An 8kg bullet is shot into a 4kg block , at rest on a frictionless horizontal surface . The bullet remains lodged in the block.The block moves into an ideal massless spring and compresses it by 8, 7cm. The spring constant of the spring is 2400n/m.What is the initial speed of the bullet?

Given that,

Initial speed, u = 20 km/s

Acceleration of plane, a = 2.4 km/h²

Time, t = 59 s

We need to find the expression to find the final velocity of an object.Let the final velocity is v.

Using the second equation of kinematics:

\(\Delta s=ut+\dfrac{1}{2}at^2\)

a is acceleration, \(a=\dfrac{v-u}{t}\)

So,

\(\Delta s=ut+\dfrac{1}{2}\times \dfrac{v-u}{t}\times t^2\\\\\Delta s=ut+\dfrac{1}{2}(v-u)t\\\\\Delta s=\dfrac{2ut+vt-ut}{2}\\\\\Delta s=\dfrac{vt+ut}{2}\\\\\Delta s=(\dfrac{v-u}{2})t\)

We can use the above formula to find the final velocity (v) of the plane.

Answer:

a. Q = 1881.73 x \(10^{-13}\) C

b. As battery is not removed so, potential difference will remain same.

c. E = 21.42 x \(10^{3}\) V/m

d. Q = 895.5 x \(10^{-13}\) C

e. Again the potential difference will not change it will remain same as 9 V

f. E = 45 x \(10^{3}\) V/m

Explanation:

Solution:

Here, Teflon is used so, the dielectric constant of the Teflon K = 2.1

Diameter = 2.1 cm

Radius = 2.1/2 cm

Radius = 1.05 cm

Radius = 0.015 m

Now, we need to find the area of each plate:

A = \(\pi r^{2}\)

A = (3.14) (\(0.015^{2}\))

A = 0.000225 \(m^{2}\)

A = 2.25 x \(10^{-4}\) \(m^{2}\)

We are given the thickness of the plate which equal to the distance between the two plates.

d = 0.20 mm = 0.2 x \(10^{-3}\) m

d = 0.2 x \(10^{-3}\)  m = distance between two plates.

Hence, the capacitance of the dielectric without the dielectric

C = \(\frac{E.A}{d}\)

Putting up the values we get,

E = 8.85 x \(10^{-12}\)

C = \(\frac{8.85 . 10^{-12} x 2.25 . 10^{-4} }{0.002}\)    

C = 99.5 \(10^{-13}\)

If dielectric is included then,

\(C^{'}\) = K C

\(C^{'}\) = (2.1) ( 99.5 x \(10^{-13}\))

\(C^{'}\) = 209.08 x \(10^{-13}\) F

As we know the voltage of the battery V = 9V So,

a) Charge before the Teflon is removed:

Q = CV

Q = \(C^{'}\)V

Q = (209.08 x \(10^{-13}\) F) (9V)

Q = 1881.73 x \(10^{-13}\) C

b) Potential Difference before the Teflon is removed = ?

As battery is not removed so, potential difference will remain same.

c) Electric Field =?

As we know,

E = V/(K.d)

E = 9V/(2.1 x 0.2 x \(10^{-3}\))

E = 21.42 x \(10^{3}\) V/m

d) After the Teflon is removed

Q = CV

Q = (99.5 \(10^{-13}\) ) ( 9)

Q = 895.5 x \(10^{-13}\) C

e) Again the potential difference will not change it will remain same as 9 V

f) Electric Field = ?

E = \(\frac{V}{d}\)  (Teflon is removed)

E = 9/0.2 x \(10^{-3}\)

E = 45 x \(10^{3}\) V/m

Answer:

432.78 Kg

Explanation:

From the question given above, the following data were obtained:

Distance apart (r) = 6.8 m

Force of attraction (F) = 5.4×10¯⁸ N

Mass of Daffy Duck (M₁) = 86.5 kg

Mass of Minnie Duck (M₂) =?

NOTE: Gravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²

The mass of Minnie Duck can be obtained as follow:

F = GM₁M₂ / r²

5.4×10¯⁸ = 6.67×10¯¹¹ × 86.5 × M₂ / 6.8²

5.4×10¯⁸ = 6.67×10¯¹¹ × 86.5 × M₂ / 46.24

Cross multiply

6.67×10¯¹¹ × 86.5 × M₂ =5.4×10¯⁸ × 46.24

Divide both side by 6.67×10¯¹¹ × 86.5

M₂ = 5.4×10¯⁸ × 46.24 / 6.67×10¯¹¹ × 86.5

M₂ = 432.78 Kg

Therefore, the mass of Minnie Duck is 432.78 Kg

Answer:

(a) The initial gravitational potential energy of the lead can be calculated using the formula:

E = mgh

where E is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height. Substituting the given values, we get:

E = (0.5 kg) × 10 m/s² × 25 m = 125 J

Therefore, the initial gravitational potential energy of the lead is 125 J.

(b) When the lead reaches the ground, all of its potential energy is converted into kinetic energy. The kinetic energy can be calculated using the formula:

E = (1/2)mv²

where E is the kinetic energy, m is the mass, and v is the velocity. At the moment of impact, the lead has a velocity of:

v = √(2gh) = √(2 × 10 m/s² × 25 m) = 10 m/s

Substituting the given values, we get:

E = (1/2) × 0.5 kg × (10 m/s)² = 25 J

Therefore, the kinetic energy of the lead on reaching the ground is 25 J.

(c) The energy gained by the lead due to the impact is converted into internal energy, which raises the temperature of the lead. The amount of energy required to raise the temperature of the lead can be calculated using the specific heat capacity formula:

Q = mcΔT

where Q is the energy gained, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. The specific heat capacity of lead is 128 J/kg°C. Substituting the given values, we get:

125 J - 25 J = (0.5 kg) × 128 J/kg°C × ΔT

ΔT = (100 J) / (64 J/kg°C) = 1.56°C

Therefore, the rise in temperature of the lead is 1.56°C.

(d) The energy transfers that have occurred from the moment the lead strikes the ground until it has cooled to air temperature again are:

Conversion of potential energy to kinetic energy upon impact

Conversion of kinetic energy to internal energy upon impact, raising the temperature of the lead

Transfer of heat energy from the lead to the surrounding air, as the lead cools down to air temperature

Answer:

Nancy Elizabeth Lieberman (nacido el 1 de julio de, 1958), apodado "Señora mágica", ] es un ex profesional jugador de baloncesto y entrenador de la WNBA (WNBA) que es actualmente un organismo de radiodifusión para los New Orleans Pelicans de la Nacional La Asociación de Baloncesto (NBA) y la entrenadora principal de Power , un equipo en el BIG3 que lideró en su Campeonato 0.]bLieerman es considerada como una de las figuras más importantes del baloncesto femenino estadounidense.

Explanation:

Answer:

D

Explanation:

Answer:

D

Explanation:

In a series circuit there is only one path for the current to complete the path....so D

Answer: Omitting g for weigh because problem omits g

Taking torque about left sawhorse

Mr * 6 = 3 * 10.5 + 4.45 * 1.8 = 31.5 + 8.0 = 39.5

Mr = 39.5 / 6 = 6.60       mass exerted upward by right sawhorse

6.6 + Ml = 10.5 + 4.45      balancing upward and downward mass

Ml = 8.4 kg        upward force (kg) exerted by left sawhorse

Check: take torque about right end

8.4 *  6 = 3 * 10.5 + 4.45 * 4.2

50.4 = 31.5 + 18.7  = 50.2       balances within rounding error

The upward force that the left sawhorse exerts on the board is 164 N.

Torque is defined as the rotational analogue of force. It is the cross product of force and the perpendicular distance.

Here,

Mass of the board, m₁ = 10.5 kg

Length of the board, L = 6 m

Torque of the board, τ₁ = m₁g x r₁

    τ₁ = 10.5 x 9.8 x (6/2)

    τ₁ = 308.7 Nm

Mass of the saw, m₂ = 4.45 kg

Length of the saw, r₂ = 6 - 1.8 = 4.2 m

Torque of the saw, τ₂ = m₂g x r₂

    τ₂ = 4.45 x 9.8 x 4.2

    τ₂ = 183.2 Nm

So,

Torque on the left saw = Torque on the board + torque on the saw

τ' = 308.7 + 183.2

τ' = 491.9

Therefore force exerted by the left saw, F = τ'/(L/2) = 491.9/3

  F = 164 N

Hence,

The upward force that the left sawhorse exerts on the board is 164 N.

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At maximum height, velocity is zero and kinetic energy will be zero.

K.E(A) = 0

P.E(A) = mgh = 200 x 9.8 x 30 = 58,800 J

K.E(B) = P.E(A) - P.E(B)

K.E(B) = 58,800 J - (200 x 9.8 x 25)

K.E(B) = 58,800 J - 49,000 J

K.E(B) = 9,800 J

K.E = ¹/₂mv²

v² = 2K.E/m

v² = (2 x 9800)/(200)

v² = 98

v = √98

v = 9.9 m/s

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Answer: i think its D.

Answer:

In an ionic bond the valence electrons are transferred from the metal

Explanation:

Answer:

the final speed of object A changed by a factor of  \(\frac{1}{\sqrt{3} }\) = 0.58

the final speed of object B changed by a factor of \(\sqrt{\frac{5}{3} }\) = 1.29

Explanation:

Given;

kinetic energy of object A, = 27 J

let the mass of object A = \(m_A\)

then, the mass of object B = \(m_B = \frac{m_A}{4}\)

work done on object A = -18 J

work done on object B = -18 J

let \(v_i\) be the initial speed

let \(v_f\) be the final speed

For object A;

\(K.E_A = 27\\\\\frac{1}{2} m_A v_i^2 = 27\\\\m_A v_i^2 = 54\\\\m_A = \frac{54}{v_i^2} ----Equation \ (1)\\\\Apply \ work-energy \ theorem;\\\\\delta K.E_A = -18\\\\\frac{1}{2} m_A v_f^2 - \frac{1}{2} m_A v_i^2 = -18\\\\\frac{1}{2} m_A ( v_f^2 \ - v_i^2 )\ =- 18\\\\v_f^2 \ - v_i^2 = -\frac{36}{m_A} ---Equation \ (2)\\\\v_f^2 \ - v_i^2 = -\frac{36v_i^2}{54}\\\\ v_f^2 \ =v_i^2 - \frac{36v_i^2}{54}\\\\ v_f^2 = \frac{54v_i^2 -36v_i^2 }{54} \\\\v_f^2 = \frac{18v_i^2}{54} \\\\v_f^2 = \frac{v_i^2}{3} \\\\\)

\(v_f = \sqrt{\frac{v_i^2}{3} }\\\\v_f = \frac{1}{\sqrt{3} } \ v_i\\\\\)

Thus, the final speed of object A changed by a factor of  \(\frac{1}{\sqrt{3} }\) = 0.58

To obtain the change in the final speed of object B, apply the following equations.

\(K.E_B_i = \frac{1}{2} m_Bv_i^2\\\\m_B = \frac{m_A}{4} \\\\K.E_B_i = \frac{1}{2}(\frac{m_A}{4} )v_i^2\\\\K.E_B_i = \frac{m_Av_i^2}{8} \\\\But, \ m_Av_i^2 = 54 \\\\K.E_B_i = \frac{54}{8} \\\\Apply \ work-energy \ theorem ;\\\\\delta K.E = -18\\\\K.E_f -K.E_i = -18\\\\\frac{1}{2}m_Bv_f^2 - \frac{1}{2} m_Bv_i^2 = -18\\\\Recall \ m_B = \frac{m_A}{4} \\\\\frac{1}{2}(\frac{m_A}{4} )v_f^2 - \frac{1}{2}(\frac{m_A}{4} )v_i^2 = -18\\\\\frac{1}{2}\times \frac{m_A}{4} (v_i^2 -v_f^2) = 18\\\\\)

\(\frac{1}{2}\times \frac{m_A}{4} (v_i^2 -v_f^2) = 18\\\\v_i^2 -v_f^2 = \frac{8}{m_A} \times 18\\\\v_i^2 -v_f^2 =\frac{144}{m_A} \\\\But , m_A = \frac{54}{v_i^2} \\\\v_i^2 -v_f^2 =\frac{144v_i^2}{54} \\\\v_f^2 = v_i^2 - \frac{144v_i^2}{54}\\\\v_f^2 = \frac{54v_i^2-144v_i^2}{54}\\\\ v_f^2 = \frac{-90v_i^2}{54} \\\\v_f^2 = \frac{-5v_i^2}{3} \\\\|v_f| = \sqrt{\frac{5v_i^2}{3}} \\\\|v_f| = \sqrt{\frac{5}{3}} \ v_i\)

Thus, the final speed of object B changed by a factor of \(\sqrt{\frac{5}{3} }\) = 1.29

Velocity is the rate of change of position with respect to time. The velocity of objects A and B is 0.577 and  1.29 times the initial velocities.

Velocity is the rate of change of position with respect to time.

Given to us

The kinetic energy of object A before work is applied,  \(KE_A = 27\rm\ J\)

Mass of object A = \(m_a\)

Mass of object B = \(m_b = \dfrac{m_a}{4}\)

Work done on both the objects, w = -18 J

We know that the kinetic energy of object A is 27 j, therefore,

\(KE_A = 27 J\\\\\dfrac{1}{2}m_av_i^2 = 27\\\\m_av_i^2 = 54\\\\m_a = \dfrac{54}{v_i^2}\)

We know that the work done on object A is -18 J, therefore,  the difference in the Kinetic energy of the object will be work,

\(KE_f - KE_i = -18\\\\\dfrac{1}{2}m_Av_f^2 -\dfrac{1}{2}m_Av_i^2 = 18\\\\v_f^2 -v_i^2 = \dfrac{-18 \times 2}{m_A}\\\\v_f^2 -v_i^2 = \dfrac{-36}{m_A}\)

Substitute the value of \(m_a\),

\(v_f^2 -v_i^2 = \dfrac{-36}{m_A}\\\\v_f^2 -v_i^2 = \dfrac{-36}{\dfrac{54}{v_i^2}}\\\\v_f^2 -v_i^2 = \dfrac{-36 v_i^2}{54}\\\\v_f^2 = \dfrac{1v_i^2}{3}+v_i^2\\\\v_f^2 = \dfrac{-36 v_i^2}{54}\\\\v_f = v_i\sqrt{\dfrac{1}{3}}\\\\v_f = 0.577v_i\)

Hence, the velocity of object A is 0.577 times the initial velocity.

Kinetic Energy of the object B,

\(KE_B = \dfrac{1}{2}m_B v_i^2\\\\KE_B = \dfrac{1}{2}\dfrac{m_A}{4} v_i^2\\\\KE_B =\dfrac{m_A}{8} v_i^2\\\\KE_B =\dfrac{m_A}{8} v_i^2\\\\KE_B =\dfrac{54}{8} \\\)

We know that the work done on object B is -18 J, therefore,  the difference in the Kinetic energy of the object will be work,

\(KE_f - KE_i = -18\\\\\dfrac{1}{2}m_Bv_f^2 -\dfrac{1}{2}m_Bv_i^2 = 18\\\\v_f^2 -v_i^2 = \dfrac{-18 \times 2}{m_B}\\\\v_f^2 -v_i^2 = \dfrac{-36}{m_B}\\\\v_f^2 -v_i^2 = \dfrac{-36}{\dfrac{m_A}{4}}\\\\v_f^2 -v_i^2 = \dfrac{-144}{m_A}\\\\}}\\\\v_f^2 -v_i^2 = \dfrac{-144}{\dfrac{54}{v_i^2}}\)

\(v_f^2 -v_i^2 = \dfrac{-144}{\dfrac{54}{v_i^2}}\\\\v_f^2 -v_i^2 = \dfrac{-144v_i^2}{54}\\\\v_f^2 = \dfrac{-144v_i^2}{54} + v_i^2\\\\v_f^2 = \dfrac{-144v_i^2}{54} + v_i^2\\\\v_f^2 = \dfrac{-5v_i^2}{3}\\\\ | v_f |= \sqrt{\dfrac{5v_i^2}{3}}\\\\v_f = \sqrt{\dfrac{5v_i^2}{3}}\\v_f = v_i\sqrt{\dfrac{5}{3}}\\\\v_f = 1.29 v_i\)

hence, the velocity of object B is 1.29 times the initial velocity.

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Answer:

the correct one is C

Explanation:

To find the answer, let's propose the solution of the problem

We create a system formed by the child and the platform so that all the forces have been internal and the angular momentum is conserved.

Initial instant. Before starting to walk

          L₀ = 0

Final moment. After the child is walking

          L_f = I₁ w₁ + m r v₂

where index 1 is used for the platform and index 2 for the child

linear and angular velocity are related

          v₂ = w₂ r

angular momentum is conserved

          0 = I₁ w₁ + m r (w₂ r)

          w₁ =  \(- \frac{m r^2}{I1} \ w_2\)

the moment of inertia of the platform bringing it closer to a disk or cylinder

         I₁ = \(\frac{1}{2}\) M r²  

sustitute

          w₁ = \(- \frac{2 m }{M} \ w_2\)

          W₁ = - \(- \frac{2 40}{30} \ w_2 = - \frac{8}{3} \ w_2\)

from here we can see that the platform and the child rotate in the opposite direction and with different angular speeds

when examining the answers the correct one is C

Answer:

Explanation:

relative to the ground the boy moves in a counter clockwise motion , now the boy and the wheel are one system

so by conservation of angular momentum their net sum of angular momentum relative to a point outside the system(say ground) should be zero

so the wheel moves in a clockwise direction , their angular velocity may or may not be same depending on I. so option D is wrong

option B is wrong because relative to ground their angular momentum should be equal and opposite

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The conservation of energy allows finding the result of the velocity of the body 2 when it reaches the ground is:

          v = 6.32 m / s

Given parameters

To find

The conservation of energy is one of the most important principles of physics, it establishes that if there is no friction force, the mechanical energy is conserved at all points, where the mechanical energy is the sum of the kinetic energy plus the different potential energies.

Let's write the energy at two points before we drop the system.

     Em₀ = U₁ + U₂

Where potential energy is

    U = m g y

They indicate that body 1 is on the ground and body 2 is at a height .

      y₂ = 8 m

      Em₀ = m₂ g y₂

Let's write the energy of the system for when body 2 is reaching the ground

       \(Em_f\) = K₂ + K₁ + U₂ + U₁

At this moment body 2 is reaching the ground, its height is zero and the height of body 1 is y₁ = 8 m. Since the two bodies are joined by the rope, they must have the same speed..

      \(Em_f\) = ½ (m₁ + m₂) v² + m₁ g y₁

As there is no friction, the energy is conserved.

      Em₀ = Em_f

      m₂ g y₂ = ½ (m₁ + m₂) v² + m₁ g y₁

The rope is inextensible, the heights are equal.

       y₁ = y₂ = y = 8.0 m

      v² = \(\frac{m2-m1}{m2+m1} \ 2g y\)  

Let's calculate.

       \(v^2 =\frac{22.9-13.6}{ 22.9+13.6} \ 2 \ 9.8 \ 8 \\ v = \sqrt{39.95}\)

      v = 6.32 m / s

In conclusion using the conservation of energy we can find the result of the velocity when the body 2 reaches the ground is:

          v = 6.32 m / s

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All the equations of motion are as follows, Displacement (s) equation, Final velocity (v) equation, Average velocity (v_avg) equation, Displacement (s) equation with average velocity, and Displacement (s) equation.

In terms of its motion as a function of time, equations of motion define how a physical system behaves. In more detail, the equations of motion define how a physical system behaves as a collection of mathematical functions expressed in terms of dynamic variables.

In conclusion, equations of motion define how a physical system behaves in terms of how its motion changes over time.

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Answer:

The  frequencies are  \(f_n = n (0.875 )\)

Explanation:

From the question we are told that

   The speed of the wave is  \(v = 0.700 \ m/s\)

   The  length of vibrating  clothesline is  \(L = 40.0 \ cm = 0.4 \ m\)

Generally the fundamental frequency is  mathematically represented as

        \(f = \frac{v}{2 L }\)

=>     \(f = \frac{ 0.700 }{2 * 0.4 }\)

=>     \(f = 0.875 \ Hz\)

Now  this other frequencies of vibration experience by the clotheslines are know as harmonics and they are obtained by integer multiple of  the fundamental frequency

So  

   The  frequencies are mathematically represented as

       \(f_n = n * f\)

=>     \(f_n = n (0.875 )\)

Where  n  =  1, 2, 3 ....

Answer: Limestone Caves

Explanation: The most common feature that can be caused purely by chemical weathering is Karst Landscape, which can lead to caverns and sinkholes.

Answer:

calculate 1.6*7.8*3.1

Explanation:

Answer:

A

Explanation:

As it begins to fall

F = ma        a = 9.81

F = .21 * 9.81 = 2.06 N

The definition of force in physics is the push or pull on a massed object that changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. The correct option is A.

Force is a physical factor that alters or has the potential to alter an object's state of rest or motion as well as its shape. Newton is the SI unit of force.

One of the most fundamental types of physical entities is the force. Due to the fact that force is a vector quantity, it possesses both a magnitude and a direction. Frictional force and contact force are the two categories under which all forces can be classified.

F = m × a

F = 0.21 × 9.81

F = 2.06 N

Thus the correct option is A.

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Answer:

To find - Value of the equation

Solution -

5x + 40

Putting value of x = (-5) in equation

5(-5) + 40

-25 + 40

15

Answer: Climate change poses to the tourism development in Fiji islands. It shows the adverse effects of the changing climate and the dangers pose by the tourism activities and also pose a major hazard for the local people in the region. It also deals with the dangerous carbon emissions and CO2 effect on the landscape, food, water, energy.

The pacific is the world`s largest ocean with a surface area of 175 million sq km and constitutes for 40% of the planet`s waters. Located in the tropical latitudes, it covers more than half the globe`s circumference. Temperature of the surface water in the western tropical regions is always more than 28 ÌŠC over a depth of several hundred meters. This makes up the world`s storage of thermal energy for exchange with atmosphere. Here the interaction between atmosphere and ocean is most extreme and influences the climate not only regionally but planet-wide. The nations of the pacific are obscured human settlements absorbed in this vast fluid universe. The ocean is the most important factor controlling the environment and life.

Answer:

A) q = 7.03 × 10^(-13) C

n ≈ 4388265 electrons

B) q = 1757.8 × 10^(-16) C

n ≈ 1097253 electrons

Explanation:

We are given;

Mass; m = 1.5 × 10^(−8)g = 1.5 × 10^(-11) kg

Speed; v = 50 m/s

Electric Field; E = 8 × 10⁴ N/C

Distance between plates; s = 2 cm = 0.02 m

A) Now, speed = distance/time

So, time(t) = distance/speed = 0.02/50 = 0.0004 s

From Newton's first law of motion, we know that;

d = ut + ½at²

But u is initial velocity and in this case it's zero.

But we are told that a drop is to be deflected by 0.30 mm. So, d = 0.3 × 10^(-3) m

Thus;

0.3 × 10^(-3) = 0 + ½a(0.0004)²

a = 3750 m/s²

Now, we know that force in motion normally can be expressed as;

F = ma

But in electric field, it's;

F = qE

Thus;

qE = ma

So, charge is; q = ma/E

Plugging in the relevant values;

q = (1.5 × 10^(−11) × 3750)/(8 × 10⁴)

q = 7.03 × 10^(-13) C

Now, number of electrons is given by the formula;

n = q/e

Where e is charge on electron with a value of 1.602 × 10^(-19) C/electron

So; n = (7.03 × 10^(-13))/(1.602 × 10^(-19))

n ≈ 4388265 electrons

B) We are told speed is now 25 m/s.

Thus;

time(t) = distance/speed = 0.02/25 = 0.0008 s

From Newton's first law of motion, we know that;

d = ut + ½at²

But u is initial velocity and in this case it's zero.

d remains 0.3 × 10^(-3) m

Thus;

0.3 × 10^(-3) = 0 + ½a(0.0008)²

a = 937.5 m/s²

Now, we know that force in motion normally can be expressed as;

F = ma

But in electric field, it's;

F = qE

Thus;

qE = ma

So, charge is; q = ma/E

Plugging in the relevant values;

q = (1.5 × 10^(−11) × 937.5)/(8 × 10⁴)

q = 1757.8 × 10^(-16) C

Now, number of electrons is given by the formula;

n = q/e

Where e is charge on electron with a value of 1.602 × 10^(-19) C/electron

So; n = (1757.8 × 10^(-16) )/(1.602 × 10^(-19))

n ≈ 1097253 electrons

Steps to formulate a logical, reasonable perspective to any situation are: gather information, identify problem, analyze the situation, consider assumptions, generate solutions, evaluate options, consider your values, make decision and monitor and adjust

Here are the six questions that you can apply to formulating a logical, reasonable perspective to any situation:

What are the issues that should be addressed?

What are the relevant facts and data related to this problem or issue?

What assumptions am I making about the problem or issue?

What are the possible solutions or outcomes, and what are the pros and cons of each?

What are my values and priorities related to this problem or issue?

What additional information do I need to make an informed decision or come to a reasonable conclusion?

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The acceleration of Thomas is 0.233 m/s^2.

Acceleration is the rate of change of velocity. Thomas the Train chugs along at a velocity of 2 m/s.

Thomas needs to go faster so more coal is shoveled into his engine and he accelerates for 10 seconds until he is going 4.33 m/s.

We are to find the acceleration of Thomas.

The formula for acceleration is given as :

acceleration = (final velocity - initial velocity) / time

In the given problem, the initial velocity of Thomas, u = 2 m/s.

The final velocity of Thomas, v = 4.33 m/s The time for which Thomas accelerates, t = 10 s.

Therefore, the acceleration of Thomas will be given as:

a = (v - u) / ta = (4.33 - 2) / 10s => 2.33 / 10s => 0.233 m/s^2

Thus, the acceleration of Thomas is 0.233 m/s^2.

To summarize, the acceleration of Thomas is 0.233 m/s^2.

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Answer:

2 kilograms

Explanation:

F = ma

2 = 1m = 2

According to problem ( considering sign convention for convex lens)

height of object = 2.25 mm;

object distance(u)= - 8.5 cm

focal length (f)= 5.5 cm

image distance(v)= ?

Using lens formula

a) Answer is :- Location of image = 15.58cm

Using magnification formula

b) Height of image = 4.12 mm

C) Magnification= 1.83

(6) Wagon B is at rest so it has no momentum at the start. If v is the velocity of the wagons locked together, then

(140 kg) (15 m/s) = (140 kg + 200 kg) v

==>   v ≈ 6.2 m/s

(7) False. If you double the time it takes to perform the same amount of work, then you halve the power output:

E / (2t ) = 1/2 × E/t = 1/2 P

Hence, the time required is approximately equal to 4 minutes and 39 seconds.

Given, Power, P = 300 W= 300J/s

Power= Energy per second

Mass, m= 0.25 kg

Initial Temperature= 20.0°C

Final Temperature= 100.0°C

Temperature difference, T =( 100-20)°C= 80.0°C

Specific heat of water, S= 4184 J/kg°C

Energy can be represented as

E=mST

where E is the energy, m is the mass, S is the specific heat of water and T is the temperature difference.

As Energy can be written as the product of time and power, E=Pt

Pt=mST

So,

t=(msT)/P

t=(0.25×4184×80)/300

Time, t = 278.934 seconds= 4 minutes and 39 seconds.

Hence, 4 minutes and 39 seconds will be required for a 300.0 W immersion heater to heat 0.25 kg of water from 20.0°C to 100.0°C.

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