The circuit to the right consists of a battery ( V 0 = 64.5 V) (V0=64.5 V) and five resistors ( R 1 = 711 (R1=711 Ω, R 2 = 182 R2=182 Ω, R 3 = 663 R3=663 Ω, R 4 = 534 R4=534 Ω, and R 5 = 265 R5=265 Ω). Find the current passing through each of the specified points. -g

Answer:

D. Battery

During the oxidation-reduction(redox) reaction, there is always flow of electrons from one point to another. The electrons are then converted to power through the battery which converts chemical energy to electrical energy. If there is zero flow of electrons then there will also be zero power.

Answer:

D. A battery.

Explanation:

A battery cell refers to a single anode and cathode separated by electrolyte used to produce a voltage and current. It is typically an electrolytic cell.

An electrolytic cell is an electrochemical cell that drives a non-spontaneous redox reaction through the application of electrical energy. They are often used to decompose chemical compounds, in a process called electrolysis.

The anode which is positive electrode undergoes oxidation i.e loss of electrons while the cathode(negative) undergoes reduction that is, accept electrons.

Answer:

2.8 rad/s

Explanation:

In absence of external forces, the total angular momentum of the system must be conserved.

The angular momentum when the arms of the student are extended horizontally is given by:

[tex]L_1 = (I_0 + 2I)\omega_1[/tex]

where:

[tex]I_0=3.8 kg m^2[/tex] is the moment of inertia of the student+stool

[tex]I=mr^2[/tex] is the moment of inertia of each mass, where:

m = 2.6 kg is one mass

r = 0.71 m is the distance of each mass from the rotation axis

[tex]\omega_1=1.8 rad/s[/tex] is the initial angular velocity

So we have

[tex]L_1=(I_0+2mr^2)\omega_1[/tex]

When the student pulls the weights to a distance of r' = 0.23 m, the angular momentum is:

[tex]L_2=(I_0+2I')\omega_2[/tex]

where:

[tex]I'=mr'^2[/tex] is the new moment of inertia of each mass, with

r' = 0.23 m

Since the angular momentum must be constant, we have:

[tex]L_1=L_2\\(I_0+2mr^2)\omega_1 = (I_0+2mr'^2)\omega_2[/tex]

and solving for [tex]\omega_2[/tex], we find the final angular velocity:

[tex]\omega_2 = \frac{I_o+2mr^2}{I_0+2mr'^2}\omega_1=\frac{3.8+2(2.6)(0.71)^2}{3.8+2(2.6)(0.23)^2}(1.8)=2.8 rad/s[/tex]

Answer:

the total number of persons between the ages of 16 and 65

Explanation:

The labour force consists of all the people who are able to work in a country or area, or all the people who work for a particular company.

The workforce of a country includes both the employed and the unemployed (labour force)

The labor force of a nation includes all employed and unemployed persons, excluding those not actively seeking work. Employed individuals have a job, while unemployed individuals are jobless but actively looking for work. The unemployment rate measures the percentage of the labor force that is unemployed.

A nation's labor force is best defined as the total number of employed and unemployed persons. Specifically, it includes all individuals who are either currently working (employed) or actively seeking employment (unemployed). The labor force does not include those who are not seeking work, such as students, stay-at-home parents, individuals with disabilities preventing them from working, or those who have taken early retirement.

The unemployment rate is a key economic indicator that represents the percentage of the labor force that is unemployed. It's important to note that to be considered unemployed, a person must be actively looking for work and available to work. This excludes people who are not actively seeking employment, who are then categorized as out of the labor force.

Lastly, the definition of 'employed' in the United States is quite broad, including those working part-time or temporarily, as well as individuals on leave but who have a job.

The work done by the gas on the bullet while the bullet travels the length of a 0.54m barrel was calculated to be 9,354.80 joules, and the work done for a 1.05m barrel length was calculated to be -5,712.50 joules.

The work done by the force of the gas on the bullet can be determined by calculating the integral of the force with respect to x, from 0 to the length of the barrel. The force is a function of x, F(x) = 16,000 + 10,000x - 26,000x^2. The work done W = ∫F(x) dx, from x = 0 to x = 0.54 m.

By integrating this function we have, W = 16,000x + 5,000x^2 - 26,000x^3/3. Substituting the upper and the lower limits in, we get W = 9,354.80 joules.

For part B) we calculate work using the same formula but changing the length of the barrel to 1.05 m. The Calculated work done by the gas on the bullet, when the length of the barrel is 1.05 m, is W = -5,712.50 joules. Here, negative work signifies that the bullet is working against the direction of the force.

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To compute the work done by the gas on the bullet as it travels the length of the barrel, we use an integral to sum the work done over the length of the barrel. The force function given is integrated across the range from 0 to the length of the barrel (either 0.5400 m or 1.05 m).

The work done by a variable force in one-dimension can be computed using the formula:

Work = ∫F(x) dx

Where F(x) is given as (16,000 + 10,000x - 26,000x^2) N and the limits of the integral are from 0 to the length of the barrel. For a 0.5400 m barrel, we evaluate the integral with these limits. Similar for the second part, using 1.05 m as the upper limit.

The actual calculations would involve integrating the function for force (F), and then substituting the limits of 0 and 0.5400 m or 1.05 m in the result to calculate the work done.

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Answer:

[tex]3.8\times 10^{-8}\ H[/tex]

Explanation:

Given the [tex]6.7\mu F[/tex] capacitor is used in an LC circuit to produce [tex]10\ kHz[/tex] frequency.

We need to find the value of inductance required.

As we know the relation between angular frequency in [tex]rad/sec[/tex] and frequency in [tex]Hz[/tex] is.

[tex]\omega =2\times \pi\times f[/tex]

Where [tex]\omega[/tex] is angular frequency and [tex]f[/tex] is frequency.

[tex]\omega=2\times \pi\times 10\times 1000=20000\pi\ rad/sec\\\omega=62832\ rad/sec[/tex]

Also, the relation between the angular frequency, capacitance and inductance is given by.

[tex]\omega^2=\frac{1}{LC}\\\\L=\frac{1}{\omega^2C} \\\\L=\frac{1}{62832^2\times6.7\times 10^{-6} } \\\\L=\frac{1}{26451}.\\ \\L=3.8\times 10^{-8}\ H[/tex]

So, [tex]3.8\times 10^{-8}\ H[/tex] inductance will be required to produce [tex]10\ kHz[/tex].

Answer:

that the angle must be increased to maintain the minimum time of discrimination due to the increase in the speed of sound in material

Explanation:

The direction of sound is detected by the difference in time of reception of each ear, the speed of the wave is

             v = d / t

             t = d / v

In air the velocity is v = 330 m / s, let's use trigonometry

           Cos 3 = d / L

           L = d / cos 3

The difference in distance is

            Δd = d - d / cos 3 = d (1- 1 / cos3)

             t = Δd / 330

When the animal is in the water the speed of sound is

              v = 1540 m / s

So time is

             t' = Δd ’/ 1540

            t ’= Dd’ / 4.67  330

So if  t = t’  is the minimum response time, the distance must be increased

            Δd ’= 4.6 Δd

            1-1 / cos θ = 4.6 (1- 1 / cos 3) = -4.6 0.00137 = -0.00631

           1 + 0.0063 = 1 / cos θ

           1.00631 = 1 / cos θ

           Cos θ = 1 / 1.00631

           Tea = 6.5

We see that the angle must be increased to maintain the minimum time of discrimination due to the increase in the speed of sound in material

Explanation:

(a)   Formula to calculate the force of kinetic friction is as follows.

             f = [tex]\mu N[/tex]

                = [tex]\mu mg Cos (\theta)[/tex]

Putting the given values into the above formula as follows.

          f = [tex]\mu mg Cos (\theta)[/tex]

           = [tex]0.118 \times 57.4 kg \times 9.8 \times Cos (28.1^{o})[/tex]

           = [tex]0.118 \times 57.4 kg \times 9.8 \times 0.882[/tex]

           = 58.54 N

Hence, the force of kinetic friction is 58.54 N.

(b)    Net force experienced by the block will be as follows.

            F = [tex]mg Sin (\theta) - f[/tex]

         ma = [tex]mg Sin (\theta) - \mu mg Cos (\theta)[/tex]

or,         a = [tex]g[Sin (\theta) - \mu Cos (\theta)][/tex]                  

                = [tex]9.8[Sin(28.1) - Cos(28.1)][/tex]

                = [tex]9.8 \times (0.471 - 0.882)[/tex]

                = 4.03 [tex]m/s^{2}[/tex]

Therefore, the acceleration is 4.03 [tex]m/s^{2}[/tex].

(c)    According to the third equation of motion,

          [tex]v^{2} = u^{2} + 2as[/tex]

                    = [tex]0 + 2 \times 4.03 \times 17.2[/tex]        

                    = 138.63 m/s

Hence, the speed she is traveling when she reaches the bottom of the slide is 138.63 m/s.

Answer:

Explanation:

mass, m = 57.4 kg

distance, d = 17.2 m

angle of inclination, θ = 28.1°

initial velocity, u = 0 m/s

coefficient of kinetic friction, μk = 0.108

(a) N is the normal reaction acting on the student.

N = mg Cosθ

N = 57.4 x 9.8 x Cos 28.1

N = 496.2 N

Friction force = μk x N

Friction force = 0.108 x 496.2 = 53.6 N

Let a is the acceleration

ma = mg Sinθ - friction force

ma = 57.4 x 9.8 x Sin 28.1 - 53.6

a = 3.7 m/s²

Let the speed is v.

v² = u² + 2ad

v² = 0 + 2 x 3.7 x 17.2

v = 11.3 m/s

Let us consider the object to be a cell.

Explanation:

As a cell grows bigger, its internal volume enlarges and the cell membrane expands. This results in the increase in volume more rapidly than does the surface area, and so the relative amount of surface area available to pass materials to a unit volume of the cell steadily decreases. This means the surface area to the volume ratio gets smaller as the cell gets larger.

Example of a cube:

Cube size            Surface area                   Volume

2cm                      2 × 2 × 6 = 24 cm²         2 × 2 × 2 = 8 cm³

4 cm                      4 × 4 × 6 = 96 cm²         4 × 4 × 4 = 64 cm³

6 cm                      6 × 6 × 6 = 216 cm²       6 × 6 × 6 = 216 cm³

8 cm                      8 × 8 × 6 = 384 cm²       8 × 8 × 8 = 512 cm³

This shows as the object gets larger, the volume of an object increases faster than the surface area.

Answer:

the final velocity of the cart is 5.037m/s

Explanation:

Using the conservation of energy

[tex]T_a + V_a = T_b + V_b[/tex]

[tex]T_a = \frac{1}{2} (m_c + m_b)v_a^2[/tex]

[tex]T_a= \frac{1}{2} (3 + 0.5)(0)^2[/tex]

= 0

[tex]V_a = (m_c + m_b)gh_a[/tex]

[tex]V_a = (3 + 0.5) * 9.81 * 1.24[/tex]

[tex]= 42.918J[/tex]

[tex]T _b = \frac{1}{2} (3 + 0.5)v_b^2 \\\\ = 1.75v_b^2[/tex]

[tex]V_b = (3 + 0.5) * 9.81 * 0\\ = 0[/tex]

[tex]T_a + V_a = T_b + V_b\\ 0 + 12.918 = 1.75v_b^2 + 0\\v_b = 4.95m/s[/tex]

Using the conservation of linear momentum

[tex](m_c + m_b)v_B = m_cv_c + m_bv_b\\(3 + 0.5) * 4.95 = 3v_c - 0.5v_b\\17.33 = 3v_c - 0.5v_b\\v_b = 6v_c - 34.66 ...............(1)[/tex]

[tex]Utilizing the relative velocity relation = v_b - v_c\\-0.6 = -v_b - v_c\\v_b = 0.6 - v_c (2)[/tex]

equate (1) and (2)

[tex]6v_c - 34.66 = 0.6 - v_c\\7v_c = 35.26\\v_c = 5.037m/s[/tex]

the final velocity of the cart is 5.037m/s

Answer:

Doppler shift of the starlight

Explanation:

To predict the movement of a star, we compare the spectra of elements found in star (H, He Na etc.), first spectra which are obtained from star and second spectra from laboratory. If spectral lines of the spectra obtained from star, are shifting towards red end (called red shift) then star is going away from earth and if shifting is towards blue (called blue shift), then star is approaching the earth. This is Doppler's shift.

Answer:

Explanation:

mass, m = 1 kg

specific heat, c = 1.5 J/g°C

rise in temperature, ΔT = 41 - 21 = 20

heat released, H = m x c x ΔT

H = 1 x 1.5 x 1000 x 20

H = 30,000 J

H = 30 kJ.

Answer:

Explanation:

on edg I got it right

Explanation:

Below is an attachment containing the solution.

Explanation:

The best methods for the transfer of heat are conduction convection, radiation and sometimes evaporation also.

Answer:Condution radiation convection

Explanation:

Final answer:

When the charge moves 0.450 m to the right, the work done is zero. When the charge moves 0.670 m upward, the work done can be calculated as (28.0 nC * Electric Field) * 0.670 m. When the charge moves 2.60 m at an angle of 45.0° downward from the horizontal, the work done can be calculated as (28.0 nC * Electric Field * cos(45.0°)) * 2.60 m.

Explanation:

In order to calculate the work done by the electric force, we can use the equation:

Work = Force * Distance

For part (a) when the charge moves 0.450 m to the right, we need to calculate the force first using the equation:

Force = Charge * Electric Field

Given that the charge is 28.0 nC and the electric field is directed vertically upward, we should consider the vertical component of the electric field. Since the charge is moving horizontally to the right, it is perpendicular to the electric field and does not contribute to the work done by the electric force. Therefore, the work done is zero.

For part (b) when the charge moves 0.670 m upward, we can calculate the force using the same equation. Since the charge moves in the same direction as the electric field, the work done is positive. The work done can be calculated as:

Work = Force * Distance = (28.0 nC * Electric Field) * 0.670 m

For part (c) when the charge moves 2.60 m at an angle of 45.0° downward from the horizontal, we can break down the movement into horizontal and vertical components. The horizontal component does not contribute to the work done by the electric force since it is perpendicular to the electric field. The vertical component contributes to the work done. We can calculate the vertical component of the distance traveled using the angle and multiply it by the electric field to get the force. The work done can be calculated as:

Work = Force * Distance = (28.0 nC * Electric Field * cos(45.0°)) * 2.60 m

Answer:

The jet will fly 2400 km.

Explanation:

Given the velocity of the jet flying toward the east is 1,500 kmph toward the east.

We need to find the distance covered in 1.6 hours.

In our problem we are given speed and time, we can easily determine the distance using the following formula.

[tex]Distance=Speed\times Time[/tex]

[tex]Distance=1500\times 1.6=2400\ km[/tex]

So, the supersonic jet will travel 2400 km in 1.6 hours toward the east from its starting point.

Answer:

The correct option is

(e)either (c) or (d) could be correct.

Explanation:

The electric field of a charge radiates out in all directions and the intensity of the electric field strength given by E = F/q₀, diminishes as the lines of force moves further away from the source. The direction of F and E is in the line of potential motion of the source charge in the field.

Equipotential surfaces are locations in the radiated electric that have the same field strength or electric potential. The work done in moving within an equipotential surface is zero and as such since

Work = Force × distance = 0 where distance ≠ 0.

The force acting between two points on an equipotential surface is also zero or the component of the force within an equipotential surface is zero and since there is a force in the electric field, it is acting at right angles to the equipotential surface which could be horizontally to the left or right directions where the equipotential surfaces due to the charge distribution are in the vertical plane.

Therefore it is either horizontally to the left, or horizontally to the right.

Answer:

a. The pulses cancel each other resulting in zero displacement.

b. The pulses reinforce each other, having a displacement of 2× amplitude or 0.56 m.

Explanation:

When the pulse are sent down the attached string  it gets reflected and we have crossing pulses as the incident and reflected pulses cross each other.

a. If the string is rigidly attached to the post then the incident and reflected pulses will have the same amplitude but different direction. That is either the reflected will be going up and the incident down thereby resulting in a cancellation or zero displacement

Incident amplitude = 0.28 m

Reflected amplitude = -0.28 m

Sum = 0.28 m - 0.28 m = 0 m

b. If the end at which the relfection occurs is free to slide, then the incident and the reflected pulses will again have the same amplitude and in this case, the same direction. Therefore;

Incident amplitude = 0.28 m

Reflected amplitude = 0.28 m

Sum = 0.28 m + 0.28 m = 0.56 m

Answer:

The answer is zero displacement (0 m)

Explanation:

If the end of the string is not free, the reflected pulse has the same amplitude but opposite polarity to the incident pulse. Because of this, for A, the result equals zero (0 m).

Answer:

[tex]h = 2.821\,m[/tex]

Explanation:

The speed of the actor before the collision is found by means of the Principle of Energy Conservation:

[tex](83\,kg)\cdot(9.807\,\frac{m}{s})\cdot (3.90\,m) = \frac{1}{2}\cdot (83\,kg)\cdot v^{2}[/tex]

[tex]v = \sqrt{2\cdot (9.807\,\frac{m}{s^{2}} )\cdot (3.90\,m)}[/tex]

[tex]v \approx 8.746\,\frac{m}{s}[/tex]

The speed after the inelastic collision is obtained by using the Principle of Momentum Conservation:

[tex](83\,kg)\cdot (8.746\,\frac{m}{s} )+(55\,kg)\cdot (0\,\frac{m}{s} ) = (83\,kg + 55\,kg)\cdot v[/tex]

[tex]v = 5.260\,\frac{m}{s}[/tex]

Lastly, the maximum height is determined by using the Principle of Energy Conservation again:

[tex]\frac{1}{2}\cdot (138\,kg)\cdot (5.260\,\frac{m}{s} )^{2} = (138\,kg)\cdot (9.807\,\frac{m}{s^{2}} )\cdot h[/tex]

[tex]h = \frac{(5.260\,\frac{m}{s} )^{2}}{9.807\,\frac{m}{s^{2}} }[/tex]

[tex]h = 2.821\,m[/tex]

Answer:7.67

Explanation:

Given

Weight of Cathy [tex]W_1=460\ N[/tex]

Force exerted by rope [tex]F=60\ N[/tex]

Mechanical advantage is the ratio of load by Pulling effort      

[tex]M.A.=\frac{Load}{Pulling\ effort}[/tex]

[tex]M.A.=\frac{460}{60}[/tex]

[tex]M.A.=7.67\ N[/tex]

Final answer:

The actual mechanical advantage of the pulley system that hoists Cathy is calculated by dividing the load force (460 N) by the effort force (60 N), resulting in an actual mechanical advantage of approximately 7.67.

Explanation:

The actual mechanical advantage (MA) of a pulley system is the ratio of the load force to the effort force. Given that Cathy, a 460-N actress, is raised with an effort of 60 N, we can calculate the actual mechanical advantage by using the formula MA = Load/Effort. By dividing 460 N by 60 N, we get an actual mechanical advantage of approximately 7.67. This implies that the pulley system is using 7.67 times less effort force to lift the load, thus increasing the efficiency of the task.

Pulley systems can provide significant mechanical advantage by allowing a smaller effort force to move a larger load. This effectiveness is heightened if the pulleys are arranged in such a way as to multiply the tension in the ropes as they support the load. With perfectly friction-free pulleys and ropes, the MA can be simply counted as the number of ropes supporting the load, making the force output nearly an integral multiple of the input force.

Answer:

Moment of inertia and angular velocity.

Explanation:

The translational kinetic energy of an object is possessed when the object is showing rotational motion. It can be given by the formula as :

[tex]KE=\dfrac{1}{2}I\omega^2[/tex]

Here,

I is the moment of inertia of the object

[tex]\omega[/tex] is the angular velocity of the object

So, the translational kinetic energy of an object is given by moment of inertia and angular velocity of the object. Hence, this is the required solution.

Answer:

The answer to the question is

3340800 m far

Explanation:

To solve the question, we note that acceleration = 29 m/s²

Time of acceleration = 8 minutes

Then if the shuttle starts from rest, we have

S = u·t+0.5·a·t² where u = 0 m/s = initial velocity

S = distance traveled, m

a = acceleration of the motion, m/s²

t = time of travel

S = 0.5·a·t² = 0.5×29×(8×60)² = 3340800 m far

Answer:

θ = 53.7°

Explanation:

Given:

- The mass of ball = M

- The mass of object = 3M

- The wire length L = 0.5 m

- The velocity of ball vi = 4.0 m/s

- The velocity of ball vf

- The velocity of object Vf

Find:

Find the maximum angle through which the block swings after it is hit.

Solution:

- When two objects collide with no external force acting on the system the linear momentum of the system is conserved. The initial (Pi) and final (Pf) linear momentum are equal:

                                  Pi = Pf

                                  M*vi = M*vf + 3M*Vf

                                  vi = vf + 3*Vf

                                  4 = vf + 3*Vf

- For elastic collision between two particles the relative velocities before and after collision have the same magnitude but opposite sign; so,

                                   vi - 0 = Vf - vf

                                   4 = Vf - vf

- Solve the above two equation simultaneously.

                                   8 = 4*Vf

                                   Vf = 2 m/s

                                    vf = -2 m/s

- When the ball hits the object it swing under the influence of gravity only. Hence, no external force acts on the object so we can apply the conservation of energy as the object attains a height h.

                                   ΔK.E = ΔP.E

                                   0.5*(3M)*Vf^2 = (3M)*(g)*(h)

                                   h = Vf^2 / 2*g

- Plug in the values:

                                   h = 2^2 / 2*9.81

                                   h = 0.2039 m

- We can see that the maximum angle can be given as θ according trigonometric relation as follows:

                                  θ = arccos [ ( L - h ) / L ]

                                  θ = arccos [ ( 0.5 - 0.2039 ) / 0.5 ]

                                  θ = 53.7°

The maximum angle through which the block swings after it is hit θ is = 53.7°

Given:

The mass of ball is = M

The mass of object is = 3M

The wire length L is = 0.5 m

The velocity of ball vi is = 4.0 m/s

Then The velocity of ball vf

After that The velocity of object Vf

Now we Find:

Find the maximum angle through which the block swings after it is hit that is :

When two objects collide with no external force acting on the system the linear momentum of the system is conserved. Then The initial (Pi) and also final (Pf) linear momentum are equal:

Pi is = Pf

M*vi is = M*vf + 3M*Vf

vi is = vf + 3*Vf

4 is = vf + 3*Vf

Now For elastic collision between two particles the relative velocities before and also after collision have the same magnitude but opposite signs; so,

vi - 0 is = Vf - vf

4 is = Vf - vf

Solve the above two equations simultaneously.

8 is = 4*Vf

Vf is = 2 m/s

vf is = -2 m/s

When the ball hits the object it swings under the influence of gravity only. Hence proof, no external force acts on the object so we can apply the conservation of energy as the object attains a height h.

ΔK.E is = ΔP.E

0.5*(3M)*Vf^2 is = (3M)*(g)*(h)

h is = Vf^2 / 2*g

Then we Plug in the values is:

h is = 2^2 / 2*9.81

h is = 0.2039 m

Now We can see that the maximum angle can be given as θ according trigonometric relation as follows:

θ is = arccos [ ( L - h ) / L ]

θ is = arccos [ ( 0.5 - 0.2039 ) / 0.5 ]

θ is = 53.7°

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To find the velocity of the first car after the collision, we can use the principle of conservation of momentum.

To find the velocity of the first car after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Before the collision:

Total momentum = (mass of first car × velocity of first car) + (mass of second car × velocity of second car)

After the collision:

Total momentum = (mass of first car × velocity of first car after collision) + (mass of second car × velocity of second car after collision)

Using the given information and the principle of conservation of momentum, we can solve for the velocity of the first car after the collision.

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Answer:

8.5m/s

Explanation:

We are given that

Mass of object=m=0.50 kg

Initial velocity, u=0

Force=F=2.88 N

Time=1.48 s

a.We know that

[tex]F=ma[/tex]

Using the formula

[tex]2.88=0.50a[/tex]

[tex]a=\frac{2.88}{0.50}=5.76m/s^2[/tex]

[tex]a=\frac{v-u}{t}[/tex]

Using the formula

[tex]5.76=\frac{v-0}{1.48}[/tex]

[tex]v=5.76\times 1.48=8.5m/s[/tex]

Hence, the velocity of the object at the end of this time interval=8.5m/s

Answer: Option (a) is the correct answer.

Explanation:

It is known that potential energy is the energy occupied by an object or substance due to its position is known as potential energy.

Therefore, more is the space occupied by an object more will be its position at a particular location. Hence, more will be its potential energy. On the other hand, smaller is the space occupied by an object, smaller will be the position holded by it.

Hence, smaller will be its potential energy.

Thus, we can conclude that for the given situation the statement, potential energy of the larger sphere is greater than that of the smaller sphere, is true.

Final answer:

The potential energy of the larger conducting sphere is less than that of the smaller sphere because electric potential is inversely proportional to radius and both spheres carry the same charge.

Explanation:

When two conducting spheres with the same excess charge but different radii are considered, the potential of each sphere is given by V = kQ/R, where V is the potential, k is Coulomb's constant, Q is the charge, and R is the radius of the sphere. Since the charge Q is the same for both spheres, but the radius R is larger for one of them, the electric potential energy will be higher for the smaller sphere since it has a smaller radius. This stems from the fact that electric potential is inversely proportional to the radius, meaning a smaller radius results in a higher potential for the same amount of charge.

The correct statement is: (d)he potential energy of the larger sphere is less than that of the smaller sphere.

Answer:

2.55 m

Explanation:

The motion of the dancer is the motion of a projectile, which consists of 2 independent motions:

- A uniform motion (constant velocity) along the horizontal direction

- A uniformly accelerated motion (constant acceleration) along the vertical direction

The horizontal range of a projectile can be found by using the equations of motions along the two directions, and it is given by:

[tex]d=\frac{v^2 sin(2\theta)}{g}[/tex]

where

v is the intial velocity

[tex]\theta[/tex] is the angle of projection

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

For the dancer in this problem, we have:

v = 5 m/s

[tex]\theta=45^{\circ}[/tex]

Therefore, the horizontal range is:

[tex]d=\frac{(5)^2(sin 2\cdot 45^{\circ})}{9.8}=2.55 m[/tex]

Answer:

(A). The tension in the rope that connects the boxes is 10.50 N.

(B). The value of m is 7 kg.

Explanation:

Given that,

Mass of box B = 5.00 kg

Mass of box A = m

Force = 40.0 N

Direction= 53.1°

Acceleration = 1.50 m/s²

Coefficient of kinetic friction = 0.30

(A). We need to calculate the tension in the rope that connects the boxes

Using balance equation

[tex]T=ma+m\cos\theta[/tex]

Put the value into the formula

[tex]T=5\times1.50+5.00\cos53.1[/tex]

[tex]T=10.50\ N[/tex]

(B). We need to calculate the value of m

Using formula of tension

[tex]T=ma[/tex]

[tex]m=\dfrac{T}{a}[/tex]

Put the value into the formula

[tex]m=\dfrac{10.50}{1.50}[/tex]

[tex]m=7\ kg[/tex]

Hence, (A). The tension in the rope that connects the boxes is 10.50 N.

(B). The value of m is 7 kg.

Answer:

Distance covered by Tevin before his tire went flat = 24 miles

Explanation:

Let x be the distance covered by Tevin before his tire went flat.

Given:

Tevin drives his bike in the town = 6 mph  

Tevin back to his house = 3 mph

Total taken time by Tevin = 12 hours

We need to find the distance covered by Tevin in 12 hours.

Solution:

Using speed formula    

[tex]Speed =\frac{Distance}{Time}[/tex]

We write the above formula for Time.

[tex]Time=\frac{Distance}{Speed}[/tex]-----------(1)

Time taken by Tevin when biking in town

Substitute speed = 6 mph and distance = x in equation 1.

[tex]Time=\frac{x}{6}[/tex]  ----------(2)

Time taken by Tevin when he is back to his house.

Substitute speed = 3 mph and distance = x in equation 1.

[tex]Time=\frac{x}{3}[/tex]   -------------(3)

Total time taken by Tevin.

Total taken time by Tevin = Time taken when biking in town + Time taken when Tevin back to his house.

Substitute time value from equation 2 and 3 in above equation and total time = 12 hours.

[tex]12=\frac{x}{6}+\frac{x}{3}[/tex]

Now, we solve the above equation for x.

[tex]12=\frac{x+2x}{6}[/tex]

[tex]12\times 6=x+2x[/tex]

[tex]72=3x[/tex]

[tex]x=\frac{72}{3}[/tex]

[tex]x=24\ mi[/tex]

Therefore, distance covered by Tevin in 12 hours is equal to 24 miles.

Answer:

Maximum velocity: Position C, Maximum positive acceleration: Position A.

Explanation:

Let consider that spring is compressed in the negative direction. Then, the maximum velocity occurs at position C, when spring is not compressed nor stretched. Since force in spring is of reactive nature, that is, the direction of force is opposed to the direction of movement, a maximum positive acceleration occurs at position A.