) fault vs. avoidability; 2) following distance; and 3) detachment from other driversYour following distance should be extended.The interior and outside mirrors, as well as a head check, can be used to assess the mirror blind spots by the driver.
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a metal conductor is connected to a battery. which statement accurately describes the current in the metal conductor?
The statement accurately describes the current in the metal conductor is it is a flow of electrons from negative to positive terminal. The correct option is A.
Conductors allow the current to pass through them. The given statements are about movement of subatomic particles.
When linked to a battery, the electric field (created by the battery) accelerates free electrons, and because they are negatively charged, they travel from the negative terminal to the positive terminal due to the electric field, gaining energy and speed. The ion is ultimately the winner (of energy) in this collision because the transit is not smooth and the electrons bump into the lattice ion.
The given question is incomplete. The complete question contains options. They are 'A.It is a flow of electrons from negative to positive terminal B.It is a flow of electrons from positive to negative terminal C.It is a flow of protons from negative to positive terminal D.It is a flow of protons from positive to negative terminal
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Derive the equation for the buoyant force from these two ideas.
The expression for the buoyant force is F = ρghs²
What is buoyant force?Buoyant force is the force exerted on a object by a liquid.
How to derive the expression for the buoyant force?Given that the pressure from the fluid at a certain depth is given by P = P₀ + ρgh where
P₀ = atmospheric pressure, ρ = density of fluid, g = acceleration due to gravity and h = depth of object in fluidWe know that the buoyant for is due to the pressure difference frm the top and bottom of the fluid.
Since
P = P₀ + ρgh
P - P₀ = ρgh
ΔP = ρgh
Now, we know that pressure difference, ΔP = F/A where
F = buoyant force and A = areaSo, making F subject of the formula, we have that
F = ΔPA
Now since the object is a perfect cube of length, s, its area at its bottom surface perpendicular to F is A = s²
So, F = ΔPA
F = ΔPs²
So, substituting ΔP into the equation, we have that
F = ΔPs²
F = ρghs²
So, the buoyant force is F = ρghs²
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an 8 3 4 -inch circular power saw rotates at 4,500 revolutions per minute. (round your answers to two decimal places.) (a) find the angular speed of the saw blade in radians per minute. incorrect: your answer is incorrect. rad/min (b) find the linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut. incorrect: your answer is incorrect. ft/min
(a) Angular speed of the saw blade in radians per minute is:
(b) The linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut is 286.68 ft/min.
What is angular speed?Angular speed formula is used to calculate the distance that the body covers in terms of rotations or revolutions to the time taken.
The angular speed of the saw blade in radians per minute is calculated as 785.39 rad/min. (b) linear speed of one of the cutting teeth in feet per minute is 286.68 ft/min
(a) Given, 4,500 revolutions per minute
rad/min = RPM * 2 * pi / 60
So, angular speed of the saw blade in radians per minute is:
rad/min = 4,500 * 2 * pi / 60 = 785.39 rad/min (rounded to two decimal places)
(b) Given, 24 cutting teeth. Circumference of a circle is given by the formula: C = 2 * pi * r
r is radius of the circle.
linear speed (v) is given by the formula: v = r * w
w is angular speed in radians per second.
So, you can find linear speed of one of the cutting teeth in feet per minute as: r = (8 3/4 inches) / 2 = 4.375 inches
C = 2 * pi * 4.375 inches = 27.54 inches
w = 785.39 rad/min
v = r * w = 4.375 inches * 785.39 rad/min = 3440.21 inches/min
3440.21 inches/min = 286.68 ft/min
So, linear speed of one of the cutting teeth in feet per minute is 286.68 ft/min.
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A car drives 40 miles at an angle of 35 degrees north of east then drives for 50 miles due north and finally 10 miles at an angle of 20 degrees north of west what is the cars resultant magnitude and direction
Answer:
Below
Explanation:
FIND TOTAL NORTH DISPLACEMENT
40 sin 35 + 50 + 10 sin 20 = 76.363 mi
FIND TOTAL E-W DISPLACEMENT
40 cos 35 - 10 cos 20 = 23.369 mi
Total resultant displacement ( using pythag theorem)
sqrt ( 76.363^2 + 23.369^2 ) = 79.86 mi
angle = arctan ( 79.23 / 23.37) = 73 ° North of East
PLEASE ANSWER MY OTHER QUESTION
cody's car acce;rates from 0m/s to 45 m/s northward in 15 seconds. what is the acceleration of the car
The acceleration of the Cody's car when moving from 0 m/s to 45 m/s is calculated to be 3 m/s².
The acceleration is described to be the rate of change of velocity. It is a vector quantity. Its S I unit is m/s². If an object in a straight line accelerates up or slows down, it is said to be accelerated. Mathematically, a = Δv/t
where, a = acceleration
Δv = change of velocity = 45 - 0 = 45 m/s
t = time = 15 sec
After plugging the values into the equation above, we have,
a = Δv/t = 45/15 = 3 m/s²
Thus, the required acceleration of the car is calculated to be 3 m/s².
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Copper wire with a diameter of 0. 5 cm is covered with a 0. 65-cm layer of insulating material having a thermal conductivity of 0. 242W/m⋅K. The air adjacent to the insulation is at 290 K. If the wire carries a current of 400 A, determinea. The convective heat-transfer coefficient between the insulation surface and the surrounding airb. The temperatures at the insulation-copper interface and at the outside surface of the insulation
The convective heat-transfer coefficient between the insulation surface and the surrounding air is approximately 19.59 W/m²K; b.
The required details for insulation surface in given paragraph
The temperatures at the insulation-copper interface is approximately 324.96 K, and at the outside surface of the insulation is approximately 305.57 K.
What is the temperature of the air surrounding the insulated copper wire?
The temperature of the air surrounding the insulated copper wire is 290 K (or 17°C or 62.6°F). This is specified in the problem statement as being the temperature of the air adjacent to the insulation. This information is important for determining the heat transfer between the insulation and the surrounding air, which will affect the temperature at the insulation-copper interface and at the outside surface of the insulation.
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A car that weighs 10,500N drives at a constant speed of v = 49.0m/s for a distance of d =
5,110m. What is the net work done on the car during this drive?
a. Wnet = 0
b. Wnet = 1.28 · 106J
c. Wnet = 2.05J
d. Wnet = 5.37 · 107J
The work that has been done in driving the car is 5.37 * 107J.
What is the net work done?We know that the force that moves the car in the forward direction is the force that is provided by the engine of the car and as such we have to look at the work that is done as the product of the force and the distance that is covered here.
We know that;
Work done = force * distance
Work done = 10,500N * 5,110m
Work done = 5.37 * 107J
A total work that has a magnitude of 5.37 * 107J has been done by the car.
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A student connects a resistor to a cell for 60 seconds.
The current through the resistor is 0. 97 A
Calculate the charge flow.
Use the equation:
charge flow = current × time
Give your answer to 2 significant figures
A student connects a resistor to a cell for 60 seconds and resistor is 0. 97. So the charge flow is 58.2 coulombs.
What is meant by resistor ?
A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device.A specified voltage can be supplied via resistors to an active device like a transistor.Modern resistors are often constructed from a carbon, metal, or metal-oxide layer.In these resistors, an insulating material is wrapped in a helix around a thin film of conductive (but still resistant) material.A passive electrical component called a resistor prevents the flow of electric current by introducing resistance. They are present in practically all electrical networks and electronic circuits. Ohms are used to measure resistance.To learn more about resistor refer to
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eating broccoli _________ chemical energy that your body converts to energy that your body needs, such as energy for movement , temperature control and other life processes. fill in the blank releases or absorbs
Eating broccoli absorbs chemical energy that your body converts to energy that your body needs, such as energy for movement , temperature control and other life processes.
What is broccoli?This refers to a green plant that is edible. It is in the cabbage famil. It has a large flowering head, stalk, and small associated leaves that are eaten as a vegetable. Broccoli is classified in the Italica cultivar group of the species Brassica oleracea.
Broccoli is a nutrient-rich vegetable that may enhance your health in a variety of ways, such as by reducing inflammation, improving blood sugar control, boosting immunity, and promoting heart health.
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How does genetics affect our chance of developing certain diseases and disorders?
Answer:
A genetic predisposition results from specific genetic variations that are often inherited from a parent. These genetic changes contribute to the development of a disease but do not directly cause it. Some people with a predisposing genetic variation will never get the disease while others will, even within the same family.
Explanation:
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a constant force fa is applied to an object of mass m, initially at rest. the object moves in the horizontal x-direction, and the force is applied in the same direction. after the force has been applied, the object has a speed of vf. which mathematical routines can be used to determine the time in which the force is applied to the object of mass m? select two answers.
t=Δpx/FA
Δt=Mvf/FA
F = ma, Newton's second rule of motion, may be used to calculate when a force is applied to an object of mass m.
The time may also be calculated using the equation of motion, vf = vi + at, where an is the acceleration and t is the time.
There are two mathematical procedures that may be used to figure out when a force is applied to an object with mass m: Newton's Second Law of Motion states that F = ma, where ma is the object's mass and an is its acceleration, and F is the applied force.
The acceleration may be found by rearranging the equation, which can then be used to calculate how long it will take the item to reach its final speed vf.
Kinematic Equation for Constant Acceleration: where vi is the starting velocity, t is the time, and an is the acceleration, vf = vi + at The time t may be calculated from the final velocity vf and the acceleration a by replacing the initial velocity with 0 (because the object is initially at rest).
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The complete question is:
A constant force FA is applied to an object of mass M, initially at rest. The object moves in the horizontal x-direction, and the force is applied in the same direction. After the force has been applied, the object has a speed of vf. Which mathematical routines can be used to determine the time in which the force is applied to the object of mass M? Select two answers.
a car slows down uniformly from a speed of 25.0 m/sm/s to rest in 9.00 ss . part a how far did it travel in that time?
The distance car travel at 9.00 s is 112.8 m.
What is the distance car travelled?Displacement is the measurement of a change in position of an object or person in meters. And acceleration is the rate of change in velocity, measured in meters per second per second (or meters per second squared).The rate of change of velocity is defined as acceleration. Acceleration usually indicates that the speed is changing, but this is not always the case. When an object moves in a circular path at a constant speed, it is still accelerating because its velocity direction changes.Acceleration of car = (v - u)/t
Here given,
v = 0 m/s
u = 25 m/s
t = 9.00 s
By substituting values,
a = (0 m/s - 25.0 m/s) / 9.00 s
a = -2.77 ms⁻²
S = V² - u² / 2a
= ((0 ms⁻¹)² - (25.0 ms⁻¹)²) / 2 x -2.77 ms⁻²
= 112.8 m
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A 45 kg boy is riding a 15 kg bicycle with a speed of 8. 0 m/s. What is the combined kinetic energy of the boy and the
bicycle?
The combined kinetic energy of the boy and the bicycle is 1920 J.
Kinetic energy is the measure of the work that an object does by virtue of its motion. Simple activities like walking, jumping, throwing, and falling involve kinetic energy.To accelerate an object, we have to apply force. To apply force, we need to do work. When work is done on an object, energy is transferred, and the object moves with a new constant speed. We call the energy that is transferred kinetic energy, and it depends on the mass and speed achieved.The SI unit of kinetic energy is Joule.Kinetic energy is transferred between objects and can be transformed into other forms of energy. Yo-Yo is a great example to describe the transformation of kinetic energy.We know that kinetic energy of a body is given by K.E. : [tex]\frac{1}{2} mv^{2}[/tex]
Here m = combined mass = 45+15 kg = 60 kg
Given speed = v = 8 m/s
Putting these values in above equation we get K.E. = 1920 J
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what is the strength of the electric field 4.0 cm from a small glass bead that has been charged to 5.0 nc ?
The strength of the electric field 4.0 cm from a small glass bead that has been charged to 5.0 nc will be 7.912 x 106 N/C.
The strength of an electric field 4.0 cm from a small glass bead that has been charged to 5.0 nC can be calculated using Coulomb's law.
According to this law, the electric field, E, is equal to the charge, Q, divided by the permittivity of free space, ε, multiplied by the distance between the charge and the point in space, r, squared.
Therefore, the electric field at a distance of 4.0 cm from the bead is equal to:
E = (5.0 nC) / (8.854 x 10-12 [tex]C^{2}/ nm^{2}[/tex]) x (0.04 m)
E = 7.912 x 106 N/C
This means that the electric field at a distance of 4.0 cm from the glass bead charged to 5.0 nC is 7.912 x 106 N/C.
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The distance an object falls (when released from rest, under the influence of Earth's gravity, and with no air resistance) is given by d(t)16t, where d is measured in feet and t is measured in seconds. A rock climber sits on a ledge on a vertical wall and carefully observes the time it takes for a small stone to fall from the ledge to the ground. A. Compute. What units are associated with the derivative, and what does it measure? b. If it takes s for a stone to fall to the ground, how high is the ledge? How fast is the stone moving when it strikes the ground (in miles per hour)?
(A) Units for derivative is d(t) = 16t^2, (B) height of the ledge is 0 feet, and stone is moving with a speed of 46.667 x s mph.
A. The units associated with the derivative of d(t) = 16t^2 are feet per second, and it measures the velocity of the object at a certain point in time.
B. To find the height of the ledge, we need to find the value of t when the stone reaches the ground. We can set d(t) = 0 and solve for t:
16t^2 = 0
t^2 = 0
t = 0
Since t = 0, the stone was dropped from rest, so the height of the ledge is d(0) = 16(0)^2 = 0 feet.
To find the velocity of the stone when it strikes the ground, we can find the derivative of d(t) = 16t^2 at t=s.
d'(t) = 32t
d'(s) = 32s
Since the stone was falling in feet per second. To convert to miles per hour we need to multiply the value by 1.46667 (conversion factor)
d'(s) x 1.46667 = 32s x 1.46667 = 46.667s mph
So the stone is moving at 46.667 x s mph when it strikes the ground.
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