When the outer wall moves at a speed of 3.0 m/s, and an 83-kg person feels a 545-N force pressing against his back then the radius of a chamber is 8.5 meters.
The radius of the chamber can be calculated using the equation
F = mv²/r, where F is the force felt by the person, m is the mass of the person, v is the velocity of the chamber and r is the radius of the chamber. In this case, F is 545 N, m is 83 kg, and v is 3.0 m/s.
Plugging in these values, we get
r= mv²/F
r= 83×3²/545
r = 8.5 m.
Therefore, the radius of the chamber is 8.5 m.
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jordan wants to see if earthworms prefer rough or smooth terrain to crawl through. What will be his independent variable
The independent variable in this investigation is the type of surface which is changing whereas, the dependent variable is the mobility of earth worm.
What is independent variable?In a experiment or investigation, there are two types of variables which are dependent and independent variable. Dependent variable are those which are dependent on other variables and are changing with respect to other variables.
Independent variables are those not dependent on any other variables and we can change the independent variable to study the change in dependent variable.
Here, the one we studying is the mobility of earth worm which is the dependent variable and the type of surface rough or smooth is the independent variable.
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A theme park is planning out a new free-fall ride. The drop is almost perfectly frictionless, with a distance of 190 meters. Assuming that the initial velocity was zero, what would be the speed at the bottom of the drop?
a-53 m/s
b-61 m/s
c-67 m/s
d-72 m/s
Answer:
Approximately [tex](-61)\; {\rm m\cdot s^{-2}}[/tex], assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].
Explanation:
Under the assumptions, the vehicle would be in a free fall. Acceleration would be constant: [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex].
Let [tex]u[/tex] denote the initial velocity of the vehicle. Let [tex]v[/tex] denote the velocity of the vehicle at the bottom of the drop. Let [tex]x[/tex] denote the displacement of the vehicle during the drop.
It is given that the initial velocity is [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex]. During the drop, displacement would be [tex]x = (-190)\; {\rm m}[/tex] (negative since the vehicle is below where it started.) The value of final velocity [tex]v[/tex] needs to be found.
It is known that the vehicle is moving downwards at the end of the fall. Therefore, the value of [tex]v\![/tex] would be negative. Apply the SUVAT equation [tex]v^{2} - u^{2} = 2\, a\, x[/tex] to find [tex]v[/tex] from [tex]u[/tex], [tex]a[/tex], and [tex]x[/tex].
[tex]\begin{aligned}v^{2} &= u^{2} + 2\, a\, x\end{aligned}[/tex].
[tex]\begin{aligned}v &= -\sqrt{u^{2} + 2\, a\, x} \\ &= -\sqrt{(0\; {\rm m\cdot s^{-1}})^{2} + 2\, (-9.81\; {\rm m\cdot s^{-2}})\, (-190\; {\rm m})} \\ &\approx (-61)\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
(Note that [tex]v[/tex] is negative.)
In other words, the velocity of the vehicle would be approximately [tex](-61)\; {\rm m\cdot s^{-1}}[/tex] at the end of the drop.
A classroom has a volume of
165 m^3. How many moles of gas
are in the room if the temperature
is 20. 0°C and the pressure is
1. 00 atm?
(Make sure to put P, V, and I
in the right units. )
(Unit = mol)
The number of moles in the room which has a volume of 165 m³ is 0.0686 moles
The volume of the classroom = 165 m³
The temperature of the room = 20°C
= 293 K
The pressure = 1 atm
The number of moles in the room can be found using the formula,
PV = nRT
where P is the pressure
V is the volume
n is the number of moles
R is the gas constant
T is the temperature
Let us rearrange the above equation, we get
n = PV/RT
Let us substitute the known values in the above equation, we get
n = 1 x 165 / 8.21 x 293
= 165 / 2405.53
= 0.0686 moles
Therefore, the number of moles in the room is 0.0686 moles
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Suppose that the railcar passes by a horn that is emitting a sound with frequency f. Which of the following describes the frequency f PS-10-1-prime.gif that the person on the railcar hears?
A. f PS-10-1-prime.gif > f before passing the horn, f PS-10-1-prime.gif < f after passing it
B. f PS-10-1-prime.gif < f before passing the horn, f PS-10-1-prime.gif > f after passing it
C. f PS-10-1-prime.gif = f before passing the horn, f PS-10-1-prime.gif = f after passing it
D. f PS-10-1-prime.gif > f before passing the horn, f PS-10-1-prime.gif > f after passing it
F PS-10-1-prime.gif > f before passing the horn, f PS-10-1-prime.gif < f after passing it describes the frequency f PS-10-1-prime.
Hence, Option A is correct.
The Doppler effect causes the frequency heard by the railcar passenger prior to passing the horn to be higher than the real frequency of the sound released, whilst the frequency heard after passing the horn is lower than the actual frequency. This is why the answer to this question is A. A railcar is a self-propelled passenger-carrying railroad vehicle. A train with a single coach and a driver's cab at one or both ends is typically referred to as a "railcar." Such vehicles are referred to as "railmotors" by several railway companies, including the Great Western.To know more about railcars here
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Suppose a molecule has neutrons, a Coulomb total electric charge, and electrons. About how many protons must it have
molecule possesses neutrons and a total electric charge of one Coulomb. e is the electronic value, 1.60 x 10-19 Coulombs, and the proton has a cost of +e while the electron has a fee of -e.
How much is one coulomb?The quantity of charge carried by a present of one amp for one second is measured in coulombs, which is the unit of measurement used in the SI for electric charge. It may also be a quality of a substance that causes magnetic and electric effects to occur. The symbol for it is C. According to math, 1 Coulomb equals 1 Ampere x 1/sec.
A coulomb quizlet: what is it?A coulomb is an unit of power charge that represents the charge that is transmitted over one ampere of current in one second. Colomb's rule. depending on the charged items, electric force.
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Written problem: I find that I can blow 1000 cm3 of air through a drinking straw in 1.3 s. The diameter of the straw is 5 mm. Find the velocity of the air through the straw.
Answer:
Below
Explanation:
Diameter of straw = .5 cm then the radius = .25 cm
AREA of the straw = pi r^2 = pi ( .25 cm)^2 = .19635 cm^2
Now we need to find the LENGTH necessary to have a volume of 1000 cm^3
1000 cm^3 = L * . 19635 cm^2
L = 5.092.958 cm <=== your blowing covers this distance in 1.3 s
5092.958 cm / 1.3 s = 3917.7 cm / s = 39.2 m/s
Three point charges are arranged at the corners of a square of side L as shown in (Figure 1) What is the potential at the fourth corner (point A)? Express your answer in terms of the variables Q, L, and the Coulomb’s constant k.
The potential at the fourth point will be [tex]\frac{k^3Q}{\sqrt{L}}[/tex]
Let q1= -2Q and q2 = 6Q. ( k.)
What does charge number three's value, q3, equal?
To remedy the issue, the charges' orientation is also necessary.
You might try using the formula (kQ/r) to get the potential at the fourth corner.
Electric potential is a scalor, therefore adding the values from the three sites is as simple as adding them all together.
The effort required to transfer a unit charge against an electric field from a reference point to a specified spot. Earth is typically chosen as the reference point, however, any location beyond the range of the electric field charge can be utilized. potential electricity.
for instance, q1=-Q, L from the 4th point
q2=3Q and the fourth point's root is L.
The solution to q3= Q L from the fourth point is just [tex]-\frac{kQ}{L} + \frac{k^3Q}{\sqrt{L}} +\frac{kQ}{L} = \frac{k^3Q}{\sqrt{L}}[/tex] (at the fourth point)
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The missing diagram is attached below:
What is Dynamics flexibility?
The capacity to move joints and muscles throughout their complete range of motion while engaging in active activity is known as dynamic flexibility.
What is meant by dynamic flexibility?The absolute range of motion that a person can acquire through movement is referred to as dynamic flexibility. In other words, the greatest range of motion is the maximum distance that may be reached, bent, or turned. The terms "dynamic flexibility" and "ballistic flexibility" are interchangeable.
Static stretches are those in which you remain in a single position—standing, sitting, or lying still—for up to 45 seconds. Dynamic stretches are regulated motions that get your ligaments, muscles, and other soft tissues ready for action and safety.
Before a workout or any sort of exercise, dynamic stretching is an excellent approach to improve flexibility and engage key muscles.
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what is the equation linking current, potential difference and voltage
Put your finger over P to compute power; this leaves I and V; hence, P = I x V.
What connection exists between voltage and potential difference?The quantity of current multiplied by the resistance equals the potential difference, which is the same as voltage. One Coulomb of charge uses one Joule of energy to move between two locations in a circuit, which is equal to a potential difference of one Volt.
What is a potential difference?Difference that might exist at all between the two points The amount of work required to move a unit positive charge along any path through one point to another without accelerating is referred to as the electric field.
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Which of the following is a thermodynamic process in which a system returns to the same conditions under which it started?
A) a cyclic process
B) an adiabatic process
C) an isovolumetric process
D) an isothermal process
A cyclic process is a thermodynamic process where the initial and final states are identical. As a result, both the system's initial and end internal energies are constant. As a result, the system's capacity to absorb heat is determined by the work it performs during a cycle.
What is a Thermodynamic Process?A thermodynamic process is one that modifies the system's thermodynamic state. A transition from an initial to a final state of thermodynamic equilibrium characterizes a change in a system. The actual course of the process is not the main focus in classical thermodynamics and is frequently disregarded.
There are several different types of thermodynamic processes, such as (a) isothermal, in which the system's temperature stays constant; (b) adiabatic, in which no heat is exchanged; (c) isobaric, in which the system's pressure stays constant; and (d) isochoric, in which the system's volume stays constant.
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A spring with a cart at its end vibrates at frequency 5.0Hz\;Hz .
A. Determine the period of vibration.
B. Determine the frequency if the cart's mass is doubled while the spring constant remains unchanged.
C. Determine the frequency if the spring constant doubles while the cart's mass remains the same.
A. The period of vibration is the time it takes for one complete oscillation to occur. It is the reciprocal of the frequency. The period of vibration can be calculated using the formula:
Period = 1/Frequency
Given that the frequency of vibration is 5.0Hz, the period of vibration is:
Period = 1/5.0 s
Period = 0.2 s
B. If the cart's mass is doubled while the spring constant remains unchanged, the frequency of vibration will not change. This is because frequency is dependent on the spring constant and the mass of the cart and not on the amplitude of the oscillation.
C. If the spring constant doubles while the cart's mass remains the same, the frequency of vibration will also double. This is because frequency is directly proportional to the square root of the spring constant. Therefore, doubling the spring constant would lead to an increase in the frequency of vibration by a factor of square root of 2.
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An object has a density of 3.25 kg/m?. If it has a total volume of 12.65m?. What is the object's mass?
Answer:
The object's mass is 41.1125 kilograms.
Explanation:
We can use the general density equation to determine the mass.
Density Equation
[tex]p=\frac{m}{V}[/tex]
[tex]p[/tex] is the density
[tex]m[/tex] is the mass
[tex]V[/tex] is the volume
Lets solve for [tex]V[/tex].
Multiply both sides of the equation by [tex]V[/tex].
[tex]p*V=\frac{m}{V}*V[/tex]
Cancel out the common factor of [tex]V[/tex] on the right side.
[tex]pV=m\\m=pV[/tex]
Now we have an equation for mass.
We are given
[tex]p=3.25[/tex]
[tex]V=12.65[/tex]
Substituting our values into our equation gives us
[tex]m=3.25*12.65\\m=41.1125[/tex]
Notice the unit of the given density
[tex]kg/m[/tex]
Our answer will be in kilograms
a large platform is initially at rest on a smooth surface. A dog on the platform starts running toward the east. The mass of the dog is one-half the mass of the platform. When the dog moves toward the east with a speed of v0, the platform moves toward the ____ with a speed _____.
Platform moves towards to west with a speed of v0/2 when the dog moves towards to east at a speed of v0, in accordance with the rule of conservation of momentum.
What is the straightforward meaning of speed?The speed at which an object's location changes in any direction. The distance travelled to the time needed to travel that distance is known as speed. Since speed only has a magnitude and no direction, it is a scalar quantity.
Is speed affected by acceleration?Acceleration is the method of changing a speed with which an object moves. If a substance's velocity does not change, it is not accelerating. Acceleration is a vector quantity.
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A 2kg block is initially at rest on a horizontal frictionless table. A force of 15N is then exerted on the block at an angle of 37° below the horizontal. The change in kinetic energy after moving 3m is?
Answer:
Approximately [tex]36\; {\rm J}[/tex].
Explanation:
Under the assumption, there is no friction to hinder the motion of the block. As a result, the increase in the kinetic energy of the block would be equal to the external work done on the block.
Let [tex]F[/tex] denote this magnitude of this force, let [tex]s[/tex] denote the magnitude displacement, and let [tex]\theta[/tex] denote the angle between this force and displacement. To find the work that this force has done on the block, use the formula:
[tex]\begin{aligned}(\text{work}) &= F\, s\, \cos(\theta)\end{aligned}[/tex].
For example, since the block in this question is moving along a horizontal table, displacement of the block would be in the horizontal direction. It is given that the angle between this force and the horizontal direction is [tex]37^{\circ}[/tex]. Thus, the angle between the force and the displacement would be [tex]\theta = 37^{\circ}[/tex].
Magnitude of this force is [tex]F = 15\; {\rm N}[/tex], while magnitude of displacement is [tex]s = 3\; {\rm m}[/tex]. The work done on this block would be:
[tex]\begin{aligned}(\text{work}) &= F\, s\, \cos(\theta) \\ &= (15\; {\rm N})\, (3\; {\rm m})\, \cos(37^{\circ}) \\ &\approx 36\; {\rm N\cdot m} = 36\; {\rm J}\end{aligned}[/tex].
Hence, the kinetic energy of this block would increase by [tex]36\; {\rm J}[/tex].
In an 11v11 adult game, I see a defender challenge for the ball. The defender misses the ball and with their momentum they accidentally but careelessly trip the opponent. The ball rolls over the touchline. What is the restart
For the Direct free kick, the game restarted.
What does a soccer direct free kick entail?There are two different kinds of free kicks used in soccer: direct and indirect.The term "direct free kick" refers to a kick that can be used as a direct strike.Indirect free kicks require a second touch before the ball can be used as a shot at goal.
A direct penalty kick is what?If a player attacks an opponent in a way that the referee deems to be irresponsible, reckless, or employing excessive force, the referee will award a direct free kick.jumps, kicks, or makes an attempt to kick.
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A microscope slide of the letter "p" is placed on the microscope stage so that it is oriented right side up with respect to the student using the microscope. What will the letter resemble when she observes the letter through the microscope?
On the microscope slide, a specimen will appear upside-down and facing left while it is actually right-side up and facing right.
What is the orientation of a microscope?The orientation of the specimen image is reversed when viewed via a microscope compared to the orientation of the actual specimen. As a result, when viewed under a microscope, the specimen will appear to be upside-down and backwards.
Coarse Adjustment Knob: To concentrate the specimen, the coarse adjustment knob, which is placed on the microscope's arm, raises and lowers the stage. With just a partial turn of the adjustment knob, the gearing system creates a significant vertical movement of the stage.
Condenser-Objective lens-Body tube-Eyepiece is the proper order for the flow of light in a compound microscope.
Use two hands at all times when moving your microscope. Lift the scope while encircling the arm with one hand.
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A certain satellite orbiting Earth has a speed of about 17,000 miles/hour. What is its approximate speed expressed to the correct number of significant figures in kilometers/second
The speed of the satellite in terms of kilometers per second is 455.89 km/sec
The speed of the satellite = 17,000 miles/hour
The speed of the satellite can be converted into kilometers/second by converting the miles into kilometers and then the hour into seconds
1 miles = 1.609 km
Thus, the speed of the satellite,
= 17,000 x 1.609 km/hour
= 27,353 km/hr
Then, the speed of the satellite in one second is
1 hour = 60 seconds
Thus, the speed of the satellite,
= 27,353 x 1/60 km/sec
= 455.89 km/sec
Thus, the speed of the satellite is 455.89 km/sec
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Part A
Determine the electric field strength in the region r ≤a. Give your answer as a multiple of Q/E0. Express your answer in terms of some or all of the variables a, b, c, r, and the constant π.
The electric field in the region r ≤a is E [tex]= - \frac{r}{4\pi a^3} . \frac{Q}{e_0} r[/tex]
The total charge is enclosed within the Gaussian surface.
Q[tex]_{enc}[/tex] = 2Q - Q = Q
Therefore, applying Gauss's law over the Gaussian surface
∫[tex]_{s}[/tex]E.dS = Q[tex]_{enc}[/tex]/ε₀ ⇒ E.4πr² = Q/ε₀ ⇒ E = Q/4πε₀r²(r)
In question solution:
A[tex]_{sphere}[/tex] = 4πr²
ΦE = ∫E⋅dA
ΦE = q/ε₀
E = q/(A⋅ε₀)
E = q/(4πr²ε₀)
for r≤a, qin = -Q
E [tex]= - \frac{r}{4\pi a^3} . \frac{Q}{e_0} r[/tex]
So, the electric field in the region is E [tex]= - \frac{r}{4\pi a^3} . \frac{Q}{e_0} r[/tex]
Your question is incomplete but most probably your full question was:
A uniformly charged ball of radius a and charge −Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has a net charge of +2Q.
Part A: Determine the electric field strength in the region r ≤a. Give your answer as a multiple of Q/E0. Express your answer in terms of some or all of the variables a, b, c, r, and the constant π.
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A very powerful vacuum cleaner has a hose 2.27 cm in diameter. With no nozzle on the hose (no change to hose area), what is the weight of the heaviest brick it can lift
A very powerful vacuum cleaner has a hose 2.27 cm in diameter. The atmospheric pressure is 1.00 atm=101,300 Pa. then vacuume cleaner generate the force F = 65.1 N
What does diameter mean?A line that is straight and cuts through the middle of a body or figure. Particularly: the length of a diameter; a line segment passing through the center of a circle with its ends on the circumference.
Calculation -:Given,
diameter of the nose is d= 2.86 cm
radius of the nose r= 1.43 cm = 1.43× [tex]10^{-2}[/tex] m
We know F=P.A
where P is the atmospheric pressure and A is the surface area of the circulsr nose F is the force exerted by vacuume cleaner on the air
∴ F=P ( [tex]\pi r^{2}[/tex])
we know atmospheric pressure, p=1.013×[tex]10^{5}[/tex] pa
F = 1.013 × [tex]10^{5}[/tex] × 3.14 (1.43 × [tex]10^{-2}[/tex]) ^2
⇒ 65.1 N
⇒ F = 65.1 N
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Why is solar energy called renewable?
Solar energy is called renewable because it is abundant in nature and can be filled repeatedly.
Energy is power or strength that can be used for various activities. Energy cannot be created but can be changed from one form to another and can be transferred.
Solar energy is energy produced from the radiant heat of sunlight that can be utilized by all living things on earth, both humans, animals and plants. Solar energy can also be used as an alternative energy because it is environmentally friendly. This energy is included in renewable energy because the amount is abundant and endless even though it is used in large quantities.
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Why does torque increase with distance?
Torque increases with distance because torque is defined as the force acting on an object multiplied by the distance from the axis of rotation. The farther the force is applied from the axis of rotation, the greater the torque will be.
To understand this, imagine a lever with a weight on the end of it. If the weight is placed closer to the pivot point of the lever, it will take less force to lift the weight than if the weight is placed farther away from the pivot point. This is because the farther the weight is from the pivot point, the greater the torque will be. The same is true for any object that is being rotated around an axis - the farther the force is applied from the axis of rotation, the greater the torque will be.
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A grocery shopper tosses a(n) 9.0 kg bag of rice into a stationary 19.1 kg grocery cart. The bag hits the cart with a horizontal speed of 6.7 m/s toward the front of the cart. What is the final speed of the cart and bag
The speed with which the cart and bag move after the collision is equal to 2.14 m/s.
Given the following data:
Mass of bag = 9.0 kg
Speed of bag = 6.7 m/s
Mass of cart = 19.1 kg
Speed of cart = 0 m/s (since it is initially at rest or stationary).
To calculate the final speed with which the cart and bag move after the collision:
Applying the law of conservation of momentum, the collision between the cart and bag is given by the formula:
Where:
M is the mass.
V is the velocity.
Substituting the given parameters into the formula, we have;
9.0 × 6.7 + 19.1 × 0 = Vf (9+19.1)
60.3 = vf (28.1)
vf = 60.3/28.1
vf = 2.14 m / s
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What is a pivot arm lever?
The forearm serves as the lever arm, while the elbow serves as the pivot. In spite of the forearm's weight and whatever additional weight the hand may be bearing, the biceps muscle exerts the force and bends the forearm. Compared to the effort, the weight is further from the pivot.
A moving bar that pivots on a fulcrum fastened to a fixed point is the lever. The lever works by exerting forces at various angles in relation to the pivot or fulcrum. Ones farther from this pivot move more quickly than points closer to it when the lever revolves around the fulcrum.
A moving bar that pivots on a fulcrum fastened to a fixed point is the lever. The lever works by exerting forces at various angles in relation to the pivot or fulcrum. Ones farther from this pivot move more quickly than points closer to it when the lever revolves around the fulcrum.
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Assume that you have a mass of 50.0 kg. Earth has a
mass of 5.97 X1024 kg and a radius of 6.38X 10 m.
What is the force of gravitational attraction
between you and Earth?
The force of gravitational attraction is 489.18N
Gravitation is a study of how two masses interact, one of which is heavier and the other lighter, and force is the force that attracts all bodies towards itself in this universe. Gravitational force is a central force that is exerted along the line joining the q of two masses, and the direction of that force depends only on their position with respect to the source mass.Gravitational force: The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.[tex]F = \frac{Gm_{1} m_{2} }{r^{2} }[/tex]
Where,
F is the gravitational force between two bodies
m1 is the mass of the first body = 50 Kg
m2 is the mass of the second body = [tex]5.97 * 10^{24} Kg[/tex]
r is the distance between the centres of two bodies = [tex]6.38 * 10^{6} m[/tex]
G = gravitational constant = [tex]6.67 * 10^{-11}[/tex]
Putting these values in above equation we get: F = 489.18N
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The __________ technique lets you turn the steering wheel as much as a half turn while still keeping both hands on the wheel.
The hand over hand technique lets you turn the steering wheel as much as a half turn while still keeping both hands on the wheel.
Turn the vehicle by lowering the steering wheel in the desired direction (for left turns, pull with your left hand, and vice versa). Relax your other hand and lower the driving wheel. Bring it down to meet your "pulling" hand above your but-tocks, along the wheel. When they come together, let go of the "pulling" hand and let the other to take con-trol.
It is not a good idea to turn off the ignition while the vehicle is in mo-tion, therefore Even though the car has a steering wheel lock, it is not a good idea to switch it off while it is going since it can cause the car to lose con-trol, which can cause problems and accidents.
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Mercury thermometer is not suitable to measure the temperature of very cold place. Why?
The use of a mercury thermometer is not suitable for the purpose of determining the temperature of extremely cold ice because at such low temperatures, mercury transforms into a translucent state, making it impossible to read.
Another reasons why mercury thermometer is not suitable to measure the temperature of the very cold place are:
Since mercury freezes at a temperature of -38.83 degrees Celsius, a mercury thermometer will not work in extremely cold temperatures. We are unable to use a thermometer that contains mercury at low temperatures because the glass could shatter at those temperatures.The body whose temperature we are measuring with the thermometer does not radiate heat in the opposite direction.When exposed to low temperatures, mercury takes on a transparent appearance, making it more challenging to obtain accurate readings.To learn more about mercury thermometer, click here:
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An object is dropped from a height of 8 m. At what height will its kinetic energy and its potential energy be equal
At the peak it has the same potential and kinetic energy.
How is kinetic energy calculated?Kinetic energy (K.E.) is inversely proportional to the square of an object's velocity and its mass: K.E. = 1/2 m v2. When a mass is measured in kilograms and a speed is measured in meters per second, the kinetic energy is measured in kilogram-meters squared per second squared.
Kinetic energy and potential energy are equivalent at what height?The velocity will be zero and the ball's displacement will be at its maximum at the highest point of the trajectory. We might state that the energy present is equivalent to the sum of the potential energy.
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A 2.6-mm-diameter sphere is charged to -4.4 nC. An electron fired directly at the sphere from far away comes to within 0.32 mm of the surface of the target before being reflected.
a. What was the electron's initial speed?
b. At what distance from the surface of the sphere is the electron's speed half of its initial value?
c. What is the acceleration of the electron at its turning point?
The correct answer to the given question is -6.944 * 10^-28 Joules
a. To find the electron's initial speed, we can use the conservation of energy. The initial kinetic energy of the electron must equal the final potential energy of the electron at its closest approach to the sphere.
Ki = 1/2 * me * v^2
v = sqrt(2Ki/me)
Ki = qe * V = (1.6 x 10^-19 C) * (-4.4 x 10^-9 C) = -6.944 x 10^-28 J
b. At the point where the speed of the electron is half of its initial value, the kinetic energy of the electron is half of its initial value. Therefore,
Ki/2 = 1/2 * me * (v/2)^2
we can solve for the distance from the surface of the sphere using the same equation as in part a, and substituting Ki/2 and v/2 for Ki and v respectively
c. The acceleration of the electron at its turning point can be found using the equation for centripetal acceleration:
a = v^2/r
where a is the acceleration, v is the speed of the electron, and r is the distance of the electron from the center of the sphere at its closest approach. We can use the value of v from part a and the distance from part b to find the acceleration.
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A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with vertical, what must this angle be if the tension in each wire is equal to 0.75 of the weight of the frame?
(Neglect any friction betweem the wall and the picture fame)
The angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰.
By using the parallelogram law of vector addition, it is possible to calculate the angle between the two wires.
a² + b² - 2abcosθ = R²
Where;
R = is the outcome vector = the frame's weight ⇒ W
Angle between the two wires equals 0.75W for the first wire's tension and 0.75W for the second wire's tension.
(0.75W)² + (0.75W)² - 2(0.75W x 0.75W) cosθ = W²
1.125W² - 1.125W² cosθ = W²
= 1.125W²(1 - cosθ)
W²/1.125W² = 1 - cosθ
0.8889 = 1 - cosθ
cosθ = 1 - 0.8889
cos θ = 0.1111
θ = arc cos(0.1111)
θ = 83.6⁰
So, the angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰
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the electrical potential due to a dipole on its axis at a point p at a large distance x from the dipole is given by v
The electrical potential due to a dipole at a point P on its axis at a large distance x from the dipole is given by the formula: V = (p * x) / (4 * pi * epsilon_0 * x^2)
Where:
p is the dipole moment, a vector quantity that represents the magnitude and direction of the dipole. It is defined as the product of the magnitude of one of the charges (q) and the distance between the charges (d), p = q*d.x is the distance from the dipole to point P, it is a scalar quantity.epsilon_0 is the electric constant or vacuum permittivity, it is a scalar quantity that relates the electric flux density to the electric field strength. Its value is approximately 8.85 x 10^-12 C^2/Nm^2.The equation assumes that point P is located on the axis of the dipole (the line connecting the two charges) and that the distance x is much larger than the size of the dipole. This means that the dipole can be considered as a point source of electric potential and the field at point P is well approximated by the field of a point charge.It's important to note that the formula gives the potential at point P due to the dipole, however, the dipole itself also has an electric field which can be found by taking the gradient of the potential.Learn more about the electrical potential here:
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