Answer:
5.95 m
Explanation:
Given that the biggest loop is 40.0 m high. Suppose the speed at the top is 10.8 m/s and the corresponding centripetal acceleration is 2g
For the car to stick to the loop without falling down, at the top of the ride, the centripetal force must be equal to the weight of the car. That is,
(MV^2) / r = mg
V^2/ r = centripetal acceleration which is equal to 2g
2 × 9.8 = 10.8^2 / r
r = 116.64 /19.6
r = 5.95 m
State and explain Gauss's law in
electrostatics and use it to determine the electric field
intensity due to a line charge.
To find:-
To find the electric field due to a point charge using Gauss's Law .Answer:-
Gauss's law in electrostatics states that the electric flux through a closed surface is equal to 1/ε0 times the charge enclosed by that surface, that is,
[tex]\implies \displaystyle \phi_E = \oint \vec{E} .\vec{ds} \\[/tex]
Also ,
[tex]\implies\displaystyle \oint \vec{E}.\vec{ds} =\dfrac{q}{\epsilon_0} \\[/tex]
Linear density of charge:-
It ise defined as charge per unit length. Mathematically,
[tex]\implies\displaystyle \lambda =\dfrac{q}{\ell} \\[/tex]
where ,
[tex] q[/tex] is the charge .[tex]\ell[/tex] is the length of the conductor.For figure see attachment.
Now let us assume that the linear density of charge is [tex]\lambda[/tex] . There is a point P near the wire at a distance of " r " from it , where we are interested in calculating the electrical field. Imagine a coaxial Gaussian cylinder of length [tex]\ell[/tex] , and radius " r " such that the point P lines on its surface.
Calculating Electrical flux through the cylinder:-
[tex]\implies\displaystyle \phi_E = 0 + 0 + \oint E.ds \\[/tex]
[tex]\implies\displaystyle\phi_E = \oint E.ds \ \cos0^o \\[/tex]
[tex]\implies\displaystyle \phi_E = \oint Eds \\[/tex]
[tex]\implies\displaystyle \phi_E = E\oint ds \\[/tex]
[tex]\implies\displaystyle \phi_E = E (2\pi r\ell) \ \ dots (1) \\[/tex]
From Gauss's law:-
[tex]\implies\displaystyle \phi_E =\dfrac{q}{\epsilon_0} \\[/tex]
[tex]\implies\displaystyle \phi_E = \dfrac{\lambda \ell}{\epsilon_0}\ \dots (2) \\[/tex]
Therefore , from equation (1) and (2) , we have;
[tex]\implies\displaystyle E \times 2\pi r \ell =\dfrac{\lambda\ell}{\epsilon_0}\\[/tex]
[tex]\implies\displaystyle \underline{\underline{\green{ E =\dfrac{1}{4\pi \epsilon_0}\dfrac{2\lambda}{r}}}}\\[/tex]
And we are done!
What happens to the acceleration of a ball if the force increases while the mass remains the same?
Answer:
if the force increases while the mass of the ball remains the same, the acceleration increases.
Explanation:
According to Newton's second law of motion, the acceleration of an object produced by a net force is directly proportional to the magnitude of the net force Fn and inversely proportional to the mass of the object m.
[tex]\displaystyle a=\frac{Fn}{m}[/tex]
Suppose the net force doubles to 2Fn. The new acceleration will be:
[tex]\displaystyle a'=\frac{2Fn}{m}=2\frac{Fn}{m}=2a[/tex]
The acceleration doubles too. Thus, if the force increases while the mass of the ball remains the same, the acceleration increases.
which can occur in a physical change
Answer:
A physical change involves a change in physical properties. Examples of physical properties include melting, transition to a gas, change of strength, change of durability, changes to crystal form, textural change, shape, size, color, volume and density.
Explanation:
15. An astronaut on the moon has a 110 kg crate and a 230 kg crate. How do the forces required to liftyihe crates straight up on the moon compare with the forces required to lift them on Earth?
Explanation:
Mass of carte 1 is 110 kg and that of crate 2 is 230 kg
Force required to lift crates is equal to its crate i.e. W = mg
On Moon, a = 1.625 m/s²
Weight of crate 1, W = 110 kg × 1.625 m/s² = 178.75 N
Weight of crate 2, W = 230 kg × 1.625 m/s² = 373.75 N
On Earth, g = 9.8 m/s²
Weight of crate 1, W = 110 kg × 9.8 m/s² = 1078 N
Weight of crate 2, W = 230 kg × 9.8 m/s² = 2254 N
Hence, this is the required solution.
The forces required to lift the crates straight up on the Moon is lesser than the forces required to lift them on Earth.
Given the following data:
Mass A = 110 kgMass B = 230 kgScientific data:
Acceleration due to gravity on Earth = 9.8 [tex]m/s^2[/tex]Acceleration due to gravity on Moon = 1.6 [tex]m/s^2[/tex]The formula for weight.Mathematically, the weight of an object is given by the formula;
[tex]Weight = mg[/tex]
Where;
m is the mass of the object.g is the acceleration due to gravity.For the weight on Moon:[tex]Weight \;A= 110 \times 1.6[/tex]
Weight A = 176 Newton.
[tex]Weight \;B=230 \times 1.6[/tex]
Weight B = 368 Newton.
For the weight on Earth:[tex]Weight \;A= 110 \times 9.8[/tex]
Weight A = 1,078 Newton.
[tex]Weight \;B=230 \times 9.8[/tex]
Weight B = 2,254 Newton.
In conclusion, the forces required to lift the crates straight up on the Moon is lesser than the forces required to lift them on Earth.
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You move 6 meters east and move 8 meters south what’s the distance and displacement
The distance travelled in total is 14 m. But the resultant displacement is the square root of the sum of squares of each distances covered in different directions, that is 10 m.
What is displacement ?Displacement is a physical quantity that, that measures how far we travelled from a mean position. The change in position is dependent on the magnitude and direction as well. Hence, displacement is a vector quantity.
The distance covered by an object is total length or sum magnitudes of the length it covered. It is a scalar quantity. Here, the distance covered is 6 + 8 = 14 m.
The resultant displacement here, is calculated as follows:
ds = √(6² + 8²) = √100 = 10 m
Therefore, the displacement of us will be 10 m.
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Why does a sound come out when you blow into a bottle?
When does the jet of air convert to vibrations?
Which of the following is the primary force that shapes the Earth's landscape?
Which undergoes greater acceleration: an airplane that goes from 1000 km/h to 1005 km/h in 10 seconds or a skateboard that
goes from zero to 5 km/h in 1 second?
Answer:
Skateboard
Explanation:
Acceleration is change in velocity over time.
a = Δv / Δt
The airplane's acceleration is:
a = (1005 km/h − 1000 km/h) / 10 s
a = 0.5 km/h/s
The skateboard's acceleration is:
a = (5 km/h − 0 km/h) / 1 s
a = 5 km/h/s
A father fashions a swing for his kids out of a long rope that he fastens to the limb of a tall tree. As one of the kids swings from this rope that is 7.00 m long his tangential speed at the bottom of the swing is 8.65 m/s. What is his angular speed in rad/s
Answer:
1.236 rad/s
Explanation:
From the question above,
v = ωr................ Equation 1
Where v = tangental speed, ω = angular speed, r = radius = length of the rope.
Make ω the subject of the equation
ω = v/r.............. Equation 2
Given: v = 8.65 m/s, r = 7.00 m
Substitute these values into equation 2
ω = 8.65/7
ω = 1.236 rad/s
Hence the angular speed is 1.236 rad/s
In deriving the axial electric field for the ring-shaped charge distribution and the electric field from a long line of charge, the component perpendicular to the resulting field is zero because of what physical property? In deriving the axial electric field for the ring-shaped charge distribution and the electric field from a long line of charge, the component perpendicular to the resulting field is zero because of what physical property? positive and negative charges cancel symmetry only net charge is important superposition integration
Answer:
d)symmetry
Explanation:
Here is the complete question
In deriving the axial electric field for the ring-shaped charge distribution and the electric field from a long line of charge, the component perpendicular to the resulting field is zero because of what physical property? Answer a)integration b)superposition c)only net charge is important d)symmetry e) positive and negative charges cancel
Solution
The perpendicular components of the resulting electric field is zero because of symmetry since the charge is evenly distributed around the ring or line of charge. At one point, there is an electric field dE due to a small charge element dq and a corresponding electric field dE' due to a small charge element dq' opposite to dq.
Since the charges are symmetrical about the center, the horizontal (or perpendicular) components of the electric fields would cancel out causing the horizontal component of the resulting electric field to be zero.
So, the perpendicular component of the resulting electric field is zero due to symmetry.
A metric unit of volume equal to a milliliter
In the early 1900s, Robert Millikan used small charged droplets of oil, suspended in an electric field, to make the first quantitative measurements of the electron’s charge. A 0.71-um-diameter droplet of oil, having a charge of , is suspended in midair between two horizontal plates of a parallel-plate capacitor. The upward electric force on the droplet is exactly balanced by the downward force of gravity. The oil has a density of 860 kg/m^3 , and the capacitor plates are 4.5 mm apart.
Part A
What must the potential difference between the plates be to hold the droplet in equilibrium?
Express your answer to two significant figures and include the appropriate units
ΔV=
Answer:
The potential difference is [tex]\Delta V = 44.40 \ V [/tex]
Explanation:
From the question we are told that
The diameter of the droplet of oil is [tex]d = 0.71 \mu m = 0.71 *10^{-6} \ m[/tex]
The density of the oil is [tex]\rho = 860 kg/m^3[/tex]
The distance of separation of the capacitor plate is [tex]l = 4.5 \ mm = 0.0045 \ m[/tex]
Generally the radius of the droplet is mathematically represented as
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{0.71 *10^{-6} }{2}[/tex]
=> [tex]r = 3.55 *0^{-7} \ m[/tex]
Generally the mass of the oil droplet is mathematically represented as
[tex]m = \rho * V[/tex]
Here V is the volume of the oil droplet which is mathematically represented as
[tex]V = \frac{4}{3} * 3.142 * (3.55 *0^{-7} )^3[/tex]
[tex]V = 1.874 *10^{-19} \ m^3[/tex]
So
[tex]m = 860 * 1.874 *10^{-19} [/tex]
=> [tex]m = 1.611 *10^{-16} \ kg [/tex]
Generally the electric force acting on the droplet is mathematically represented as
[tex]F = E * q[/tex]
Here q is the charge on an electron with value [tex]q = 1.60*10^{-19}\ C[/tex]
This force is equivalent to the weight of the droplet which is mathematically represented as
[tex]W = mg[/tex]
So
[tex]E * q = m * g[/tex]
Here E is the electric field which is mathematically represented as
[tex]E = \frac{\Delta V}{l}[/tex]
[tex]\frac{\Delta V}{l} * q = m * g[/tex]
=> [tex]\Delta V = \frac{m * g * l }{q}[/tex]
=> [tex]\Delta V = \frac{1.611 *10^{-16} * 9.8 * 0.0045 }{1.60*10^{-19}}[/tex]
=> [tex]\Delta V = 44.40 \ V [/tex]
What is the equivalent temperature in kelvin if you have a metal at 50°F?
A.
50 K
B.
150 K
C.
283 K
D.
300 K
Answer:
The answer is C 283 kelvin
Answer: C.
283 K
Explanation: edmentum
Doctors were furious. Their patients didn't care about regular medicine anymore. All they wanted was a wave of Dr. Mesmer's wand. The doctors griped — and groused — and fussed — and fumed. What is most likely the meaning of the word furious?
A quietly curious B quite thrilled C mildly annoyed D extremely angry
Answer:
am pretty sure the answer is d
PLEASE HELP!!!! Which is the best example of a non-inertial frame of reference? (1 point)
A. a roller coaster maintaining its speed as it curves around a bend
B. a falling feather in which the upward force due to air resistance equals the force of gravity
C. a spaceship traveling at 947 m/s with its engines off
D. a boat at rest on calm water
Answer: B
Explanation:
A - No, because this has nothing to do with curves
B - Yes, because it explains gravity and it it forced down by gravity
C - No, because this has nothing to do with a rocket ship an dhow much it can travel per #.
D - No, because This has nothing to do with a boat on water and it explain nothing about gravity or how fast it is.
I Hope This Helped!
Answer:a roller coaster maintaining its speed as it curves around a bend
Explanation: gradpont
Phoebe wants to measure the volume of a small, irregularly
shaped rock. Which of the following instruments would be best
for Phoebe to use?
Answer:
A graduated cylinder
Explanation:
My bill at Office Depot came to $92.35 before my teacher discount. Once the clerk applies
my 15% teacher discount, how much will I have to pay?
$106.20
$13.85
$78.50
$92.35
Answer: $78.50 or C.
Explanation:
$92.35 x 15% or .15 is $78.50
A man is pulling a box with the force of 10N. There is nobody else on the other side of the box. What is the total amount of force on the box? *
A wind tunnel draws atmospheric air at 20°C and 101.3 kPa by a large fan located near the exit of the tunnel. If the air velocity in the tunnel is 80 m/s, determine the pressure in the tunnel.
Answer:
The pressure in the tunnel is 97.45 kPa
Explanation:
Given;
atmospheric pressure, P₁ = 101.3 kPa
air velocity in the tunnel, v₂ = 80 m/s
density of air at 20°C, ρ = 1.204 kg/m³
pressure in the tunnel, P₂ = ?
Apply Bernoulli's equation;
P₁ + ¹/₂ρv₁² + ρgz₁ = P₂ + ¹/₂ρv₂² + ρgz₂
v₁ = 0
z₁ = z₂ = 0
P₁ = P₂ + ¹/₂ρv₂²
P₂ = P₁ - ¹/₂ρv₂²
P₂ = 101.3 kPa - (0.5 x 1.204 x 80²)
P₂ = 101.3 kPa - 3.8528 kPa
P₂ = 97.45 kPa
Therefore, the pressure in the tunnel is 97.45 kPa
What was the instantaneous speed of Bear A at 5 seconds in meters/min? (No unit conversions necessary, no units required for answer. Type your answer.)
Answer: The answer is 40.
Explanation: There is a typo, they mean 5 minutes. Five minutes is the line between zero and 10, and the dot matches up at 5 and 200. 200 divided by 5= 40.
Two charged objects, A and B, are exerting an electric force on each other. What will happen if the charge on A is increased?
А. The charge on B will decrease.
В. The charge on B will increase.
C. The electric force between A and B will decrease.
D. The electric force between A and B will increase.
Answer: The forces acting on both of them will increase in magnitude.
Explanation:
According to Coulomb's law, the electrostatic force between two bodies is proportional to the product of their two charges. If the charge on A is increased this product increases in size (it must have been non-zero to begin with, since there was a force between them at first). Thus, the force between them rises.
Answer:
d. seems like the right answer.
Explanation:
A coil is wrapped with 206 turns of wire on the perimeter of a circular frame (of radius 31 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is directed perpendicular to the plane of the coil. This field changes at a constant rate from 23 mT to 54 mT in 24 ms. What is the magnitude of the induced average E in the coil, over the time interval 24 ms during which the field changes? Answer in units of V.
Answer:
E = -80.33 V
Explanation:
For this exercise we use Faraday's law of induction
E = - N d[tex]\phi _{B}[/tex] / dt
where the magnetic flux is
\phi _{B} = B A cos θ
In the exercise they indicate that the magnetic field is perpendicular to the coil, therefore the normal of the coil area and the field has the same direction, consequently the angle is zero. Since the area is constant
E = - N A dB / dt
let's look for each term
a =π r²
they tell us that the variation in the field is linear
dB / dT = (B_f-B₀) / t
we substitute
E = - N (π r²) (B_f -B₀) / t
let's calculate
E = - 206 π 0.31² (54 - 23) 10⁻³ / 24 10⁻³
E = -80.33 V
If you walk North for 40 feet and then walk East for 30 feet, what is your total distance
travelled? What is your displacement?
Answer:
The person travelled a total distance of (40+30) feet = 70 feet
Displacement= 50feet (im not positive on the displancement)
displacemeny is the shortest distance between two pionts
Explanation:
Which of the following graphs shows the motion of an object that starts to travel forward, stops for several seconds, then returns to its original position?
Answer:
Pls can you send the following graphs
how does a fly function in a energy pyramid
Answer:
A pyramid of energy shows the relative amount of energy available at each trophic level of a food chain or web. On average, about 10 percent of the energy available within one trophic level is transferred to the next level.
Explanation:
To a stationary observer, a man jogs east at 2 m/s and a woman jogs west at
3 m/s. From the woman's frame of reference, what is the man's velocity?
Answer:
5 m/s east
Explanation:
i just took the test and it was correct
Answer:
Just took the test. 5 m/s east.
Explanation:
If the length of an ax is 20 cm and the width is 5 cm what is the MA of a knife?
O 2
0 4
O 10
O6
Answer:
4
Explanation:
From the question given above, the following data were obtained from:
Length of an axe = 20 cm
Width = 5 cm
Mechanical advantage (MA) =.?
The mechanica advantage is simply defined as the ratio of the length to the width of the axe. Mathematically, it is expressed as:
Mechanical advantage = length /width
With the above formula, we can obtain the mechanical advantage of the axe as follow:
Length of an axe = 20 cm
Width = 5 cm
Mechanical advantage (MA) =.?
MA = 20/5
MA = 4
Therefore, the mechanical advantage (MA) of the axe is 4
please please please please please please
9514 1404 393
Answer:
Mona
Explanation:
Speed is the slope of the position vs. time curve. The higher speed will have the greater slope.
Mona's curve has a greater slope, so Mona is fastest.
A two-liter bottle of your favorite beverage has just been removed from the trunk of your car. The temperature of the beverage is 35°C, and you always drink your beverage at 10°C. (a) How much heat energy must be removed from your two liters of beverage (in kJ)? (b) You are having a party and need to cool 10 of these two-liter bottles in one-half hour. What rate of heat removal, in kW, is required? (c) Assuming that your refrigerator can accomplish this and that electricity costs 8.5 cents per kW-hr, how much will it cost to cool these 10 bottles (in $)?
Answer:
a) 209.3 kilojoules must be removed from two liter of beverage, b) A rate of heat removal of 1.163 kilowatts is required to cool down 10 2-liter bottles, c) Cooling 10 2-L bottles during 30 minutes costs 4.9 cents.
Explanation:
a) How much heat energy must be removed from your two liters of beverage?
At first we suppose that the beverage has the mass and specific heat of water and that there are no energy interactions between the bottle and its surroundings.
From the First Law of Thermodynamics and definition of sensible heat, we get that amount of removed heat ([tex]Q[/tex]), measured in kilojoules, is represented by the following formula:
[tex]Q = \rho \cdot V\cdot c\cdot (T_{o}-T_{f})[/tex] (Eq. 1)
Where:
[tex]\rho[/tex] - Density of the beverage, measured in kilograms per cubic meter.
[tex]V[/tex] - Volume of the bottle, measured in cubic meters.
[tex]c[/tex] - Specific heat of water, measured in kilojoules per kilogram-Celsius.
[tex]T_{o}[/tex], [tex]T_{f}[/tex] - Initial and final temperatures, measured in Celsius.
If we know that [tex]\rho = 1000\,\frac{kg}{m^{3}}[/tex], [tex]V = 2\times 10^{-3}\,m^{3}[/tex], [tex]c = 4.186\,\frac{kJ}{kg\cdot ^{\circ}C}[/tex], [tex]T_{o} = 35\,^{\circ}C[/tex] and [tex]T_{f} = 10\,^{\circ}C[/tex], then:
[tex]Q = \left(1000\,\frac{kg}{m^{3}}\right)\cdot (2\times 10^{-3}\,m^{3})\cdot \left(4.186\,\frac{kJ}{kg\cdot ^{\circ}C} \right) \cdot (35\,^{\circ}C-10\,^{\circ}C)[/tex]
[tex]Q = 209.3\,kJ[/tex]
209.3 kilojoules must be removed from two liter of beverage.
b) You are having a party and need to cool 10 of these two-liter bottles in one-half hour. What rate of heat removal, in kW, is required?
The total amount of heat that must be removed from 10 2-L bottles is:
[tex]Q_{T} = 10\cdot (209.3\,kJ)[/tex]
[tex]Q_{T} = 2093\,kJ[/tex]
If we suppose that bottles are cooled at constant rate, then, rate of heat removal is determined by this formula:
[tex]\dot Q = \frac{Q_{T}}{\Delta t}[/tex] (Eq. 2)
Where:
[tex]Q_{T}[/tex] - Total heat, measured in kilojoules.
[tex]\Delta t[/tex] - Time, measured in seconds.
[tex]\dot Q[/tex] - Rate of heat removal, measured in kilowatts.
If we know that [tex]Q_{T} = 2093\,kJ[/tex] and [tex]\Delta t = 1800\,s[/tex], we find that rate of heat removal is:
[tex]\dot Q = \frac{2093\,kJ}{1800\,s}[/tex]
[tex]\dot Q = 1.163\,kW[/tex]
A rate of heat removal of 1.163 kilowatts is required to cool down 10 2-liter bottles.
c) Assuming that your refrigerator can accomplish this and that electricity costs 8.5 cents per kW-hr, how much will it cost to cool these 10 bottles (in $)?
A kilowatt-hour equals 3600 kilojoules. The electricity cost is equal to the removal heat of 10 bottles ([tex]Q_{T}[/tex]), measured in kilojoules, and unit electricity cost ([tex]c[/tex]), measured in US dollars per kilowatt-hour. That is:
[tex]C = c\cdot Q_{T}[/tex]
If we know that [tex]c = 0.085\,\frac{USD}{kWh}[/tex] and [tex]Q_{T} = 2093\,kJ[/tex], the total cost of cooling 10 bottles is:
[tex]C = \left(0.085\,\frac{USD}{kWh}\right)\cdot \left(2093\,kJ\right)\cdot \left(\frac{1}{3600}\,\frac{kWh}{kJ} \right)[/tex]
[tex]C = 0.049\,USD[/tex]
Cooling 10 2-L bottles during 30 minutes costs 4.9 cents.
-Cesar the monkey observed the swinging behaviors of his parents. He is now able to swing from branch to branch after much practice. The observation of his parents swinging and practicing what he saw mainly involved _____ neurons; the neurons that are the basis of
Motor
Mirror
Sensory
Reticular
The observation of his parents swinging and practicing what he saw mainly involved sensory neurons.
There are five senses in the human body, they are;
SightSmellTouch TasteHearingInformation is passed to the central nervous system (CNS) from each of these senses.
The neurons that convey sensory information of sight, smell, touch, taste and hearing to the brain are called sensory neurons.
Thus, the observation of his parents swinging and practicing what he saw mainly involved sensory neurons.
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