The sphere has to be launched 4 times the initial height, h, to hit the same target.
What is the time of motion of the first sphere?The time taken for the first sphere to hit the target is calculated as follows;
d = V₀t₁
where;
V₀ is the initial horizontal velocityd is the horizontal distance travelled by the spheret is the time of motiont₁ = d/V₀
The height travelled by the ball;
h = ¹/₂gt₁²
t₁² = 2h/g
t₁ = √(2h/g)
The time of motion of the second sphere when it is launched at a speed of 2V₀.
t₂ = d/2V₀
t₂ = ¹/₂(d/V₀)
t₂ = ¹/₂(t₁)
The height of fall of the second sphere;
¹/₂(t₁) = √(2h/g)
[¹/₂(t₁)]² = 2h/g
t₁²/4 = 2h/g
t₁² = 4(2h/g)
Thus, the height the sphere need to be launched in order to hit the same target is determined by applying kinematic equation.
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Please help and explain will mark brainiest!!!
The particles or energy in a transverse wave travel up and down, perpendicular to the direction of the wave travel.
What is electromagnetic wave?
Electromagnetic waves are type of wave that do not require material medium for their propagation.
This type of waves travels in vacuum or in open medium.
Examples of electromagnetic waves include the follows;
Gamma raysx-raysultraviolet raysvisible lightinfra redmicro wavessound wavesElectromagnetic waves are known as transverse waves due to their mode of propagation.
In transverse wave, the particles of the medium travels perpendicular to their mode of vibration.
Thus, the particles or energy in a transverse wave travel up and down, perpendicular to the direction of the wave travel.
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Exciting the electrons in an iron increases the energy in the iron atom which can cause heating how might a magnetic field be used to excite electrons in atoms
Magnetic fields can be used to excite electrons in atoms because a magnetic field can pull or push electrons.
What is the effect of magnetic field on electron?Magnetic fields pull and push electrons which leads to the excitation of electrons. Metals have electrons that are loosely held together. Moving a magnet around a coil of wire around a magnet pushes the electrons in the wire that creates an electrical current. The magnetic force will not change the speed of an electron because the magnetic force is always perpendicular to the speed. Current in these coils causes the deflection of the electrons that is perpendicular to the magnetic field which is to the direction of the electrons.
So we can conclude that magnetic fields can pull or push electrons so that a magnetic field can be used to excite electrons.
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Two students, Jenny and Cho, are investigating motion.
Jenny walks in a straight line.
Cho measures the distance Jenny has walked at 10 s intervals.
State two measuring instruments the students should use.
Answer:
1: a measuring instruments the students should use for time is a stopwatch
2: a measuring instruments the students should use for distance is a measuring tape
Explanation:
pls mark brainliest
b. Which station broadcasts waves with a shorter wavelength
Answer:
blue and purple light
Explanation:
Light waves have very, very short wavelengths. Red light waves have wavelengths around 700 nanometers (nm), while blue and purple light have even shorter waves with wavelengths around 400 or 500 nm.
while riding a roller coaster, a girl drops an object. the roller coaster was rising vertically at a velocity of 11.0m/s and was 5.00m above the ground when the object was dropped. how long does it take to reach the ground
Answer:
Approximately [tex]0.388\; {\rm s}[/tex], assuming that air resistance is negligible and that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].
Explanation:
Initial vertical velocity of the object: [tex]u = 11.0\; {\rm m\cdot s^{-1}}[/tex], upwards (same as that of the rollercoaster.)
Initial height of the object: [tex]h_{0} = 5.00\; {\rm m}[/tex].
If air resistance is negligible, this object will accelerate downwards at a constant [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex]. Note that [tex]a[/tex] is negative since the object is accelerating downwards.
The SUVAT equation [tex]h = (1/2)\, a\, t^{2} + u\, t + h_{0}[/tex] gives the height [tex]h[/tex] of this object at time [tex]t[/tex]. Note that while the initial height is [tex]5.00\; {\rm m}[/tex], [tex]h = 0[/tex] when the object reaches the ground.
Since acceleration [tex]a[/tex], initial velocity [tex]u[/tex], and initial height [tex]h_{0}[/tex] are all given, setting [tex]h\![/tex] to [tex]0[/tex] and solving for [tex]t[/tex] will give the time it takes for this object to reach the ground:
[tex](1/2)\, a\, t^{2} + u\, t + h_{0} = 0[/tex].
[tex](1/2)\, (-9.81) \, t^{2} + 11.0\, t + 5.00 = 0[/tex].
[tex](-4.905)\, t^{2} + 11.0\, t + 5.00 = 0[/tex].
Solve this equation for [tex]t\![/tex] using the quadratic formula. Note that [tex]t > 0[/tex] since [tex]t[/tex] denotes the amount of time required for the object to reach the ground.
[tex]\begin{aligned} t &= \frac{-11.0 + \sqrt{11.0^{2} - 4 \times (-4.905) \times 5.00}}{2\times (-4.905)} \\ &\approx 0.388\; {\rm s}\end{aligned}[/tex].
The other root of this quadratic equation is negative and isn't a valid solution to the question.
In other words, it will take approximately [tex]0.388\; {\rm s}[/tex] for this object to reach the ground.
to measure the speed of an airplane, a narrow strip heater is attached to the wing of an airplane 0.01 m from the leading edge. a heat flux of 300 w/m2 is electrically dissipated and the temperature difference between the heater and the surrounding air is measured to be 1 oc. assume that the temperature of the wing is uniform. what is the speed of the aircraft?
The speed of the aircraft with a narrow strip heater attached = 370.97 m/s
The distance of the strip heater attached to the wing from the leading
edge, x = 0.01 m
Heat flux, q = 300 W/m²
The temperature difference between the heater and surrounding air,
ΔT = 1°C
The properties of the air are
The density of air, ρ = 1 kg/m³
Specific heat at constant pressure, CP = 1 kJ /kg K
Thermal conductivity, k = 0.02 W/mk
Viscosity, ν = 1.5 x 10⁻⁵ m²/s
Dynamic viscosity,
μ = ρ.ν
= 1 x 1.5 x 10⁻⁵
= 1.5 x 10⁻⁵ N s / m²
Prandtl number,
[tex]\displaystyle P_r =\frac{\mu. CP}{k}[/tex]
= 1.5 x 10⁻⁵ x 1 x 10³ / 0.02
= 0.75
Heat flux,
q = hₓ ΔT
300 = hₓ x 1
hₓ = 300 W / m² C
So, the local Nusselt number is
[tex]\displaystyle Nu_x = 0.332 Re_x^{1/2} P_r^{1/3}[/tex]
[tex]\displaystyle \frac{h_x.x}{K} = 0.332 \frac{v.x}{\nu}^{1/2}P_r^{1/3}[/tex]
where v is the velocity of the aircraft
[tex]\displaystyle\frac{300 * 0.01}{0.02} = 0.332 \left( \frac{v*0.01}{1.5 * 10^{-5}}\right)^{1/2} (0.75)^{1/3][/tex]
By further simplifying, we get
150 = 0.332 x 0.9085 x 25.82 x [tex]v^{1/2}[/tex]
v = 370.97 m/s
Therefore, the speed of the aircraft is 370.97 m/s
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The skater eventually comes to a stop.
What has happened to all of the skater's
original potential energy?
The potential energy of a roller coaster is 50 joules. The kinetic energy of the same coaster is 50 joules. What is the mechanical energy of the coaster?.
Mechanical energy of the coaster is 100 joules.
We need to know about mechanical energy to solve this problem. Mechanical energy is the sum of the potential energy and kinetic energy of an object. It can be written as
E = KE + PE
where E is mechanical energy, PE is potential energy and KE is kinetic energy.
From the question above, the given parameters are
KE = 50 J
PE = 50 J
By substituting the given parameters, we can calculate mechanical energy
E = KE + PE
E = 50 + 50
E = 100 J
The total energy is 100 joules
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Predict what will happen when the bicep muscle exerts force on the lower arm bone.
Answer:
the soft drink will be elevated by the lower arm
Explanation:
firstly, muscles can only pull on bones to cause movement so if the bicep applies force on the lower arm bone, it will pull it up.Find the acceleration of the 1kg block m the following diagram 5n 4n 5n
Explanation:
56777^7744 hold the 4 nd add 2
Just before Sarah started her laboratory work, she made a hot cup of tea. She left the tea on her desk while she worked because she never takes food or drink into the lab area. When she finished collecting data, Sarah's cup of tea was cool. What energy transfer caused her tea to cool?
The energy transfer between cup tea and surrounding caused her tea to cool according to newtons law of cooling.
The pace at which a body is exposed to radiation alters its temperature is roughly proportional to the temperature difference between the item and its surroundings, and the provided difference is small. The cooling law of Newton is this.
Heat is transported more quickly and a person's body temperature changes more quickly the higher the temperature difference between a system and its surroundings. When the temperature difference between the body and its surroundings is small, the rate of cooling of a body is directly related to the temperature difference and the surface area exposed.
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josh and taylor, standing face-to-face on frictionless ice, push off each other, causing each to slide backward. josh is much bigger than taylor. after the push, which of the two is moving faster?
After the push, Taylor will be moving faster because he has a smaller mass.
What is the force applied by each person?The force exerted by each person is determined by applying Newton's second law of motion.
F = ma
where;
m is the mass of the persona is the acceleration of the personThe force applied by each person depends on the mass and acceleration.
mass of Josh > mass of Taylor
Since Josh has a greater mass, he will be able impact more force on Taylor causing Taylor to move faster after the push.
Thus, the speed of each person after the push, depends on the force received by each person at the opposite end.
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a 21.6 gram arrow is shot through a 7.5 cm apple. if the arrow enters the apple at 35.5 m/s and emerges with a speed of 25.3 m/s in the same direction, what is the magnitude of the force with which the apple has resisted the arrow? (assume force is exerted only on the tip of the arrow)
The magnitude of the force with which the apple has resisted the arrow is 88.06 Newton.
Using, work-energy theorem,
According to which, the work done by the all the forces on the body is equal to the change in kinetic energy of the body.
So, we can write,
Work done = ∆KE
We know,
Work done = force × displacement
The force is the resistive force by the apple and the displayed is given to be 0.075 meters.
So, we can write,
F(0.075) = 1/2M(V²-U²)
Where,
M is the mass of apple,
V is final velocity,
U is initial velocity.
Putting all the values,
F(0.075) = 1/2(0.0213)((25.3)²-(35.5)²)
Solving further,
F = 88.06 Newton
The resistive force of the apple is 88.06 Newton.
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When inflating a balloon, which of the following represents an equal but opposite force acting on the balloon?
A.) releasing the balloon
B) the air entering the balloon
C) tying the balloon
D) the expansion of the balloon
When inflating a balloon, the expansion of the balloon represents an equal but opposite force acting on the balloon; option D.
What are equal and opposite forces?Forces are agents which cause a change in the motion of an object moving in a straight line or an object at rest to change its position.
According to the third law of motion, reaction and action are equal and opposite forces.
This law is seen in the inflation of balloons.
When a balloon is being inflated, the force applied in inflating the balloon pushes against the wall of the balloon. The balloon acts in an equal opposite direction by forcing the air molecules together, thus increasing the pressure of the air inside the balloon.
Therefore, an equal and opposite force is exerted by the air molecules o the air molecules.
When the balloon is released, the air is forcefully forced out in the opposite direction.
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Answer:
its D
Explanation:
the person above is correct too
Two objects with the same mass have the same force applied to them. What can be said of their acceleration?
A. Their acceleration will be the same.
B. Their acceleration will be different.
C. Their acceleration will depend on their net force, which is not provided.
D. Their acceleration will depend on their weight, which is not provided.
A force of 30 N to the right is applied to an object. An opposite force of 20 N to the left is applied to the same object. What is the net force applied to the object?
A. 10 N to the left
B. 50 N to the right
C. 50 N to the left
D. 10 N to the right
Answer:
Explanation:
A. Their acceleration will be the same. F=ma, a = F/m. If F and m are the same, acceleration will be the same.
B. Their acceleration will be different.
C. Their acceleration will depend on their net force, which is not provided.
D. Their acceleration will depend on their weight, which is not provided.
======
A force of 30 N to the right is applied to an object. An opposite force of 20 N to the left is applied to the same object. What is the net force applied to the object?
A. 10 N to the left
B. 50 N to the right
C. 50 N to the left
D. 10 N to the right
Add the two vectors: 30R = +30, 20L = -20 Sum = +10 or 10R
The force acting on two bodies will be the same if they have same mass and same acceleration. But the acceleration is dependant on the net force of the body and thus option C is correct. The net force of the body is 10 N to the right.
What is force?Force is an external agent or factor which change an object from its state of rest or motion. The force to be applied depends on the mass and acceleration of the body by the equation F = ma.
Acceleration of a moving body is dependant on the direction and thus the direction of force and net force. Thus the two objects having the same mass and same force f applied to them, the acceleration may not be the same. Thus option C is correct.
The two force acting on a body in opposite direction will cancel each other in magnitude. Thus 20N of force to the right will be cancel by 20 N to the left. Remaining 10N will be there to the right direction. Hence, option D is correct.
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the radius of a circular oil slick expands at a rate of 3 m/min. (a) how fast is the area of the oil slick increasing when the radius is 58 m? (use symbolic notation and fractions where needed.)
1092.72 square meters / min, area of the oil slick increasing.
Area = pi*r^2
da/dt = pi*2r*(dr/dt)
da/dt = pi*(2)*(58)*3 = 1092.72 square meters / min.
In a two-dimensional plane, a circle's area is the space it takes up. The area of a circle is another term for the area that lies within a circle's perimeter. A = r2, where r is the circle's radius, is the equation for a circle's surface area. The square unit, such as m2, cm2, in2, etc., is used to measure area. The formula for the area of a circle is (Pi) = 22/7 or 3.14, where (Pi) = r2 or d2/4 in square units. The ratio of a circle's diameter to circumference is known as pi.
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a window-mounted air conditioner removes 3.5 kj from the inside of a home using 1.75 kj work input. how much energy is released outside and what is its coefficient of performance?
The amount of heat released outside is 3.5 kJ and the coefficient of performance is 2.
What is efficiency of a machine?The efficiency of the a machine or any device is the measure of effectiveness of the device. Efficiency describes how a machine converts input energy to output energy without wasting much of the input energy.
Mathematically, efficiency of a machine is given as;
E = output energy / input energy x 100%
The coefficient of performance (COP) of a heat pump, refrigerator or air conditioning system is a ratio of useful heating or cooling provided to work required.
The energy released outside = 3.5 kJ
COP = 3.5 kJ / 1.75 kJ
COP = 2
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An engineer is troubleshooting trying to figure out the value of a capacitor. She knows that the charge value is 480 coulombs and the power supply feeds 110 V. What's the capacitor value?Question 19 options:A) 128B) 4.36C) 0.88D) 5,400
We can use the formula of the capacitance
[tex]C=\frac{Q}{V}[/tex]where C is the capacitance, Q is the charge and V is the voltage.
In our case
Q=480 C
V= 110 V
[tex]C=\frac{480}{110}=4.36\text{ F}[/tex]The value of the capacitor is 4.36 F
ANSWER B) 4.36F
9. a supply plane needs to drop a package of food to scientists working on a glacier inalaska. the plane flies 100 m above the glacier at a speed of 150 m/s. how far short of the target should it drop the package?
[tex]X=150m/s * 4.518s =677.63m[/tex] far short of the target it will drop the package.
How far short of the target should it drop the package?First we can find the total time in order to reach the ground using the following kinematic formula:
[tex]y_{f} =y_{i}+v_{iy}+ \frac{1}{2} gt^{2}[/tex]
And replacing we have:
[tex]-100 =0+0- \frac{1}{2} (9.8)t^{2}[/tex]
And solving for t we got:
[tex]t=\sqrt{ \frac{2* (-100)}{-9.8} }=4.518 s[/tex]
And now we can find the final distance on the x axis using the formula:
[tex]D = Vxt[/tex]
The velocity on x not changes and is the same plane speed [tex]Vx=150m/s[/tex] , if we replace we got:
[tex]X=150m/s * 4.518s =677.63m[/tex]
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Efficiency of Machines Quick Check
Which is the equation for a machine's efficiency? (1 point)
O Efficiency
O Efficiency input energy - output energy
input energy . 100
=
=
=
output energy
input energy
O Efficiency output energy
O Efficiency input energy + output energy
=
. 100
The equation for a machine's efficiency is Efficiency = Output energy / Input energy * 100
Efficiency = ( Output energy / Input energy ) * 100
The efficiency of an ideal machine is 100% where Output energy is equal to Input energy. The efficiency cannot be greater than 100% in any machine. Because work done by the machine cannot be more than the work done on the machine.
The efficiency of a machine in real world is always less than 1 because some of the input energy is lost as friction or heat in any type of machine. So the ideal machine is possible in real world applications.
Therefore, the equation for a machine's efficiency is Efficiency = Output energy / Input energy * 100
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a 100 n box is at rest on a tabletop where the coefficients of friction are 0.4 static and 0.3 kinetic. what force of friction will be present if you push on it horizontally westward with 35 n? give magnitude and direction of friction force.
A 100 n box is at rest on a tabletop where the coefficients of friction are 0.4 static and 0.3 kinetic. static force of friction will be present if you push on it horizontally westward with 35 N.
W = 100N - Ms = 0.4 Mi = 0.3
F = 35N
F = W = 100N
Now, limiting friction is
Fl = mi. N
or fi = 0.4x 100 = 40N
Here, limiting friction is greater than the applied force so, box will not move and remain at rest.
so, here only static friction will work.
fs = F = 35N
fs = 35N
fs = 35N static friction force
What is static friction force?
Static friction is the force that prevents an object from moving along a path. When two fabrics slide over each other, this friction occurs. All around us is friction. For example, when we walk, our feet touch the floor.
When we move, the backward movement of our foot puts pressure on the floor while the other foot moves forward. Furthermore, when we apply this frictional force to the floor, the floor beneath our feet exerts an equal and opposite force. This is consistent with one law of motion.
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A school bus moves 200 meters in 20 seconds, and another 100 meters in the next 10 seconds.
Calculate its average speed in m/s.
Answer: 300 m/s
Explanation:
So If it moves 200 metres in 20 seconds and then another 100 metres this is changing the total distance travelled to 300 metres. Also, it moves this distance extra distance in 10 seconds therefore the total time is 30 seconds.
speed = distance / time
speed = 300 / 30
speed = 10 m/s
After travelling a total of 300 metres and spending a total of 30 seconds in motion, the school bus travels at an average speed of 10 metres per second (m/s).
To figure out how fast the school bus was going on average, we need to know how far it went and how long it took to get there.
First, we add up the two lengths the school bus travelled: 200 metres plus 100 metres equals 300 metres.
Next, we add up how long it took to go both distances: 20 seconds plus 10 seconds equals 30 seconds.
Here's how to figure out the average speed:
Average Speed = Total Distance Travelled / Total Time Spent
Putting the numbers in:
Average Speed = 300 metres in 30 seconds
10 metres per second (m/s) is the average speed.
So, the school bus's usual speed is 10 m/s.
Average speed is the general rate of movement over a certain amount of time, no matter how it changes during the trip. In this case, the bus went 300 metres in 30 seconds, which means it went 10 m/s on average.
It's important to know that instantaneous speed is not the same as usual speed. Instantaneous speed is the speed of the bus at any given time during its trip. This speed could change as the bus speeds up, slows down, or stays at the same speed.
Calculating the average speed is helpful for figuring out how well something works generally, figuring out how efficient it is, and comparing different trips or types of transportation. But it might not take into account all the details of a given trip, such as different speeds or stops along the way. For a full picture of how the bus moves, it may be necessary to think about other things.
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A particle’s position along the x-axis is described by the functionx(t) = A t + B t2,where t is in seconds, x is in meters, and the constants A and B are given below.Randomized VariablesA = -4.9 m/sB = 6.9 m/s2q. Enter expression interms of A,B, t for the velocity of the particle as a function of time? What time will the velocity be zero?
Given,
The position function is, x(t)=At+bt²
A=-4.9 m/s
B=6.9 m/s²
The velocity is described as the rate of change if the displacement with time.
That is, the velocity is the time derivative of the displacement.
Therefore on differentiating the given function with respect to the time, we get the expression for the velocity.
i.e.,
[tex]\begin{gathered} v(t)=\frac{d(At+Bt^2)}{dt} \\ =A+2Bt \end{gathered}[/tex]Therefore the expression for the velocity is A+2Bt
To know at what time the velocity will be zero,
[tex]A+Bt=0[/tex]On simplifying the above equation,
[tex]t=\frac{-A}{B}[/tex]On substituting the known values in the above equation,
[tex]t=\frac{-(-4.9\text{ )}}{6.9}=0.71\text{ s}[/tex]Therefore the velocity will be zero at 0.71 s
a child moves on x axis at a starting point 10cm it moves till it reaches point 70cm then it goes back to 5.
What's the displacement?
What's the distance?
The displacement on x-axis is 75 cm and the distance that moved by the child is 80 cm
The term displacement refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. And distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.We are given that,
Starting point of child = d₁ = 10cm
Reaching point of the child = d₂ = 70cm
Move back = 5cm
Therefore, total distance covered by a child can be given as,
Δd = 10cm + 70 cm = 80 cm
Thus, the total distance is 80cm and a child moves back 5cm then the displacement would be given as,
Displacement = total distance cover - distance move back
Displacement = 80cm - 5 cm = 75 cm
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the shape of an atomic orbital is associated with group of answer choices the spin quantum number (ms). the principal quantum number (n). the angular momentum quantum number (l). the magnetic quantum number (ml). the magnetic and spin quantum numbers, together.
The shape of an atomic orbital is associated with the principal quantum number (n).
Why do atoms have orbitals?
The wave character of the electrons (or electron pairs) in an atom is described by atomic orbitals, which are mathematical functions. They provide a method for calculating the likelihood that an electron will be located in a particular area surrounding the atom's nucleus. An atom can have any number of orbitals, according to the quantum atomic model.
Why do a wave's orbitals affect the shape of the wave?The function of the wave will therefore be determined by the distance from the nucleus and not by its direction. Any particle's orbital shrinks in size but maintains a spherical geometry as its center quantum number drops.
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what is the momentum of an 7.2- kgkg bowling ball rolling at 3.0 m/sm/s ? express your answer to two significant figures and include the appropriate units.
Answer: 20.16kg.m\s
Explanation: Here is given that M= 7.2 Kg, and v= 2.8 m/s So, momentum ,P=M. v = (7.2*2.8) = 20.16 Kg. m/s, which is a number having four significant digits. but we have to provide the answer in two significant digits. Therefore, to convert
an archer shoots an arrow toward a 300-g target that is sliding in her direction at a speed of 2.15 m/s on a smooth, slippery surface. the 22.5-g arrow is shot with a speed of 42.0 m/s and passes through the target, which is stopped by the impact. what is the speed of the arrow after passing through the target?
24.46 m/s is the speed of the arrow after passing through the target.
p=mv
Conservation of momentum: m1v1=m2v2
The target has a mometum of -(.3kg)(2.15m/s)
the arrow has a mometum of (.0225kg)(42.0m/s)
After impact the mometum of the target is 0 Ns since its velocity is zero.
After impact the velocity of the arrow can be determined with conservation of momentum calculations.
Δp(arrow)=-Δp(target)
m(arrow)v(arrow)i+m(target)v(target)i=m(arrow)v(arrow)f+m(target)v(target)f
(.0225kg)(42.0m/s)-(.3kg)(2.15m/s)=(.0225kg)vf(arrow)
the final velocity of the arrow should be equal to((.0225kg*42.0m/s)-(.3kg*2.15m/s))/.0225kg
v(arrow) final = 24.46 m/s
What is momentum?Momentum is a quantity used to describe the state of motion of an object with non-zero mass. Therefore momentum can be applied to any moving object. If
m is the mass of a body and v is the velocity of that body, the impulse momentum can be expressed as p=m.v
Since velocity is considered a vector, momentum is also considered a vector. This means that the impulse has a significant magnitude and direction—an impulse indicated by a vector or arrow. For example, if a ball of a certain mass moves with a certain speed, it has momentum. When the ball hits the wall, it stops and thus carries its momentum over the wall. Therefore momentum is always conserved.To learn more about momentum, refer;
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psychology is the ___ study of behavior and mental processes
Answer:
scientific study
Explanation:
I hope that helps
Answer:
scientific studies
give me brainlyest please
a parallel-plate capacitor is connected to a battery. the energy of the capacitor is u0 . the capacitor is then disconnected from the battery and the plates are slowly pulled apart until the plate separation doubles. the new energy of the capacitor is u . find the ratio u/u0 .
The ratio u/u0 : 1/2
As the distance is doubled and the battery is connected, we know that Capacitance is given by: [tex]C= \frac{\epsilon_0 A}{d}[/tex]
As the distance between the plate is doubled, C will become: [tex]C= \frac{\epsilon_0 A}{2d} = \frac{C}{2}[/tex]
Now, as the battery is connected, Voltage will remain constant, therefore Charge Q will become: [tex]Q=\frac{CV}{2}[/tex]
The energy before doubling the distance between the plates was, U0 :
[tex]U_0 = \frac{1}{2}QV = \frac{1}{2}CV^2[/tex]
After doubling the distance, the Energy will become U:
[tex]U = \frac{1}{2}QV = \frac{1}{4}CV^2[/tex]
Therefore, the ratio will be:
[tex]\frac{U}{U_0} = \frac{\frac{1}{2}CV^2}{\frac{1}{4}CV^2} = \frac{1}{2}[/tex]
What is capacitor ?A capacitor is a bipolar electrical device that can store energy in the form of an electrical charge. It consists of two electrical conductors separated by a distance. The space between the conductors can be filled with a vacuum or an insulating material known as a dielectric. The ability of a capacitor to store charges is called capacitance. Capacitors store energy by keeping opposite charges away from each other. The simplest model of a capacitor is a parallel plate, which consists of two metal plates with a gap between them. However, different types of capacitors are manufactured in different shapes, styles, lengths, circumferences and materials.
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Which vehicle has an acceleration of 5 m/s²?
A a bicycle, when its speed changes from rest to 2.5 m/s in 2s
B a car, when its speed changes from rest to 15 m/s in 5s
C a lorry, when its speed changes from rest to 20 m/s in 15s
D a motorbike, when its speed changes from rest to 50 m/s in 10s
The vehicle has an acceleration of 5 m/s² - A motorbike, when its speed changes from rest to 50 m/s in 10s
What is an acceleration ?
Acceleration is the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.
Acceleration is a vector quantity since it has both a magnitude and a direction. A vector quantity is also velocity. The velocity vector change during a time interval divided by the time interval is the definition of acceleration.
All the vehicles have an initial velocity ( u) = 0
A- For bicycle
Final velocity (v) = 2.5m/s time (t) = 2s
acceleration = 2.5/2 = 1.25m/s2
B- For car
Final velocity (v) = 15m/s time (t) = 5s
acceleration = 15/5 = 3m/s2
C- For lorry
Final velocity (v) = 20m/s time (t) = 15s
acceleration = 20/15= 1.33m/s2
D- For motorbike
Final velocity (v) = 50m/s time (t) = 10s
acceleration = 50/10= 5m/s2
Option D is the correct answer as the motorbike will have an acceleration of 5m/s2.
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