An electric heater is rated at 1430 W, a toaster at 890 W, and an electric grill at 1760 W. The three appliances are connected in parallel to a common 120 V circuit. How much total current does this circuit draw?

Answer:

From ohms law,

V=IR

R=V/I =12.0/150 =0.08 ohm.

Answer:

v = 10.1 m/s

Explanation:

As we know that by the law of conservation of volume the rate of volume flowing through the pipe will remain conserved

so here we have flow rate given as

[tex]Q = Area\times velocity[/tex]

now we have

[tex]A_1 v_1 = A_2 v_2[/tex]

now we have

[tex]A_1 = 3.70 \times 10^{-2} m^2[/tex]

[tex]v_1 = 0.260 m/s[/tex]

[tex]A_2 = 9.50 \times 10^{-4} m^2[/tex]

now from above equation we have

[tex]v_2 = \frac{A_1}{A_2} v_1[/tex]

[tex]v_2 = \frac{3.70\times 10^{-2}}{9.50\times 10^{-4}}(0.260)[/tex]

[tex]v_2 = 10.1 m/s[/tex]

Answer:

t = 141.55 years

Explanation:

As we know that the radius of the wire is

r = 2.00 cm

so crossectional area of the wire is given as

[tex]A = \pi r^2[/tex]

[tex]A = \pi(0.02)^2[/tex]

[tex]A = 1.26 \times 10^{-3} m^2[/tex]

now we know the free charge density of wire as

[tex]n = 8.50 \times 10^{28}[/tex]

so drift speed of the charge in wire is given as

[tex]v_d = \frac{i}{neA}[/tex]

[tex]v_d = \frac{1190}{(8.50 \times 10^{28})(1.6 \times 10^{-19})(1.26\times 10^{-3})}[/tex]

[tex]v_d = 6.96 \times 10^{-5} m/s[/tex]

now the time taken to cover whole length of wire is given as

[tex]t = \frac{L}{v_d}[/tex]

[tex]t = \frac{310 \times 10^3}{6.96 \times 10^{-5}}[/tex]

[tex]t = 4.46 \times 10^9 s[/tex]

[tex]t = 141.55 years[/tex]

Answer:

d. 5.7 x 10⁴ J

Explanation:

I = moment of inertia of the flywheel = 0.525 kg-m²

w₀ = initial angular speed of the flywheel = 69.1 rad/s

w = final angular speed of the flywheel = 471 rad/s

W = work done by the engine on the flywheel

Work done by the engine is given as

W = (0.5) I (w² - w₀²)

Inserting the values

W = (0.5) (0.525) (471² - 69.1²)

W = 5.7 x 10⁴ J

Answer:

Part a)

Final charge on C : q = 1.875

Part b)

Ratio for A = 6 : 1.25

Ratio for B = -1 : 1.875

Ratio for C = 0

Explanation:

When two identical metal sphere are connected together then the charge on them will get equally divided on both after connecting them by conducting wire

So here we have

[tex]q_A = + 6q[/tex]

[tex]q_B = -q[/tex]

[tex]q_c = 0[/tex]

Step 1: We connected A and B and then separate them

so we have

[tex]q_A' = q_B' = 2.5q[/tex]

Step 2: We connected A and C and then separate them

so we have

[tex]q_A'' = q_c' = 1.25q[/tex]

Step 3: We connected B and C and then separate them

so we have

[tex]q_c'' = q_b'' = 1.875q[/tex]

The final charge on sphere C is 2.5q. Before touching, the total charge is +5q, which remains the same after all interactions, demonstrating conservation of charge.

When identical conductive spheres come into contact, the charges redistribute evenly across both spheres. If Sphere A is initially charged with +6q and Sphere B has a -q charge, touching them together allows their total charge to be shared, resulting in each sphere having (6q - q)/2 = 2.5q. After separation, both spheres A and B would have a charge of 2.5q. By touching Sphere C, which is uncharged, to A and then B in sequence, C gains a fraction of the charge from each, ending up with (2.5q)/2 from A and (2.5q)/2 from B, which totals 2.5q, since touching B does not change the charge obtained from A.

Before contact, the total charge is +5q (+6q from A and -q from B). After all the interactions, the total charge remains the same, +5q, but redistributed: A and B with 2.5q each and C with 2.5q.

In general, the total charge before and after remains constant, demonstrating conservation of charge.

Answer:

12 m

Explanation:

f = 0.2 Hz, v = 2.4 m/s

v = f x λ

Where, λ is the wavelength

λ = v / f = 2.4 / 0.2 = 12 m

The wavelength is defined as the distance between two consecutive crests or troughs.

So, the distance between two consecutive crests is 12 m.

Answer:

[tex]\Delta \rho =0.18/mL326gm[/tex]

Explanation:

we have error in division of 2 quantities is related as

[tex]z=\frac{a}{b}\\\\\frac{\Delta z}{z}=\frac{\Delta a}{a}+\frac{\Delta b}{b}[/tex]

where [tex]\Delta a,\Delta b[/tex] are errors in quantities a,b

Thus error in density becomes

[tex]\Delta \rho =\rho _{0}\times(\frac{\Delta m}{m}+\frac{\Delta V}{V})[/tex]

Applying values we get

[tex]\Delta \rho =\frac{4.635}{1.13} \times(\frac{0.002}{4.635}+\frac{0.05}{1.13})[/tex]

thus [tex]\Delta \rho =0.18326gm/mL[/tex]

Answer:

541.89 Watt

Explanation:

Consider the motion of rock on rough surface

μ = Coefficient of kinetic friction = 0.63

acceleration caused to kinetic friction is given as

a = - μg

a = - (0.63) (9.8)

a = - 6.2 m/s²

v₀ = initial velocity of the rock = 9.25 m/s

t = time taken to stop

v = final velocity = 0 m/s

Using the equation

v = v₀ + a t

0 = 9.25 + (- 6.2) t

t = 1.5 sec

m = mass of the rock = 19 kg

Energy lost due to friction is given as

E = (0.5) m (v₀² - v²)

E = (0.5) (19) (9.25² - 0²)

E = 812.84 J

Average thermal power is given as

[tex]P = \frac{E}{t}[/tex]

[tex]P = \frac{812.84}{1.5}[/tex]

P = 541.89 Watt

Answer:

55.6 nC

Explanation:

The electric field at the surface of a charged sphere has the same expression of the electric field produced by a single point charge located at the centre of the sphere and having the same charge of the sphere, so it is given by

[tex]E=k\frac{Q}{r^2}[/tex]

where

[tex]k=9\cdot 10^9 N m^2 C^{-2}[/tex] is the Coulomb's constant

Q is the charge on the sphere

r is the radius of the sphere

In this problem we know

E = 890 N/C is the magnitude of the electric field on the sphere

r = 0.750 m is the radius of the sphere

So by re-arranging the equation we can find the net charge on the sphere:

[tex]Q=\frac{Er^2}{k}=\frac{(890)(0.750)^2}{9\cdot 10^9}=5.56\cdot 10^{-8} C=55.6 nC[/tex]

To find the net charge within the surface of the sphere, we can use Gauss's Law. The net electric flux through a closed surface enclosing a charge is equal to the charge divided by the electric constant, ε₀. Given the electric field and the radius of the sphere, we can calculate the net charge using the equation derived from Gauss's Law.

The electric field everywhere on the surface of a thin, spherical shell is radially inward and has a magnitude of 890 N/C. To find the net charge within the surface of the sphere, we can use Gauss's Law. The net electric flux through a closed surface enclosing a charge is equal to the charge divided by the electric constant, ε₀. In this case, the closed surface is the spherical shell and the electric field is constant on the surface, so the net electric flux is equal to the electric field multiplied by the surface area of the sphere. The surface area of the sphere is given by 4πr², where r is the radius of the sphere. Setting the net electric flux equal to the charge divided by ε₀, we can solve for the charge.

Given that the electric field is 890 N/C, the radius of the sphere is 0.750 m, and the electric constant, ε₀, is 8.99 x 10⁹ Nm²/C², we can plug in these values to solve for the charge.

Let Q be the net charge within the sphere's surface:

Net electric flux = Electric field * Surface area

Q / ε₀ = Electric field * Surface area

Q / (8.99 x 10⁹ Nm²/C²) = (890 N/C) * (4π(0.750 m)²)

Q = (890 N/C) * (4π(0.750 m)²) * (8.99 x 10⁹ Nm²/C²)

Solving this equation will give us the net charge within the sphere's surface.

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Answer:

option C

multiplication factor n = 1 when volume change to half and pressure become double

Explanation:

we know by Ideal Gas law:

P1V1 = nRT1

P2V2 = nRT2

according to the question

pressure is doubled and volume is reduced to half  

so we have

new pressure = 2*P1

new volume = V1/2

hence,

(2P1) * (V1/2) = nRT2

P1V1 = nRT2

we have now

nRT1 = nRT2

we get

T1 = T2

thus no change in temperature

we know that internal energy is given as

internal energy = nCvT,

since temperature is directly proportional to internal energy and since temperature remains constant therefore internal energy remains constant

So there is no change in internal energy

thus, multiplication factor n = 1 when volume change to half and pressure change to double

Answer:

[tex]Area = 0.126 m^2[/tex]

Explanation:

Since the crossection of cylinder is of circular shape

so here the crossectional area will be given as

[tex]A = \pi r^2[/tex]

here we know that radius of the cylinder will be

[tex]R = 20 cm[/tex]

so in SI units it is given as

[tex]R = 0.20 m[/tex]

now we have

[tex]Area = \pi (0.20)^2[/tex]

[tex]Area = 0.126 m^2[/tex]

Answer:

Part a)

[tex]q_2 = -6.8 \mu C[/tex]

Part b)

[tex]F = 0.700 N[/tex]

direction = downwards

Explanation:

As we know that the negative charge will experience the force due to some other charge below it

the force is given as

[tex]F = 0.700 N[/tex]

now we know that

[tex]F = \frac{kq_1q_2}{r^2}[/tex]

now plug in all data

[tex]0.700 = \frac{(9 \times 10^9)(0.550\mu C)q_2}{0.220^2}[/tex]

[tex]0.700 = 1.022\times 10^5 q_2[/tex]

[tex]q_2 = -6.8 \mu C[/tex]

since this is a repulsion force so it must be a negative charge

Part b)

As per Newton's III law it will exert equal and opposite force on it

So here the force on the charge below it will be same in magnitude but opposite in direction

so here we have

[tex]F = 0.700 N[/tex]

direction = downwards

Answer:

Radius = 7.75 mm

Explanation:

magnetic field inside a point in the wire is given as

[tex]B = \frac{\mu_0 i r}{2\pi R^2}[/tex]

now we have

[tex]3mT = \frac{\mu_0 i (6mm)}{2\pi R^2}[/tex]

now outside wire magnetic field is given as

[tex]B = \frac{\mu_0 i}{2\pi r}[/tex]

now we have

[tex]1.50 mT = \frac{\mu_0 i}{2\pi(20 mm)}[/tex]

now divide above two equations

[tex]2 = \frac{6 mm\times 20 mm}{R^2}[/tex]

[tex]R = 7.75 mm[/tex]

Answer:

55.79 minutes

Explanation:

Volume of water = 5200 L = 5.2 m^3

Diameter = 3 cm

radius, r = 1.5 cm = 0.015 m

v = 2.2 m/s

The volume of water coming out in 1 second = velocity x area

                                                       = 2.2 x 3.14 x 0.015 x 0.015

                                                       = 1.55 x 10^-3 m^3

1.55 x 10^-3 m^3 water flows = 1 second

5.2 m^3 water flows = 5.2 / (1.55 x 10^-3) = 3345.57 second

                                                                    = 55.79 minutes

Answer:

2.05 x 10^8 m /s

Explanation:

c = 3 x 10^8 m/s

μ = c / v

where, μ is the refractive index, c be the velocity of light in air and v be the velocity of light in the medium.

μ = 1.461

1.461 = 3 x 10^8 / v

v = 3 x 10^8 / 1.461

v = 2.05 x 10^8 m /s

Answer:

Tangential speed, v = 314.15 m/s

Explanation:

It is given that,

Mass of the object, m = 15 kg

It is moving in a circle of radius, r = 10 m

Time period, t = 0.2 seconds

We need to find the tangential velocity of the object. It is given by :

[tex]v=\dfrac{2\pi r}{t}[/tex]

Where

v = tangential speed

[tex]v=\dfrac{2\pi \times 10\ m}{0.2\ s}[/tex]

v = 314.15 m/s

So, the tangential speed of the object is 314.15 m/s. Hence, this is the required solution.

Answer:

37.725 A

Explanation:

B = magnitude of the magnetic field produced by the electric wire = 0.503 x 10⁻⁴ T

r = distance from the wire where the magnetic field is noted = 15 cm = 0.15 m

i = magnitude of current flowing through the wire = ?

Magnetic field by a long wire is given as

[tex]B = \frac{\mu _{o}}{4\pi }\frac{2i}{r}[/tex]

Inserting the values

[tex]0.503\times 10^{-4} = (10^{-7})\frac{2i}{0.15}[/tex]

i = 37.725 A

A book that slides across a level, carpeted floor with an initial speed of 3.25 m/s and comes to rest after 3.25 m, has a coefficient of kinetic friction of 0.166.

A book slides across a level, carpeted floor with an initial speed (u) of 3.25 m/s. It comes to rest (final speed = v = 0m/s) after 3.25 m (s).

Since this is a uniformly decelerated rectilinear motion, we can calculate the acceleration (a) using the following kinematic expression.

[tex]v^{2} = u^{2} + 2as\\\\(0m/s)^{2} = (3.25m/s)^{2} + 2a(3.25m)\\\\a = -1.63 m/s^{2}[/tex]

The negative sign only explains that the friction opposes the movement. We can calculate the force exerted by the friction (F) using Newton's second law of motion.

[tex]F = m \times a[/tex]    [1]

where,

We can also calculate the force of friction using the following expression.

[tex]F = k \times N = k \times m \times g[/tex]    [2]

where,

Given [1] = [2], we get,

[tex]m \times a = k \times m \times g\\\\k = \frac{1.63 m/s^{2} }{9.81 m/s^{2}} = 0.166[/tex]

A book that slides across a level, carpeted floor with an initial speed of 3.25 m/s and comes to rest after 3.25 m, has a coefficient of kinetic friction of 0.166.

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This question involves the concepts of the equations of motion, Newton's Second Law, and Frictional Force.

The coefficient of kinetic friction is found to be "0.15".

First, we will use the third equation of motion to find out the acceleration of the book:

[tex]2as = v_f^2-v_i^2\\[/tex]

where,

a = acceleration = ?

s = distance covered = 3.25 m

vf = final speed  = 0 m/s

vi = initial speed = 3.25 m/s

Therefore,

[tex]2a(3.25\ m) = (0\ m/s)^2-(3.25\ m/s)^2\\\\a=\frac{-10.56\ m^2/s^2}{7\ m/s}[/tex]

a = - 1.51 m/s² (negative sign indicates deceleration)

Now the force can be calculated using Newton's Second Law of motion:

F = ma

This force is also equal to the frictional force:

F = μmg

comparing both forces, we get:

ma = μmg

a = μg

[tex]\mu = \frac{a}{g} = \frac{1.51\ m/s^2}{9.81\ m/s^2}[/tex]

μ = 0.15

Learn more about equations of motion here:

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The attached picture shows the equations of motion.

Answer:

0.51 m

Explanation:

Given :

Plank length = 2.65 m

Distance from the ledge from which the cable is attached = 79.7 cm = 0.797 m

Angle = 40.3 degree

Mass of the man, m = 76.4 kg

Now the net torque acting on the plank is zero.

Therefore, maximum torque applied by cable is

    = 2648 x 0.797 x cos (40.3)

    = 1609.5 N-m

We know that the man should apply the same torque,

Therefore, x [tex]\times[/tex]76.4 [tex]\times[/tex] g = 1609.5

                  x =2.14 m

Therefore, length to the end of the plank is = 2.65-2.14

                                                                         =0.51 m

Answer:

Rate = k[aryl halide][nucleophile]

Explanation:

The simple aryl halides are almost inert to usual nucleophilic reagents but considerable activation on the ring can be produced by the addition of strongly electron-attracting substituents on either the ortho or para positions, or both. These groups deactivate the ring to allow the attack of the nucleophille on the ring.

Thus, these reactions can occur by following addition-elimination mechanism in which the nucleophille first attacks the aryl halide and then the elimination of the leaving group takes place.

Kinetic studies of this type of mechanism demonstrate that the reactions are of second-order kinetics– first order w.r.t. nucleophile and also, first-order w.r.t. aromatic substrate. The rate determining step (r.d.s.) is the formation of the addition intermediate.

Thus,

Rate = k[aryl halide][nucleophile]

Answer:

5400 W-hr

Explanation:

Given:

Power used by energy efficient bulb = 15 W

Power used by incandescent bulb = 60 W

Total time of bulb used = 4 hours/day × 30 days = 120 hours

Now,

Energy used by the individual bulb by using them for 120 hours

we know,

Energy = Power × Time

thus,

Energy consumed by energy efficient bulb = 15 W × 120 hour = 1800 W-hr

Energy consumed by  incandescent bulb = 60 W × 120 hour = 7200 W-hr

hence,  the energy saved will be = 7200 - 1800 = 5400 W-hr

Final answer:

Calculating the monthly energy savings involves finding the difference in power consumption between a 60 W incandescent bulb and a 15 W energy efficient bulb, multiplying by the daily usage, and the number of days in a month. The savings are 45 W per hour, equating to 180 Wh/day and 5.4 kWh/month.

Explanation:

The question asks how much energy is saved each month by using an energy efficient light bulb instead of an incandescent light bulb for 4 hours a day. To calculate the energy saved, we need to determine the difference in power consumption between the two types of bulbs, multiply that difference by the number of hours used per day, and then by the number of days in a month.

Firstly, we find the power saved per hour:

60 W (incandescent) - 15 W (efficient) = 45 W saved per hour

Next, we calculate the daily savings:

45 W x 4 hours/day = 180 Wh/day

Finally, we calculate the monthly savings:

180 Wh/day x 30 days/month = 5400 Wh/month

Since 1 kWh = 1000 Wh, the saving is 5.4 kWh/month

This is the amount of energy saved by using the energy efficient bulb instead of the incandescent bulb for 4 hours each day over a month.

The light leaves the glass at about 42° relative to its normal

[tex]\texttt{ }[/tex]

Let's recall Snell's Law about Refraction as follows:

[tex]\boxed{n_1 \sin \theta_1 = n_2 \sin \theta_2}[/tex]

where:

n₁ = incident index

θ₁ = incident angle

n₂ = refracted index

θ₂ = refracted angle

[tex]\texttt{ }[/tex]

Given:

incident angle = θ₁ = 30°

index of refraction of air = n₃ = 1.0

index of refraction of glass = n₂ = 1.5

index of refraction of water = n₁ = 1.33

Asked:

refracted angle = θ₃ = ?

Solution:

Surface between Glass - Water:

[tex]n_1 \sin \theta_1 = n_2 \sin \theta_2[/tex]

[tex]\sin \theta_2 = \frac{n_1}{n_2} \sin \theta_1[/tex] → Equation A

[tex]\texttt{ }[/tex]

Surface between Air - Glass:

[tex]n_2 \sin \theta_2 = n_3 \sin \theta_3[/tex]

[tex]\sin \theta_3 = \frac{n_2}{n_3} \sin \theta_2[/tex]

[tex]\sin \theta_3 = \frac{n_2}{n_3} (\frac{n_1}{n_2} \sin \theta_1)[/tex] ← Equation A

[tex]\sin \theta_3 = \frac{n_1}{n_3} \sin \theta_1[/tex]

[tex]\sin \theta_3 = \frac{1.33}{1.0} \times \sin 30^o[/tex]

[tex]\sin \theta_3 = \frac{1.33}{1.0} \times \frac{1}{2}[/tex]

[tex]\sin \theta_3 \approx 0.665[/tex]

[tex]\boxed{\theta_3 \approx 42^o}[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Light

The angle at which the light leaves the glass is approximately 19.5°.

When a light ray crosses from one medium to another, such as from water to glass, it undergoes refraction, which causes the ray to bend. The angle between the incident ray and the normal to the surface of the glass is called the angle of incidence. To find the angle of incidence, we can use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction of the two media.

In this case, the index of refraction of water (n1) is 1.33 and the index of refraction of glass (n2) is 1.5.

The angle of incidence (θ1) is given as 30°. We can use the formula: n1*sin(θ1) = n2*sin(θ2) to solve for θ2, the angle at which the light leaves the glass.

Plugging in the values, we get: 1.33*sin(30°) = 1.5*sin(θ2).

Solving for θ2 gives us θ2 = sin^(-1)((1.33*sin(30°))/1.5).

Evaluating this expression, we find that θ2 is approximately 19.5°.

Answer:

[tex]v = 4.51 \times 10^3 m/s[/tex]

Explanation:

electric field = 2170 N/C

now the speed of the charge particle is given as

[tex]v = 5.45 \times 10^3 m/s[/tex]

here we know that charge particle moves without any deviation

so we will have

[tex]qvB = qE[/tex]

now magnetic field in this region is given as

[tex]B = \frac{E}{v}[/tex]

[tex]B = \frac{2170}{5.45 \times 10^3}[/tex]

[tex]B = 0.398 T[/tex]

Now another charge particle enters the region with different speed and experience the force upwards

[tex]F = qE - qvB[/tex]

[tex]1.54 \times 10^{-9} = (4.10\times 10^{-12})[2170 - v(0.398)][/tex]

[tex]375.6 = 2170 - v(0.398)[/tex]

[tex]v = 4.51 \times 10^3 m/s[/tex]

The answer is: [tex]9.43 \times 10^5 \, \text{m/s}[/tex].

To determine the speed of the different particle that enters the velocity selector, we need to consider the forces acting on it due to the electric and magnetic fields. The net force acting on a charged particle in an electric field [tex]\( E \)[/tex] and a magnetic field [tex]\( B \)[/tex] is given by the Lorentz force equation:

[tex]\[ \vec{F} = q\vec{E} + q(\vec{v} \times \vec{B}) \][/tex]

where [tex]\( q \)[/tex] is the charge of the particle, [tex]\( \vec{v} \)[/tex] is the velocity of the particle, [tex]\( \vec{E} \)[/tex] is the electric field, and [tex]\( \vec{B} \)[/tex] is the magnetic field.

For the particles that pass through the velocity selector without being deflected, the forces due to the electric and magnetic fields must cancel each other out. This means that:

[tex]\[ qE = qvB \][/tex]

where [tex]\( v \)[/tex] is the speed of the particles that pass through undeflected.

Given that the electric field [tex]\( E \)[/tex] is 2170 N/C directed vertically upward, and the particles are traveling east, the magnetic field [tex]\( B \)[/tex] must be directed south to produce a force that cancels the electric force. The speed [tex]\( v \)[/tex] of the undeflected particles is given as [tex]\( 5.45 \times 10^3 \)[/tex] m/s.

Now, for the different particle with a charge of [tex]\( +4.10 \times 10^{-12} \)[/tex] C, the net force [tex]\( F \)[/tex] acting on it is [tex]\( 1.54 \times 10^{-9} \)[/tex] N, pointing directly upward. This means that the magnetic force is not sufficient to cancel the electric force, and the net force is due to the electric force only:

[tex]\[ F = qE \][/tex]

We can use this equation to find the speed [tex]\( v' \)[/tex] of the different particle. Since the net force is equal to the electric force, the magnetic force must be zero. This implies that the velocity of the particle is such that the magnetic force component is equal and opposite to the electric force component, but since the net force is not zero, the particle is not moving at the correct speed to pass through undeflected.

Let's solve for the speed [tex]\( v' \)[/tex] of the different particle:

[tex]\[ F = qE \][/tex]

[tex]\[ 1.54 \times 10^{-9} \, \text{N} = (4.10 \times 10^{-12} \, \text{C})(2170 \, \text{N/C}) \][/tex]

[tex]\[ v' = \frac{F}{qB} \][/tex]

We know [tex]\( F \), \( q \), and \( E \)[/tex], but we need to find [tex]\( B \)[/tex] from the information given for the undeflected particles:

[tex]\[ qvB = qE \][/tex]

[tex]\[ vB = E \][/tex]

[tex]\[ B = \frac{E}{v} \][/tex]

[tex]\[ B = \frac{2170 \, \text{N/C}}{5.45 \times 10^3 \, \text{m/s}} \][/tex]

[tex]\[ B = 3.98 \times 10^{-4} \, \text{T} \][/tex]

Now we can find [tex]\( v' \)[/tex]:

[tex]\[ v' = \frac{1.54 \times 10^{-9} \, \text{N}}{(4.10 \times 10^{-12} \, \text{C})(3.98 \times 10^{-4} \, \text{T})} \][/tex]

[tex]\[ v' = \frac{1.54 \times 10^{-9}}{1.6322 \times 10^{-15}} \][/tex]

[tex]\[ v' = 9.43 \times 10^5 \, \text{m/s} \][/tex]

Therefore, the speed of the different particle is [tex]\( 9.43 \times 10^5 \) m/s[/tex].

Answer:

13.79 revolutions

Explanation:

Velocity of ball = v = 34.5 m/s

Spin rate of ball = 26 revolutions/s

Distance between home plate and pitching mound = s = 18.3 m

Time taken by the ball to reach the home plate = t

[tex]t=\frac{18.3}{34.5}\ s[/tex]

Number of revolutions the ball completes is

[tex]26\times \frac{18.3}{34.5}=13.79[/tex]

∴Number of revolutions the ball completes before reaching home plate is 13.79

Answer:

The number of revolutions is 13.78

Explanation:

Given data:

v = speed = 34.5 m/s

d = distance = 18.3 m

spin rate = 26 rev/s

The time taken is equal to:

[tex]t=\frac{d}{v} =\frac{18.3}{34.5} =0.53s[/tex]

The number of revolutions is equal:

N = 0.53 * 26 = 13.78 rev

Answer:

[tex]v_f = 27.9 m/s[/tex]

Explanation:

Component of the weight of the truck along the inclined plane is given as

[tex]F_1 = W sin\theta[/tex]

[tex]F_1 = 15000 sin15[/tex]

[tex]F_1 = 3882.3 N[/tex]

also the engine is providing the constant force to it as

[tex]F_2 = 8000 N[/tex]

now the net force along the the plane is given as

[tex]F_{net} = 8000 + 3882.3[/tex]

[tex]F = 11882.3 N[/tex]

mass of the truck is given as

[tex]m = \frac{w}{g} = 1529 kg[/tex]

now the acceleration is given as

[tex]a = \frac{F}{m}[/tex]

[tex]a = 7.77 m/s^2[/tex]

now the speed of the truck after travelling distance of d = 50 m is given as

[tex]v_f^2 = v_i^2 + 2 a d[/tex]

[tex]v_f^2 = 0 + 2(7.77)(50)[/tex]

[tex]v_f = 27.9 m/s[/tex]

Answer:

a). The potential is highest at the center of the sphere

Explanation:

We k ow the potential of a non conducting charged sphre of radius R at a point r < R is given by

[tex]E=\left [ \frac{K.Q}{2R} \right ]\left [ 3-(\frac{r}{R})^{2} \right ][/tex]

Therefore at the center of the sphere where r = 0

[tex]E=\left [ \frac{K.Q}{2R} \right ]\left [ 3-0 \right ][/tex]

[tex]E=\left [ \frac{3K.Q}{2R} \right ][/tex]

Now at the surface of the sphere where r = R

[tex]E=\left [ \frac{K.Q}{2R} \right ]\left ( 3-1 \right )[/tex]

[tex]E=\left [ \frac{2K.Q}{2R} \right ][/tex]

[tex]E=\left [ \frac{K.Q}{R} \right ][/tex]

Now outside the sphere where r > R, the potential is

[tex]E=\left [ \frac{K.Q}{r} \right ][/tex]

This gives the same result as the previous one.

As [tex]r\rightarrow \infty , E\rightarrow 0[/tex]

Thus, the potential of the sphere is highest at the center.

Answer:

a) Magnitude of the average velocity from t = 0 to t = 2 s = 2.24 m/s

b) Magnitude of the average velocity from t = 0 to t = 5 s = 3.16 m/s

Explanation:

a) Velocity is rate of change of position.

A particle's position coordinates (x, y) are (1.0 m, 3.0 m) at t = 0

A particle's position coordinates (x, y) are (5.0 m, 5.0 m) at t = 2.0 s

Displacement = (5-1)i + (5-3)j = 4i + 2j

Change in time = 2s

Velocity

      [tex]v=\frac{4i+2j}{2}=2i+j[/tex]

Magnitude of velocity

      [tex]v=\sqrt{2^2+1^2}=2.24m/s[/tex]

b) Velocity is rate of change of position.

A particle's position coordinates (x, y) are (1.0 m, 3.0 m) at t = 0

A particle's position coordinates (x, y) are (14.0 m, 12.0 m) at t = 5.0 s

Displacement = (14-1)i + (12-3)j = 13i + 9j

Change in time = 5s

Velocity

      [tex]v=\frac{13i+9j}{5}=2.6i+1.8j[/tex]

Magnitude of velocity

      [tex]v=\sqrt{2.6^2+1.8^2}=3.16m/s[/tex]

Answer:

The baseball does not reach the wall, because the ball falls at 125.33 meters and the wall is at 150 meters

Explanation:

V= 37.5 m/s

α= 30º

g= 9.8 m/s²

Vx= V * cos(30º) = 32.47 m/s

Vy= V * sin(30º) = 18.75 m/s

flytime of the baseball:

t= 2 * Vy/g

t= 3.86 sec

distance of baseball fall:

d= Vx * t

d= 125.33 m

Answer: 18.67 m wall

Explanation:this is projectile.

For Max height,

H = v²sin²©/2g

H= (37.5)²sin²(30)/(2*9.81)

H = 17.919 m

But he is standing 0.751 m above ground, so total height = 17.919+0.751= 18.67m

The object is moving along a circular path. Given the time restriction, it completes a half revolution, which equates to half the circumference of the circle. Therefore, the object travels approximately 31.4 units.

The object is moving on a circular trajectory defined by r(t) = <10 cos 6t, 10 sin 6t>. This equation describes a circular path with a radius of 10 units. To find out how far the object travels, we can use the formula for the circumference of a circle, which is 2πr. However, since the time t varies from 0 to π, the object only makes a half revolution along the circle. So, the total distance the object travels would be equal to half the circumference of the circle, which is πr.

Substituting r = 10, we get, distance traveled = π*10 = 31.4 units approx.

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Answer:

option (a)

Explanation:

The direction of magnetic field is given by Fleming's left hand rule.

If we spread the fore finger, middle finger and the thumb of our right hand such that they are mutually perpendicular to each other, then the direction of force is in the direction of thumb, direction of magnetic field is given by the direction of fore finger and the middle finger indicates the direction of current .

Here, current is upwards, magnetic force is rightwards, so the direction of magnetic field is given in outwards from the screen.