The dielectric constant of the wax is 4.
The energy stored in a capacitor is proportional to the square of the charge divided by the capacitance but doubling the plate spacing halves the capacitance. Capacitance is directly proportional to the electrostatic force field between the plates. This magnetic field gets stronger the closer the plates are to each other. Therefore, the capacitance increases as the distance between the plates decrease.
Therefore, we can conclude that doubling the area and distance between the plates of a parallel plate capacitor does not change the capacitance. A capacitor consists of two conductive plates separated by an insulator and is used to store an electrical charge. When you apply a voltage to a capacitor, one plate will be negatively charged and the other plate will be positively charged.
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in an emergency stop to avoid an accident, a shoulder strap seat belt holds a 60 kg passenger firmly in place. if the car were initially traveling at 90 km/h and came to a stop in 5.5 s along a straight, level road, what was the average force applied to the passenger by the seat belt?
Answer:
272.727N
Explanation:
Force is equal to the product of mass and acceleration. We know the mass of the person (60kg), so we just need to find how much they are decelerating when coming to a stop.
We do this using the motion equation v=u+at, where v is the final velocity, u is initial velocity, a is acceleration, and t is time. Noting 90km/hr=25m/s, we get:
0=25+5.5a
a=-4.5454545m/s^2
Force = mass * acceleration = 60 * 4.545 = 272.727N
a hot air balloon is rising vertically with a velocity of 10.0 feet per second. a very small ball is released from the hot air balloon at the instant when it is 1280 feet above the ground. use a(t)
the final velocity of the hot air balloon before touching the ground is 286.16 ft/s.
the final velocity can be calculated as follows:
initial velocity of the sphere, u = 10 ft/s
Acceleration due to gravity, g = 32 ft/s²
Ground clearance, h = 1280 feet
The time it takes for the ball to hit the ground is calculated as:
[tex]h= ut +\frac{1}{2}gt^2\\ 1280= 10t + (0.5X 32 )t^2\\1280 = 10t +16t^2\\16t^2+ 10t-960 = 0[/tex]
then we can solve the quadratic equation using formula method
[tex]t=\frac{ -b+/- \sqrt{b^2-4ac} }{2a} \\t = \frac{ -10+/- \sqrt{10^2-4(16X1280)} }{2(16)}\\t= 8.63[/tex]
The final velocity of a hot air balloon is calculated as:
v = u + gt
v = 10 + (8.63 × 32)
v = 286.16 ft/sec
therefore, the final velocity of the hot air balloon before touching the ground is 286.16 ft/s.
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What is the potential energy of a 25 kg bicycle resting at the top of a hill 3 m high? (Formula: PE = mgh)
The potential energy of a 25 kg bicycle resting at the top of a hill 3 m high will be 735 J
potential energy = m*g*h
where
m = mass
g = acceleration due to gravity
h = height
potential energy = 25 * 9.8 * 3 = 735 J
The potential energy of a 25 kg bicycle resting at the top of a hill 3 m high will be 735 J
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how much energy must be transferred into 2kg of iron to raise its temperature by 5C?
Answer:
Explanation:
Around 500 volt energy
starting from rest, a disk rotates about its central axis with constant angular acceleration. in 5.0 s, it rotates 25 rad. during that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity?
a) The angular acceleration of a disk is 2.0 rad/s².
b) The average angular velocity of the disk is 5 rad/s.
What is angular acceleration?The temporal rate at which angular velocity changes is known as angular acceleration. The standard unit of measurement is radians per second per second.
Rotational acceleration is another name for angular acceleration. It is a numerical representation of the variation in angular velocity over time.
A pseudoscalar, angular acceleration, exists. If the angular speed rises counterclockwise, the sign of angular acceleration is taken to be positive; if it grows clockwise, it is taken to be negative. Angular acceleration is used to study the motion of rotating objects like the wheel, fan, and earth.
Assume that the sense of rotation is positive.
This means that w, α, and other quantities will then be positive also.
a) we know,
25 rad = 1/2 α 5²
α = 2.0 rad/s²
∴ the angular acceleration of a disk is 2.0 rad/s².
b) w avg = Δθ/Δt
w avg = 25rad/5s
w avg = 5rad/s
∴ the average angular velocity of the disk is 5 rad/s.
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when astronomers have examined rich clusters of galaxies with their instruments, they have found that these clusters
Astronomers have examined rich clusters of galaxies with their instruments, They have found that these clusters have giant elliptical galaxies than poor clusters
what are giant elliptical galaxies?Elliptical galaxies are the most abundant type of galaxies found in the universe but because of their age and dim qualities, they're frequently outshone by younger, brighter collections of stars.
Elliptical galaxies lack the swirling arms of their more well-known siblings, spiral galaxies. Instead, they bear the rounded shape of an ellipse, a stretched-out circle.
One of the most famous elliptical galaxies is Cygnus A, which is located roughly 600 million light-years from Earth and is an extremely bright radio source. Cygnus A is not only well-known to astronomers, but has a place in science fiction; it was featured in the 1985 novel "Contact," a Carl Sagan story that later inspired a Hollywood movie of the same name.
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a car speeds up from 22 m/s to 26 m/s in 2 seconds. what is the average acceleration of the car
Answer:
2 m/s^2
Explanation:
Acceleration is change in velocity over change in time
(26-22) m/s / 2 s = 2 m/s^2
Gravity obeys an inverse square relation. This statement implies that the force due to gravity betweentwo massesa.will increase as the distance between the two masses increases.*b.will decrease as the square of the distance between the two masses increases.c.will cause the two masses to move away from each other.d.will cause the two masses to move in a straight line.e.will cause the two masses to orbit each other.
The inverse square relation implies that force resulting from gravity between two masses will decrease as the square of the distance between the two masses increases.
The force of gravity between any two objects is given by,
F = GM₁M₂/R²
Where,
M₁ and M₂ are the masses of the bodies.
R is the distance between them.
We know, if the masses are constant. then the force of gravity will be inversely proportional to the square of the distance between them.
This is what inverse square relation means here.
As the force of gravity and the square of the distance are inversely proportional to each other,
So, when the square of the distance between the masses increases, the force of gravity between the decreases.
Hence of all the options provided, b is the correc0,t which says, the force will decrease on increasing the inverse square of the distance.
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3.-A 10 newton forces gives a mass m1 an acceleration a. A 20 newton force gives another mass m2 the same acceleration a. What is the ratio of m1 to m2?
Answer:
1/2
Explanation:
We know that F = ma, so F1 = m1.a1 and F2 = m2.a2.
F1 = 10
F2 = 20
To simplify things consider a1 = a2 = 1
To find m1 divide by a to both sides; m1 = F/a = 10/1 = 10.
To find m2 divide by a to both sides; 21 = F/a = 20/1 = 20.
Ratio of m1 to m2 = 10/20 = 1/2
when you measure gravity at any location on this equipotential surface you would get the same result?
There are an infinite number of points where the gravitational potential is always the same. They are called equipotential surfaces. Of course, mean sea level itself is not an equipotential surface.
Forces other than gravity, such as temperature, salinity, ocean currents, and wind, are at work. The size of the gradient vector field (which describes the steepness of the gradient) is not the same for all points on the contour. Therefore, the strength of gravity varies along the geoid, and the geoid is not, as one blogger put it, "the same shape of gravity wherever you stand."
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Which of acceleration, age, speed, temperature, and velocity are vector quantities?.
Speed, temperature, and age are not vector numbers, whereas velocity and acceleration are vector quantities.
Define vector quantity.Vector is quantity has both magnitude and direction. It is represented by an arrow whose length is proportional to the quantity's magnitude and whose direction is the same as the quantity.
While a vector lacks position, it does have magnitude and direction. Since they have a magnitude and a direction, velocity and acceleration are both vector quantities.
An object is accelerating if its speed doesn't change but its direction does. It's critical to keep in mind that acceleration and velocity don't necessarily follow the same path.
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a gyroscope flywheel of radius 2.83 cm is accelerated from rest at 14.2 rad/s2 until its angular speed is 2760 rev/min. (a) what is the tangential acceleration of a point on the rim of the flywheel during this spin-up process? (b) what is the radial acceleration of this point when the flywheel is spinning at full speed? (c) through what distance does a point on the rim move during the spin-up?
The tangential acceleration of the gyroscope flywheel is 40.186 x [tex]10^{-2[/tex] m/[tex]s^2[/tex], Radial acceleration of gyroscope flywheel is 2364.08 [tex]m/s^2[/tex] and During the spin up process the distance moved by a point on rim is 83.24 m.
What is meant by tangential acceleration?The centripetal force causes an acceleration known as radial acceleration, which is measured in radians per square second. Radial acceleration is directed toward the center.Tangential acceleration occurs when a body or object moves at a speed that is not uniform.a gyroscope flywheel of radius, R = 2.83 cm =2.83 x [tex]10^{-2}[/tex] m
[tex]\omega_0 = 0[/tex]
[tex]\omega = 2760 X \frac{2\pi}{60} rad/sec[/tex]
[tex]\alpha = 14.2 rad/ sec^2[/tex]
The tangential acceleration :
[tex]a_t = R\alpha[/tex] =2.83 x [tex]10^{-2}[/tex] m x 14.2 [tex]rad/s^2[/tex] =40.186 x [tex]10^{-2[/tex] m/[tex]s^2[/tex]
The radial Acceleration :
[tex]a_r = R\omega^2\\=(2.83 X 10^-2) (2760 X \frac{\pi}{30} )^2[/tex] =2364.08 [tex]m/s^2[/tex]
During the spin up process the distance moved by a point on rim
d = [tex]R\theta[/tex]
where [tex]\theta =\frac{ \omega^2 - \omega_0^{2}}{2\alpha}[/tex]
= [tex]\frac{(2760 X \pi/30)^2}{2 X 14.2}[/tex] =2941.42 rad
d = 2.83 x [tex]10^{-2}[/tex] x 2941.42 =83.24.m
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with the time base set to 500 ns/div, four cycles of a waveform occupies10 divisions. what is the period and the frequency of the waveform
The period of this waveform is 2 milliseconds and its frequency is 2 kilohertz.
The period of a waveform is the time it takes for one complete cycle. The frequency of a waveform is the number of times that cycle repeats per second.
The time base is set to 500 ns/div, which means that each division represents 500 nanoseconds. Four cycles of a waveform occupies 10 divisions, so we can calculate the frequency as follows:
1) 4 cycles = 4x500ns
= 2ms
2) 2ms = 2 x 1/2 ms
3) 1/2 ms = 1/2 x 1 ms
4) 1ms = 1000us
5) 1000us / 500 ns / div = 2000 Hz
In conclusion, the period of this waveform is 2 milliseconds and its frequency is 2 kilohertz.
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