The electric potential V(z) on the z-axis is : V = [tex](\frac{Q}{a^2} ) [ (a^2 + z^2)^{\frac{1}{2} } -z[/tex]
The magnitude of the electric field on the z axis is : E = kб 2[tex]\pi[/tex]( 1 - [z / √(z² + a² ) ] )
Given data :
V(z) =2kQ / a²(v(a² + z²) ) -z
Determine the electric potential V(z) on the z axis and magnitude of the electric fieldConsidering a disk with radius R
Charge = dq
Also the distance from the edge to the point on the z-axis = √ [R² + z²].
The surface charge density of the disk ( б ) = dq / dA
Small element charge dq = б( 2πR ) dr
dV [tex]\frac{k.dq}{\sqrt{R^2+z^2} } \\\\= \frac{k(\alpha (2\pi R)dR}{\sqrt{R^2+z^2} }[/tex] ----- ( 1 )
Integrating equation ( 1 ) over for full radius of a
∫dv = [tex]\int\limits^a_o {\frac{k(\alpha (2\pi R)dR)}{\sqrt{R^2+z^2} } } \,[/tex]
V = [tex]\pi k\alpha [ (a^2+z^2)^\frac{1}{2} -z ][/tex]
= [tex]\pi k (\frac{Q}{\pi \alpha ^2})[(a^2 +z^2)^{\frac{1}{2} } -z ][/tex]
Therefore the electric potential V(z) = [tex](\frac{Q}{a^2} ) [ (a^2 + z^2)^{\frac{1}{2} } -z[/tex]
Also
The magnitude of the electric field on the z axis is : E = kб 2[tex]\pi[/tex]( 1 - [z / √(z² + a² ) ] )
Hence we can conclude that the answers to your question are as listed above.
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As a block falls through the air by 40 meter it does work equal to -1800 joule. Determine the mass of a block.
Answer:
m = 4.5 kg
Explanation:
w = - 1800 j
Fd = - 1800 j
mgd = - 1800 j
m = - 1800 ÷(gd)
m = - 1800 ÷( 10×-40)
m = 4.5 kg
You are riding a bicycle up a gentle hill. It is fairly easy to increase your potential
energy, but to increase your kinetic energy would be harder.
True or false
Examine the image below:
Which term describes the wave phenomenon in the image?
Answer:
C
Explanation:
Reflection.
match each term to its definition.
the vocabulary
Volt
electric potential energy
electric potential difference
electric potential
the definitions
the SI unit of electric potential difference
difference in electric potential between two positions
potential energy an electric charge has due
to its location in a field
electric potential energy of a charged particle divided by its charge
here are the answers
Electric potential difference is the difference in electric potential between two positions and it is measured in volts.
What is electric potential energy?This is the potential energy of an electric charge has due to its location in a field.
What is electric potential?The electric potential of a charged particle is the electric potential energy of the charged particle divided by its charge magnitude.
What is electric potential difference?Electric potential difference is the difference in electric potential between two positions.
What is volt?Volt is the SI unit of electric potential difference.
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Which statement correctly describes the relationship between frequency and wavelength?
A :As the frequency of a wave increases, the longer its wavelength is
B: As the frequency of a wave increases, the shorter its wavelength is.
C: As the frequency of a wave increases, its wavelength remains the same.
Answer:
It is B
Explanation:
Option B talks about how the frequency of the wave increases the shorter it's wavelengths
Answer:
It's b
Explanation:
static frictional Force
Answer:
The static frictional force is the force between the magnetic forces statically and contains only two objects during this physical reaction. It results in electricity and a slight shock.
An experiment is set up as follows:
A mass m = 9.4kg is sent down a frictionless ramp with an initial velocity of 2.5m/s. The ramp is 87cm
long and has an angle of 36°above the horizontal. At the bottom of the ramp is a horizontal surface with a
kinetic friction coefficient of μk = 0.27. At the far side of the horizontal surface, 48cm away, is a spring with
k-constant ks = 3,413.7N
m that will be compressed as the mass collides with the spring. The experiment
ends as the spring is fully compressed and the mass is at rest.
Note: The distance that the spring is compressed is in addition to the 48cm.
7) Find the initial energy of the mass. (10pts)
8) How far will the spring compress if there is no surface friction under the spring? (10pts)
9) How far will the spring compress if the surface friction continues under the spring? (20pts)
(a) The initial energy of the mass is 76.485 J.
(b) The compression of the spring in the absence of friction is 21.2 cm.
(c) The compression of the spring in the presence of friction is 19.4 cm.
Initial energy of the massThe initial energy of the mass is determined as follows;
E = K.E + P.E
E = ¹/₂mv² + mgh
where;
h is the height of the rampE = ¹/₂mv² + mg x Lsinθ
P.E = ¹/₂(9.4)(2.5)² + (9.4)(9.8)(0.87)(sin36)
P.E = 76.485 J
Compression of the spring when there is no surface tensionThe compression of the spring in the absence of friction is calculated as follows;
Ux = E
¹/₂kx² = 76.485
kx² = 2(76.485)
x² = (2 x 76.485)/k
x = √(2 x 76.485)/k
x = √(2 x 76.485 / 3413.7)
x = 0.212 m
x = 21.2 cm
Compression of the spring in presence of frictionThe compression of the spring in the presence of friction is determined by applying the principle of conservation of energy.
E - Fd = Ux
E - μmgd = ¹/₂kx²
76.11 - (0.27 x 9.4 x 9.8 x 0.48) = ¹/₂(3413)x²
64.17 = 1706.5x²
x² = 0.0376
x = √0.0376
x = 0.194
x = 19.4 cm
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A basketball player must jump 1.2m in the air in order to dunk. What is the total time he is in the air?
Answer:
0.98 [sec].
Explanation:
1) the time when the player is moving up equals the time the player falls, it can be 't'. Then
2) the equation of moving down can be written as
[tex]\frac{g*t^2}{2} =h, \ where[/tex]
g=10 [m/s²], t - time, h - the given height.
3) according to the formula above the time spent to moving down is:
[tex]t=\sqrt{\frac{2h}{g}};[/tex]
[tex]t=\sqrt{\frac{2.4}{10}}=\sqrt{0.24} =0.49[s].[/tex]
4) finally, the total time is t*2=0.98[sec].
Topic : Collisions and Conservation of Momentum
1. Two children are standing still on ice and push off each other. Each has a momentum after the push. Do they violate the conservation of law? Initial momentum is zero.
2. Describe how the conservation law works with elastic and inelastic collisions.
3. In general, for elastic collisions with stationary objects, when will the first object bounce back? When will it follows the stationary object after the collision?
4. What is the use of airbags in vehicles?
5. Why are seatbelt designed to be stretchable?
It is amount of force or motion that cause the movement or moving of body.
Thus it is well explained.
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1.No they do not violate the conservation of law. Because the initial momentum can be zero.
2. The momentum is conserved in both elastic and inelastic collision.
What is the law of conservation of momentum?The momentum of the body before the contact is always equal to the momentum of the body after the impact, according to the rule of conservation of momentum.
According to the law of conservation of momentum;
Momentum before collision =Momentum after collision
[tex]\rm m_1u_1 + m_2u_2 = v(m_1 + m_2)[/tex]
1.No they do not violate the conservation of law. Because the initial momentum can be zero.
2. The momentum is conserved in both elastic and inelastic collision. Hence the conservation law works with elastic and inelastic collisions.
3. An elastic collision is one in which kinetic energy is conserved, meaning that the total kinetic energy before and after the impact is the same.
The object bounces once after the body gets struck. When the body's final velocity is zero it follows the stationary object after the collision.
4.. Airbags are meant to inflate automatically in the case of an abrupt deceleration or impact force indicative of a collision.
When the bag is fully inflated, it protects the driver and/or passenger by Increasing cushioning around the driver's neck, head, and spine.
5. Stretchable seatbelts are meant to allow a passenger's considerable velocity to be slowly reduced, preventing the passenger from being flung forward abruptly.
As a result, if the automobile collides, serious casualties can be avoided.
Hence no they do not violate the conservation of law. Because the initial momentum can be zero.
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The force of a hammer drives a nail into wood. This is an example of?
A. An unbalanced force.
B. Gravitational force.
C. Friction.
D. Balanced forces.
Answer:
A. An unbalanced force.
Explanation:
There needs to be a net force in order for the nail to be driven into presumably the wall. Without the net force then the hammer and nail wouldn't move.
Ways in which a teacher plays a role in the literacy development of the learners
Answer:
encourage all attempts at reading, writing, and speaking
Explanation:
Find out the three methods of energy transfer (conduction, convection and radiation). think about
2 situations of daily life where you know or think you know that each one applies
Explanation:
conduction- putting a metal spoon in fire
convection- boiling water. In ventilation
Radiation- suns heat reaches us by radiation. heat from fire place reaches us by radiation.
Need help with the following - question 2
Answer:
Find the change in momentum of the upper stage, that is:
∆p = m(vf - vi)
m being the mass of the upper stage
vf being the final velocity which was given
vi being the initial which was also given
find ∆p
then use ∆p in the same equation
∆p being the answer you got above
m being the mass of the lower stage (given)
vi being the initial velocity (given)
vf being the final velocity of the lower stage which you were asked to find
Explanation:
During a collision the change in momentum (∆p) for both objects is equal regardless of their speeds or masses before or after the equation
A horizontal push of 197 N is applied to a 49.1 kg crate to slide it along a level floor. The crate is accelerating at 3.337 m/s2 (speeding up). What is the magnitude of the kinetic friction force between the crate and the floor
The magnitude of the kinetic friction force between the crate and the floor is 33.15 N.
Kinetic frictional force
The magnitude of kinetic frictional force is determined by applying Newton's second law of motion as shown below;
F - Ff = ma
where;
Ff is kinetic frictional forcea is acceleration of the crateF is the applied forceSubsitute the given parameters and solve for kinectic frictional force
197 - Ff = 49.1(3.337)
197 - Ff = 163.85
Ff = 33.15 N
Thus, the magnitude of the kinetic friction force between the crate and the floor is 33.15 N.
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To travel at a constant speed, a car engine provides 24 KW of useful power. The driving force on the car is 600 N. At what speed does it travel?
[tex]\text{Given that,}\\ \\\text{Power,} ~P=24~ KW = 24000~ W\\\\\text{Force,} ~F=600~N\\\\\text{We know that,}\\\\P=Fv\\\\\implies v = \dfrac{P}{F} = \dfrac{24000}{600}=40~ ms^{-1}\\\\\\\text{It travels at 40 m/s}[/tex]
The resultant of two vectors is of magnitude 3 units and 4 units is 1 units, what is the value of their dot product?
Answer:
A dot B = C is the vector equation for this expression
A · B = A B cos θ
3 * 4 cos θ = 1 the value 1 is their dot product
cos θ = 1 / 12 = .083 θ = 85.2 deg
If a 40 N block is resting on a rough horizontal table with a
coefficient of static friction p=0.60, then what is the force of
static friction acting on the block?
Based in the relationship between static frictional force and coefficient of static friction, the force of static friction is 24 N.
What is friction?Friction is a force that opposes the relative motion of an object moving over another at their surafce of contact.
Frictional force is constant for each type of material. This constant is known as coefficient of friction.
The coefficient of friction is given as follows:
Coefficient of friction = Frictional force/normal reactionFrom the data given:
coefficient of static friction p = 0.60Weight of block = 40 NForce of static friction = 0.60 × 40
Force of static friction = 24 N.
Therefore, the force of static friction is 24 N.
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I NEED HELP FAST
Match the term with the appropriate image
A) Focal length
B) Object position
C) Image position
1st image - B) Object position
2nd image - A) Focal length
3rd image - C) Image position
object position is from the lens to the object.image position is from the lens to where both rays meet together.Focal length is where the ray meets the principal axis.How fast must a proton move so that its kinetic energy is 70% of its total
energy?
I thought it would be 0.7c but that is wrong. I really don't know how to do this type of problem and my text book isn't any help.
Try this solution, all the details are in the attachment. note, the answer is marked with orange colour. If it is possible, check the provided solution in other sources.
Answer: ≈0.81c.
Select the correct answer. Based on the law of conservation of energy, which statement is correct? O A. Energy is always being added to all parts of the Universe. O B. Energy is often destroyed in some parts of the Universe. O C. Energy in a closed system cannot change forms. O D. Energy in an isolated system remains constant.
Answer:
d. energy in an isolated system remains constant.
Explanation:
energy can neither be replaced or destroyed
A man of mass 70 kg climbs stairs of vertical height 2.5m. Calculate the work done against the force of gravity. (Take g = 9.81 ms?)
Answer:
1716.75 J
Explanation:
Step 1: First check what we are provided with. As per given question we have:
mass (m) = 70 kg, height (h) = 2.5 m and acceleration due to gravity (g) = 9.81 m/s².
Step 2: Check what we are asked to find out.
Work done = Change in Potential energy
The stuff required to solve this question is potential energy. Using the formula: P = mgh. Where P is Potential energy, m is mass, g is acceleration due to gravity and h is height.
Step 3: Substitute the known values in the above formula.
→ P = 70 × 2.5 × 9.81
→ P = 1716.75 J
Hence, the work done against the force of gravity is 1716.75 J.
Explain why is dressing table mirror may become dirsty if wiped with a cloth on a warm day.
When you rub a dry cloth across glass, it creates charged static electricity, which attracts little non-charged dust particles.
A grasshopper jumps at a 63.0 angle with an initial velocity of 4.22 m/s. how far away does it land
The grasshopper is 1.47 m far away from the point where it jumps to the point where its lands.
To calculate the distance of the landing point of the grasshopper to the point where its jumps, we use the formula of range.
What is horizontal range?Range can be defined as the horizontal distance between the point of projection to the point where the projectile hit the plain again.
R = u²sin2∅/g........... Equation 1Where:
R = Distance between the point of jump and the point at which it landsu = initial velocity∅ = angleg = acceleration due to gravityFrom the question,
Given:
u = 4.22 m/s∅ = 63°g = 9.8 m/s²Substitute these values into equation 1
R = (4.22)²sin(2×63)/9.8R = 1.47 mHence, The grasshopper is 1.47 m far away from the point where it jumps to the point where its lands.
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Which of the following is NOT an example of force?
A. gravity
B. mass
C. a push
D. remain at rest
Answer:
D. remain at rest
Explanation:
The resistance of a 60.-watt lightbulb operated at
120 volts is approximately
Answer:
The resistance of a 60 watt light bulb designed to operate at 120 volts is 240 Ω.
Explanation:
Read the materials on Biomolecules. Summarize and creatively translate them into a poem describing
what you have learned about biomolecules write your answer
Biomolecules are fundamental for life. They required both energy supply and building structures.
What are biomolecules?Biomolecules are organic molecules that fundamental for life and must be ingested from the regular diet.
Biomolecules include proteins (e.g., meal proteins), lipids (fats) and also carbohydrates (e.g., glucose).
Biomolecules required both energy supply (e.g., glucose) and building structures (e.g., amino acids in proteins).
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Please help solve. Image down below
Answer:
thats is so hard
Explanation:
i cant answer that
A professional golfer swings a golf club, striking a golf ball that has a mass of 55.0 g. The club is in contact with the ball for only 0.00410 s. After the collision, the ball leaves the club at a speed of 32.0 m/s. What is the magnitude of the average force (in N) exerted on the ball by the club?
The magnitude of the average force exerted on the ball by the club is 429.27 N.
What is force?Force can be defined as the product of mass and acceleration
To calculate the force exerted on the ball by the club, we use the formula below.
Formula:
F = m(v-u)/t............ Equation 1Where:
F = Force exerted on the ballm = mass of the ballv = Final velocityu = initial velocityt = timeFrom the question,
Given:
m = 55 g = 0.055 kgu = 0 m/sv = 32 m/st = 0.0041 sSubstitute these values into equation 1
F = 0.055(32-0)/0.0041F = 429.27 NHence, The magnitude of the average force exerted on the ball by the club is 429.27 N.
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A curve is banked at an angle of 29.1 degrees above the horizontal and the road surface has a coefficient of static friction of 0.4. What must the radius of curvature be for the safe minimum speed of 27.1 m/s?
Hi there!
We can begin by summing the forces acting on the car.
Along the axis of the incline, the forces of friction and gravity are working. The force of friction points towards the top of the ramp, while the force of gravity works towards the bottom.
We can use trigonometry to determine the force due to gravity along the ramp.
[tex]F_g = Mg sin\theta[/tex]
The force due to friction is equal to:
[tex]F_f = \mu N[/tex]
The normal force is the vertical component of the force due to gravity, so:
[tex]F_f = \mu Mgcos\theta[/tex]
Now, the combination of these two forces produces a component of the centripetal force. Drawing a diagram, we see that the true centripetal force is the HYPOTENUSE, while these forces sum up to its horizontal component along the ramp.
Therefore:
[tex]F_c sin\theta = Mgsin\theta - \mu Mgcos\theta[/tex]
The centripetal force is equivalent to:
[tex]F_c = \frac{Mv^2}{r}[/tex]
m = mass (kg)
v = velocity (m/s)
r = radius (m)
Rewrite:
[tex]\frac{Mv^2}{r}sin\theta = Mgsin\theta - \mu Mgcos\theta[/tex]
Cancel out 'M'.
[tex]\frac{v^2}{r}sin\theta = gsin\theta - \mu gcos\theta[/tex]
Rearrange to solve for 'r'.
[tex]r = \frac{v^2sin\theta}{gsin\theta - \mu gcos\theta}[/tex]
Plug in values and solve.
[tex]r = \frac{(27.1^2)sin(29.1)}{(9.8)sin(29.1) - 0.4(9.8)cos(29.1)} = \boxed{266.365 m}[/tex]
The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. The lift of a wing with an area
of 280 square feet is 27,800 pounds when the plane is going 220 miles per hour. Find the lifting force on the wing if the plane slows down to 130 miles per hour.
(Leave the variation constant in fraction form or round to at least 5 decimal places. Round off your final answer to the nearest pound.)
Answer:
If the lifting force varies jointly with wing surface area and the square of the plane's velocity, then:
F = kAv²
If the lift is 27,800 pounds when the area is 190 sq. ft and the velocity is 230 mph, then the constant of proportionality is:
27,800 = k(190)(230)²
k = (27,800) / (190)(230)² = 139/50255
The lifting force the plane slows down to 200 mph is:
F = (139/50255)(190)(200)²
F = 21,020.79
Rounded to the nearest pound, the lifting force is 21,021 pounds.