An electron is accelerated from rest by an electric potential difference of 437 V, and then enters a region of uniform magnetic field. The magnetic field is oriented perpendicular to the velocity with a magnitude of 42.8 mT. What will the radius of the electron's path be once it enters the magnetic field

Meniscus formed by water and mercury (In capillary tube and beaker):

Because the water wets the glass and seeps up the tube's side when it is contained in a glass tube, the meniscus (surface) of the water has a concave form. And in mercury, the meniscus is lower than the meniscus in the beaker because the intermolecular force between the mercury atom is stronger than the force within a wall of a container which is why mercury forms a lower meniscus.  

What are meniscus?:

The meniscus arises when the liquid and the container walls have different attractive forces acting on the molecules of the liquid.

A meniscus is created through adhesion, which is related to water's relatively high surface tension. The molecules in the glass beaker's wall are drawn to the water molecules. Whereas cohesion is the intermolecular attraction of similar molecules.

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The initial velocity of the hockey puck is obtained as 22 m/s.

The frictional force of the hockey puck is the force that causes it to stop. Now;

Ff = μmg

Ff = 0. 51 * 0.16 Kg * 9.8 m/s^2

Ff = 0.8 N

Now;

F = mv^2/2x

Where;

m = mass

v = velocity

x = distance

v =√ 2xF/m

v = √ 2 * 47.7 * 0.8 / 0.16

v = 22 m/s

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Answer:

Point A

Explanation:

Because it reaches maximum height

Rewrite the equation as

[tex]y = (x-1) (x-2) x^{-1/2}[/tex]

Then by the product rule, the derivative is

[tex]\dfrac{dy}{dx} = (x-2) x^{-1/2} + (x-1) x^{-1/2} - \dfrac12 (x-1) (x-2) x^{-3/2}[/tex]

and we can factorize this as

[tex]\dfrac{dy}{dx} = \dfrac12 x^{-3/2} \left(2 (x-2) x^{3/2-1/2} + 2 (x-1) x^{3/2-1/2} - (x-1) (x-2)\right)[/tex]

[tex]\dfrac{dy}{dx} = \dfrac12 x^{-3/2} \left(2 (x-2) x + 2 (x-1) x - (x-1) (x-2)\right)[/tex]

[tex]\dfrac{dy}{dx} = \dfrac12 x^{-3/2} (3x^2 - 3x - 2)[/tex]

[tex]\dfrac{dy}{dx} = \dfrac{3x^2 - 3x - 2}{2x^{3/2}}[/tex]

and optionally expanded once more (if only to match the provided "Ans") to

[tex]\dfrac{dy}{dx} = \dfrac32 x^{2-3/2} - \dfrac32 x^{1-3/2} - x^{-3/2}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac32 x^{1/2} - \dfrac32 x^{-1/2} - x^{-3/2}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac32 \sqrt x - \dfrac3{2\sqrt x} - \dfrac1{\sqrt{x^3}}[/tex]

(A) The angle of this in polar coordinates is 30⁰.

(B) The North/South and East/West components of its displacement is 250 m and 433 m respectively.

60° N of W lies in the fourth quadrant;

θ = 90 - 60 = 30⁰

in polar coordinate = (r,θ) = (500 m, 30⁰)

Dy = D sinθ

Dy = 500 m x sin(30) = 250 m

Dx = D cosθ

Dx = 500 m x cos(30) = 433 m

Thus, the angle of this in polar coordinates is 30⁰.

The North/South and East/West components of its displacement is 250 m and 433 m respectively.

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The density of the glass can be determined using the formula:

Density is defined as the ratio of mass and volume of a substance.

The mass of the glass = Final mass of beaker  - initial mass  of beaker (Mf - Mi)

The initial mass of the beaker is not given.

Volume of the glass marble = 20 cm³

Density of the glass = (Mf - Mi)/20 cm³

Therefore, the density of the glass is determined from the ratio of the mass and volume of the glass.

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The cost of the 1.4KW kettle is 0.945 p.

The cost of electricity is computed from the cost of electricity. We have to know the cost of electricity that is charged for the 1.4kW kettle.

Now let the power consumed=

1.4kW * 0.075 hrs = 0.105 KWhr

Then;

1 KWhr costs  9p

0.105 KWhr costs 0.105 KWhr *  9p/1 KWhr

= 0.945 p

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a) The motion along the vertical direction and the motion along the horizontal direction.

b) The object remains in the air for a time period of 2usin(θ)/g.

Any object that is thrown in the air when gravity is acting on it is called a projectile. The motion of this projectile is called projectile motion.

When the projectile is thrown in the air at some angle θ, then there are two independent motions taking place at the same time. First is the component of motion along the vertical direction along which gravity acts. Second is the component of motion along the horizontal direction along which the object moves with a constant velocity. No force acts along the horizontal direction. The horizontal motion does not affect the vertical motion and the converse is also true. So these are independent of each other.

The time of flight is the time during which a projectile remains in the air. This time of flight is calculated using the formula,

T=2usin(θ)/g

where T is the time of flight, u is the initial velocity and g is the acceleration due to gravity.

Hence, the object remains in the air for a time period of 2usin(θ)/g.

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Answer: A positively charged insulating rod is brought close to an object that is suspended by a string. If the object is repelled away from the rod, we can conclude that the object is positively charged.

Explanation: To find the answer, we need to know more about the Electric charges and its properties.

Thus, from the above, we can conclude that, when a positively charged insulating rod is brought close to an object that is suspended by a string. If the object is repelled away from the rod, we can conclude that the object is positively charged.

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Answer:

positively charged

Explanation:

when a positively charged object is being repelled, that means the charge should be the same for both.

Radius of curvature of the concave mirror is 36 cm.

To find the answer, we need to know about the relation between focal length and radius of curvature.

Here, radius of curvature= 2×18 cm = 36cm

Thus, we can conclude that the radius of curvature of the concave mirror is 36cm.

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The magnitude of the net force that the rods exert after an electron is released at point P is 2.885 × 10⁻¹⁵ N.

Given values:

Length of non-conducting rod, l = 1.20 m

Charge on positive rod, +Q = +2.50 μC = +2.50 × 10⁻⁶ C

Charge on negative rod, -Q = -2.50 μC = -2.50 × 10⁻⁶ C

Distance from point P of each rod, x = 60 cm = 0.60 m

Calculation of Net electric force exerted on point P:

Consider an electron released at point P, then the net electric force exerted will be given as:

F = e. E_net       - ( 1 )

Step 1:

The net electric field value is given as:

E_net  = E₁ cos Φ + E₂ cos Φ      

           = 2E₁ cos Φ                  -( 2 )

where, E₁ & E₂ are electric fields due to positive and negative rod                

            respectively.

            Φ is phase angle

Step 2:

The electric field due to positive rod is given as:

E₁ = k (λ/r)             - ( 3 )

where, k is Coulomb's force constant

            λ is linear charge density

            r is distance between point P and half of the rod.

Now, the linear charge density is given as:

λ = Charge/length = Q/x

The value of r is given as:

r = √x²-a²

where, x is length of rod

           a is half length of rod

Applying values in above equation, we get:

r = √x²-(x/2)²

r = √(1.20 m)²-(1.20/2)²

  = √1.08

  = 1.04 m

Substituting all the determined values in equation 3 we get:

E₁ = k (λ/r)

   = k [(Q/x)/r]

   = k [ Q/xr ]

   = (9×10⁹ Nm²/C²) [ |+2.50×10⁻⁶ C|/(1.20 m)(1.04 m)]

   = 1.803×10⁴ N/C

Step 3:

Similarly, the electric field due to negative rod is given as:    

E₂ = k [ Q/xr ]

    = (9×10⁹ Nm²/C²) [ |-2.50×10⁻⁶ C|/(1.20 m)(1.04 m)]

    = 1.803×10⁴ N/C

Step 4:

Consider equation 2:

E_net  = 2E₁ cos Φ

From the figure we get the phase angle as:

Φ = tan⁻¹ (0.60 m/0.60 m)

   = tan⁻¹ ( 1 )

   = π/4  

Now, the electric field produced due to each rod is equal and mutually perpendicular. Thus, the net electric field after applying values can be calculated as:

E_net = 2(1.803×10⁴ N/C) cos π/4

          = 2(1.803×10⁴ N/C) (0.5)

          = 18030 N/C

Step 5:

Consider equation 1 :

F = e. E_net

where, e is charge on an electron

Applying values in above equation we get:

F = (1.6 × 10⁻¹⁹ C)(18030 N/C)

  = 2.885 × 10⁻¹⁵ N

Therefore, the magnitude of the net force that the rods exert after an electron is released at point P is  2.885 × 10⁻¹⁵ N.

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The acceleration of the car and the time required to reach this speed will be 8 m/s² and 10 sec.

The rate of velocity change concerning time is known as acceleration.

Given data;

Initial velocity, u=0  m/s

Final velocity, v= 80 m/sec

Distance travelled,s =900m

From Newton's third equation of motion;

v²=u²+2as

a =(v²-u²)/2s

Substitute the given values;

a = (80²-0)/2 ×900

a = 6400/1800

a=8 m/s²

The time required to reach this speed is found in Newton's first equation of motion as;

v = u+at

Substitute the given values;

80 = 0 + 8t

t=80/8

t = 10 sec

Hence, the acceleration of the car and the time required to reach this speed will be 8 m/s² and 10 sec.

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The friction force does the greatest magnitude of work on the crate

Consider all four forces. The normal force does no work at all, since there is no motion in the direction of that force, perpendicular to the ramp. The force of gravity is smaller than the force of friction, since you still need to push the crate to get constant velocity. The force of you pushing is also smaller than the force of friction, since you are moving down a ramp, and are therefore assisted by gravity. Therefore the force doing greatest magnitude of work is the force of friction. Note that, even though the frictional work is negative, it still has the greatest magnitude

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Option D is correct : This positive charge will veer east

It is given that the particle has a positive charge.

So, the direction of the force on the positive charge (and also the acceleration) is in the same direction as the electric field.

Now the electric field is uniform and points in east, the force on it [tex]F=qE[/tex]will also be pointed towards the east.

The positive charge was initially moving north, which means that the velocity vector was in the direction of north and when a positive charge first reaches an area with an electric field and force pointing east, its velocity vector will change to be along the electric field, or east.

That’s why a positive charge traveling north enters a region where the electric field is uniform and points east will veer east.

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The impulse and change in momentum of an object moving with a force 30N then hits a wall to a stop in 0.5s is 15Ns.

Impulse is the integral of force over time. It is calculated by multiplying the force applied by the time as follows:

∆p = Force × time

According to this question, an object is moving with a force 30N and then hits a wall to a stop in 0.5s.

Impulse = 30N × 0.5s = 15Ns

Therefore, the impulse and change in momentum of an object moving with a force 30N then hits a wall to a stop in 0.5s is 15Ns.

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When the mass of Earth doubles, acceleration due to gravity doubles as well.

Apply Newton's second law of motion;

F = mg --- (1)

where;

F = GmM/R²  --- (2)

where;

Solve (1) and (2)

mg =  GmM/R²

g = GM/R²

when the mass of Earth doubles, acceleration due to gravity becomes;

g' = G(2M)/R²

g' = 2(GM/R²)

g' = 2g

Thus, when the mass of Earth doubles, acceleration due to gravity doubles as well.

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Option (a) B3 supergiant is correct.

Just before it exploded, the star that became supernova 1987A was a B3 supergiant.

Any star with extremely high intrinsic luminosity and relatively vast size is referred to as a supergiant star.

B3 supergiant is a blue supergiant.

An OB supergiant, often known as a blue supergiant (BSG), is a hot, brilliant star like Rigel.

The hottest stars in the universe are blue supergiants, with temperatures ranging from 10,000 K to 50,000 K or higher.

A type II supernova known as SN 1987A occurred in the Milky Way's dwarf satellite galaxy, the Large Magellanic Cloud.

Red supergiants are the most frequent supernova progenitors, and it was once thought that only red supergiants could explode as supernovae. However, because SN 1987A's parent star, was a B3 blue supergiant, this notion had to be reexamined.

Hence, just before it exploded, the star that became supernova 1987A was a B3 supergiant.

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Given the data from the question, the potentiel energy is most in A

To obtain the correct answer to the question, we shall determine the potential energy in each case

PE = mgh

Where

Case A

PE = mgh

PE = 2.5 × 9.8 × 1.4

PE = 34.3 J

Case B

PE = mgh

PE = 2.5 × 0 × 0

PE = 0 J

Case C

PE = mgh

PE = 1 × 9.8 × 2

PE = 19.6 J

SUMMARY

Thus potential energy is most in A

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Answer:

measured at constant temperature and pressure

Hope this helps :)

II.  The work done by frictional force is zero.

Work is said to be done when an applied force moves an object over a given distance.

Work done by friction = μ(Fn)d

where;

Since the frictional force could not prevent the block from sliding, we can conclude that the work done by frictional force is zero.

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The part of laser printer that applies a positive charge to the paper in order to attract the toner particles is known as transfer roller.

What is a laser printer:

A laser printer is a kind of printer that uses the electrostatic digital printing process to perform printing. It makes use of the static electricity and toner powder in place of liquid ink.

The toner is applied to specific areas which are dependent on the charge difference created or on the static electricity.

Following are the components of a laser printer:

        This unit of a laser printer generally consists of a laser diode, a

        scanning motor and a polygon mirror.
        It also consists of two-beam alignment lenses.

        This unit of laser printer consists of three drums, namely primary

        charging roller (PCR), organic photoconductive drum (OPC) , and

        image transfer roller (ITR).
        The transfer roller is also present at a close vicinity of the  

        printer's  toner cartridge.

        This unit of laser printer consists of a pressure roller and a fuser                roller, where the fuser roller assembly consists of a heating

        element.

Therefore, the transfer roller unit of a laser printer applies a positive charge to the paper that attracts the toner particles to it.

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Answer:

Newton's corpuscular theory stated that light consisted of particles that travelled in straight lines. Huygens argued that if light were made of particles, when light beams crossed, the particles would collide and cancel each other. He proposed that light was a wave.

If the primary wire's power is 10 A and one branch's power is 4 A, another branch's power will be 6A.

According to Kirchhoff's current law (KCL), the total current flowing through a parallel route circuit's junction equals the total current flowing away from it.

Provided that one of the two branches through which power exits the intersection has a flow of 4A, and also that the junction's overall flow entering it is 10A, the entire current going the junction should be 10A.

Consequently, the second wire's power may be expressed as;

I = I1+ I2 [ where I= total current (10A);

                I1= current in one branch (4A) &

                I2= current in another branch]

⇒I2 = I - I1

⇒I2 = 10A - 4A

⇒I2 = 6A

Therefore, it can be concluded that when the primary wire bears 10A power having 4A in one of its branches, another branch carries 6A power.

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Answer:

In pair production, after the loss of Kinetic energy, the angular separation between the two photons is 180°.

Explanation:

Therefore, the angle of separation between the two photons is 180°.

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Answer:

Average Velocity = 3.65 m/s

Explanation:

Average Velocity  [tex]=\frac{Total Displacement}{Total Time}[/tex] [tex]=\frac{22.1-3.85}{5}=\frac{18.25}{5}=3.65[/tex]

The average velocity of a ball that rolls from x=3.85m to x=22.1m in 5 seconds is -3.65 m/s.

Given the following values:

Initial position, x = 3.85 m

Final position, x'= 22.1 m

Initial time, t = 0 seconds

Final time, t'= 5 seconds

The average velocity can be computed from the ratio of change in displacement and time.

The average velocity is given as:

v = (x'-x)/(t'-t)

v = (22.1-3.85)/(5-0)

v = -3.65 m/s

Hence, the average velocity of a ball that rolls from x=3.85m to x=22.1m in 5 seconds is -3.65 m/s.

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Answer:

See below

Explanation:

TOTAL distance = x meters   (not given how far he ran from scrimmage line)

Displacement =  x - 2   meters     ( although football uses yards not meters)

The number of oscillations completed by the pendulum is 2736.

The amplitude of the pendulum is 3.47 m.

The given motion is an underdamped motion. So its frequency will be similar to that of a simple harmonic motion.

The frequency of oscillation is defined as the number of oscillations completed in unit time. It is calculated using the formula.

f=(1/2π)*√(l/g)

where f is the frequency, l is the length of the pendulum, and g is the acceleration due to gravity.

Given the length of the wire l=13.9 m and acceleration due to gravity g=9.8 m/s^2. The frequency of oscillation is:

f=(1/(2*3.14)) * √(13.9/9.8)

f=0.19 Hz (approximately)

Since the pendulum started oscillating at 8:00 am, 4 hours has been passed when it shows 12:00 pm. So time t=4 hours or t=4*3600. Hence t=14400 s. The total number of oscillations is then given by the formula,

n=ft

where n is the number of oscillations.

n=0.19*14400=2736.

In damping motion, the amplitude of the pendulum decreases with time. The amplitude of the pendulum is given by the formula,

A' = A exp (-b*t)

where A' is the amplitude after time t, A is the initial amplitude, b is the damping constant, and t is the time.

Here A=1.2 m, b=0.010 kg/s and t=14400 s.

A' = 1.2 exp (-0.010*14400)

A'=3.47 m (approximately)

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The type of circuit which have been made is the series circuit in this scenario.

This is a complete path which involves the whole electric current flowing through the various parts such as resistor etc..

There is only one path of current in which it does not undergo any form of split during motion.

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Answer:

leaves will deverge

Explanation:

because of the nagwtive charge will become positive