Initially stationary, a train has a constant acceleration of 0.8 m/s2. (a) What is its speed after 27 s? m/s (b) What is the total time required for the train to reach a speed of 41 m/s?

Answer:

q = 2.997*10^-4C

Explanation:

In order to find the required charge that the penny have to have, to acquire an upward acceleration, you take into account that the electric force on the penny must be higher than the weight of the penny.

You use the second Newton law to sum both electrical and gravitational forces:

[tex]F_e-W=ma\\\\qE-mg=ma[/tex]             (1)

Fe: electric force

W: weight of the penny

q: required charge = ?

m: mass of the penny = 3g = 0.003kg

E: magnitude of the electric field = 100N/C

g: gravitational acceleration = 9.8m/s^2

a: acceleration of the penny = 0.19m/s^2

You solve the equation (1) for q, and replace the values of the other parameters:

[tex]q=\frac{ma+mg}{E}=\frac{m(a+g)}{E}\\\\q=\frac{(0.003kg)(0.19m/s^2+9.8m/s^2)}{100N/C}\\\\q=2.997*10^{-4}C[/tex]

It is necessary that the penny has a charge of 2.997*10^-4 C, in order to acquire an upward acceleration of 0.19m/s^2

Answer:

dr = 0.71 ft/min

the balloon's radius is increasing at 0.71 ft/min when the radius is 7ft.

Explanation:

Given;

Rate of inflation dV = 140pift^3/min

Radius r = 7 ft

Change in radius = dr

Volume of a spherical balloon is;

V = (4/3)πr^3

The change in volume can be derived by differentiating both sides;

dV = (4πr^2)dr

Making dr the subject of formula;

dr = dV/(4πr^2)

Substituting the given values;

dr = 140π/(4π×7^2)

dr = 0.714285714285 ft/min

dr = 0.71 ft/min

the balloon's radius is increasing at 0.71 ft/min when the radius is 7ft.

Answer:

C is the correct answer

Explanation:

Answer:

578.2 N

Explanation:

The computation of reading on the scale is shown below:-

Data provided in the question

Weight of a girl = 59 kg

Constant rate = 8 m/s

Since the elevator is descended so the acceleration is zero

As we know that

Reading on the scale is

[tex]F = m\times g[/tex]

where,  m = 59 kg

g  [tex]= 59 \times 9.8 m/s^2[/tex]

So, the reading on the scale is

= 578.2 N

Therefore for computing the reading on the scale we simply applied the above formula.

Answer:

F' = F/16

So, the force of gravity has become 16 times less than initial value.

Explanation:

The force of gravity between two planets, is given by the following formula:

F = Gm₁m₂/r²   ----------- equation 1

where,

F = Force of gravity between two planets

G = Gravitational Constant

m₁ = Mass of one planet

m₂ = Mass of other plant

r = Distance between two planets

Now, if the distance between the planets (r) is 10 times smaller, then Force of gravity will become:

F' = Gm₁m₂/(4r)²

F' = (1/16) (Gm₁m₂/r²)

using equation 1:

F' = F/16

So, the force of gravity has become 16 times less than initial value.

Answer:

Frequency= 0.25m

Period= 4.0 secs

Explanation:

Clay is surfing on a wave with a speed of 5.0m/s

The wave crests are 20m apart

Therefore, the frequency of the wave can be calculated as follows

Frequency= wave speed/distance

= 5.0/20

= 0.25m

The period (T) can be calculated as follows

T= 1/frequency

T = 1/0.25

T= 4.0secs

Hence the frequency is 0.25m and the period is 4.0 secs

Answer:

q/6Eo

Explanation:

See attached file pls

Answer:

The temperature of silver at this given resistivity is 2971.1 ⁰C

Explanation:

The resistivity of silver is calculated as follows;

[tex]R_t = R_o[1 + \alpha(T-T_o)]\\\\[/tex]

where;

Rt is the resistivity of silver at the given temperature

Ro is the resistivity of silver at room temperature

α is the temperature coefficient of resistance

To is the room temperature

T is the temperature at which the resistivity of silver will be two times the resistivity of iron at room temperature

[tex]R_t = R_o[1 + \alpha(T-T_o)]\\\\\R_t = 1.59*10^{-8}[1 + 0.0038(T-20)][/tex]

Resistivity of iron at room temperature = 9.71 x 10⁻⁸ ohm.m

When silver's resistivity becomes 2 times the resistivity of iron, we will have the following equations;

[tex]R_t,_{silver} = 2R_o,_{iron}\\\\1.59*10^{-8}[1 + 0.0038(T-20)] =(2 *9.71*10^{-8})\\\\\ \ (divide \ through \ by \ 1.59*10^{-8})\\\\1 + 0.0038(T-20) = 12.214\\\\1 + 0.0038T - 0.076 = 12.214\\\\0.0038T +0.924 = 12.214\\\\0.0038T = 12.214 - 0.924\\\\0.0038T = 11.29\\\\T = \frac{11.29}{0.0038} \\\\T = 2971.1 \ ^0C[/tex]

Therefore, the temperature of silver at this given resistivity is 2971.1 ⁰C

Answer:

The major difference is the capacity of both batteries. The AA battery has a higher capacity (a higher current) than the AAA battery.

Explanation:

The AA batteries and the AAA batteries are very similar in their voltage; both of them have 1.5 V.

The difference between these two batteries is their size and also the current that they have. The AAA battery is smaller than the AA battery, which means that the amount of electrochemical material is lower, so the AA battery has a higher capacity (a higher current) than the AAA battery. Generally, AA battery has 2400 mAh capacity and AAA battery has a capacity of 1000mAh; this means that AA battery has almost three times the capacity of an AAA battery.      

Furthermore, the size of the AA battery makes it more common than the AAA battery and therefore has higher commercial demand.                                  

I hope it helps you!

Answer:

The angular displacement is  [tex]\theta = 28.33 \ rad[/tex]

Explanation:

From the question we are told that

     The speed of the driver is  [tex]v =13 \ m/ s[/tex]

     The acceleration of the driver is  [tex]a = 1.02 \ m/s^2[/tex]

      The time taken is [tex]t = 0.70 \ s[/tex]

      The radius of the tire is  [tex]r = 33 cm = 0.33 \ m[/tex]

The distance covered by the car during this  acceleration can be  calculated using the equation of motion as follows

        [tex]s = v*t +\frac{1}{2} * a * t^2[/tex]

Now substituting values  

       [tex]s = 13 * 0.70 +\frac{1}{2} * 1.02 * (0.700)^2[/tex]

      [tex]s = 9.35 \ m[/tex]

Now the angular displacement of the car with respect to the tire movement can be  represented mathematically as

      [tex]\theta = \frac{s}{r}[/tex]

substituting values

      [tex]\theta = \frac{9.35}{0.33}[/tex]

      [tex]\theta = 28.33 \ rad[/tex]

Answer:

The object has an excess of [tex]10^{13}[/tex] electrons.

Explanation:

When an object has a negative charge he has an excess of electrons in its body. We can calculate the number of excessive electrons by dividing the charge of the body by the charge of one electron. This is done below:

[tex]n = \frac{\text{object charge}}{\text{electron charge}}\\n = \frac{-1.6*10^{-6}}{-1.6*10^{-19}} = 1*10^{-6 + 19} = 10^{13}[/tex]

The object has an excess of [tex]10^{13}[/tex] electrons.

Answer:

C You should deflect the ball back toward your friend.

Explanation:

This is because it would result in a completely inelastic collision, and the final velocity of me would be found using,

with m= mass, V=velocity, i=initial, f=final:

mV(me,i) +mV(ball,i) = [m(me)+m(b)]V(f)

So V(f) would be just the momentum of the ball divided by just MV mass of the ball and it will be higher resulting in inelastic collision

Answer:

A. You should catch the ball.

Explanation:

Catching the ball maximizes your speed by converting most of the momentum of the flying ball into the momentum of you and the ball. Since the ice is smooth, the friction between your feet and the ice is almost negligible, meaning less energy is needed to set your body in motion. Catching the ball means that you and the ball undergoes an inelastic collision, and part of the kinetic energy of the ball is transferred to you, setting you in motion. Deflecting the ball will only give you a relatively small speed compared to catching the ball.

Answer:

The force is  [tex]F = 8*10^{-12} \ N[/tex]

Explanation:

From the question we are told that

     The rate at which ATP molecules are used is [tex]R = 80 ATP/ s[/tex]

       The energy provided by a single ATP is  [tex]E_{ATP} = 0.8 * 10^{-19} J[/tex]

       The velocity of the kinesin is  [tex]v = 800 nm/s = 800*10^{-9} m/s[/tex]

The power provided by the ATP in one second is  mathematically represented as

       [tex]P = E_{ATP} * R[/tex]

substituting values

       [tex]P = 80 * 0.8*10^{-19 }[/tex]

       [tex]P = 6.4 *10^{-18}J/s[/tex]

Now  this power is mathematically represented as

       [tex]P = F * v[/tex]

Where  F  is  the force the kinesin is exerting

  Thus  

          [tex]F = \frac{P}{v}[/tex]

substituting values

            [tex]F = \frac{6.4*0^{-18}}{800 *10^{-9}}[/tex]

           [tex]F = 8*10^{-12} \ N[/tex]

The force exerted by the kinesin  is 8  × 10-12 N.

Let us recall that power is defined as the rate of doing work. Hence, power = Energy/Time.

Since;

Energy  =  0.8 × 10-19 J/molecule

Number ATP molecules transported per second = 80 ATP molecules/s

Power =  0.8 × 10-19 J/molecule × 80 ATP molecules/s

Power = 6.4  × 10-18 J

Again, we know that;

Power = Force × Velocity

Velocity of the ATP molecules =  800 nm/s or 8 × 10-7 m/s

Force = Power/velocity

Force =  6.4  × 10-18 J/ 8 × 10-7 m/s

Force = 8  × 10-12 N

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Answer:

3.85 percent

Explanation:

From the question,

Percentage error = (error/actual)×100................ Equation 1

Given: actual center of mass = 15 cm, error = 15.6-15 = 0.6 cm

Substitute these values into equation 1

Percentage error = (0.6/15.6)×100

Percentage error = 3.85 percent

Hence the percentage error of the uniform mass = 3.85 percent

Answer:

94.248 g/sec

Explanation:

For solving the total current of the blood passing first we have to solve the cross sectional area which is given below:

[tex]A_1 = \pi R^2\\\\A_1 = \pi (1)^2\\\\A_1 = 3.1416 cm^2[/tex]

And, the velocity of blood pumping is 30 cm^2

Now apply the following formula to solve the total current

[tex]Q = \rho A_1V_1\\\\Q = (1)(3.1416)(30)\\\\[/tex]

Q =  94.248 g/sec

Basically we applied the above formula So, that the total current could come

Answer:

is this a company name.? java is a computer software right..

Answer:

T₂ = 95.56°C

Explanation:

The final resistance of a material after being heated is given by the relation:

R' = R(1 + αΔT)

where,

R' = Final Resistance = 207.4 Ω

R = Initial Resistance = 154.9 Ω

α = Temperature Coefficient of Resistance of Tungsten = 0.0045 °C⁻¹

ΔT = Change in Temperature = ?

Therefore,

207.4 Ω = 154.9 Ω[1 + (0.0045°C⁻¹)ΔT]

207.4 Ω/154.9 Ω = 1 + (0.0045°C⁻¹)ΔT

1.34 - 1 = (0.0045°C⁻¹)ΔT

ΔT = 0.34/0.0045°C⁻¹

ΔT = 75.56°C

but,

ΔT = Final Temperature - Initial Temperature

ΔT = T₂ - T₁ = T₂ - 20°C

T₂ - 20°C = 75.56°C

T₂ = 75.56°C + 20°C

T₂ = 95.56°C

Answer:

The work required to move this charge is 0.657 J

Explanation:

Given;

magnitude of charge, q = 4.4 x 10⁻⁶ C

Electric field strength, E =  3.9 x 10⁵ N/C

distance moved by the charge, d = 50 cm = 0.5m

angle of the path, θ = 40°

Work done is given as;

W = Fd

W = FdCosθ

where;

F is the force on the charge;

According the coulomb's law;

F = Eq

F = 3.9 x 10⁵ x 4.4 x 10⁻⁶  = 1.716 N

W = FdCosθ

W = 1.716 x 0.5 x Cos40

W = 0.657 J

Therefore, the work required to move this charge is 0.657 J

Answer:

a law stating that like charges repel and opposite charges attract, with a force proportional to the product of the charges and inversely proportional to the square of the distance between them.

Answer:

V = 0.45 Volts

Explanation:

First we need to find the total current passing through the wire. That can be given by:

Total Current = I = (Current Density)(Surface Area of Wire)

I = (Current Density)(2πrL)

where,

r = radius = 1.5/2 mm = 0.75 mm = 0.75 x 10⁻³ m

L = Length of Wire = 6.5 m

Therefore,

I = (4.07 x 10⁻³ A/m²)[2π(0.75 x 10⁻³ m)(6.5 m)]

I = 1.25 x 10⁻⁴ A

Now, we need to find resistance of wire:

R = ρL/A

where,

ρ = resistivity of iron = 9.71 x 10⁻⁸ Ωm

A = Cross-sectional Area = πr² = π(0.75 x 10⁻³ m)² = 1.77 x 10⁻⁶ m²

Therefore,

R = (9.71 x 10⁻⁸ Ωm)(6.5 m)/(1.77 x 10⁻⁶ m²)

R = 0.36 Ω

From Ohm's Law:

Voltage = V = IR

V = (1.25 x 10⁻⁴ A)(0.36 Ω)

V = 0.45 Volts

Answer:

L = 0.60 m

The length in metres should be 0.60 m

Explanation:

A pipe open at both ends can have a standing wave pattern with resonant frequency;

f = nv/2L ........1

Where;

v = velocity of sound

L = length of pipe

n = 1 for the fundamental frequency f1

Given;

Fundamental frequency f1 = 294 Hz

Velocity v = 350 m/s

n = 1

From equation 1;

Making L the subject of formula;

L = nv/2f1

Substituting the given values;

L = 1×350/(2×294)

L = 0.595238095238 m

L = 0.60 m

The length in metres should be 0.60 m

Answer:

3g/(8π²) ≈ 0.372 m

Explanation:

Draw a free body diagram.  There is a weight force at the center of the pendulum.

Sum of the torques about the pivot:

∑τ = Iα

mg (½ L sin θ) = (⅓ mL²) α

3g sin θ = 2L α

α = 3g/(2L) sin θ

For small θ, sin θ ≈ θ.

α = 3g/(2L) θ

θ" = 3g/(2L) θ

The solution of this differential equation is:

θ = θ₀ cos(√(3g/(2L)) t)

So the period is:

T = 2π / √(3g/(2L))

If the period is 1 second:

1 = 2π / √(3g/(2L))

√(3g/(2L)) = 2π

3g/(2L) = 4π²

L = 3g/(8π²)

L ≈ 0.372 m

The length of the pendulum rod is 0.37 m.

The time period of a pendulum is defined as the time taken by the pendulum to complete one oscillation.

Here,

The mass of the pendulum, m = 2 kg

Time period of the pendulum, T = 1 s

Since, the pendulum is suspended from the pivot and is oscillating, at the position of the pendulum when it makes an angle θ with the pivot, there is a force of weight acting at the center of the pendulum.

The length of pendulum at that point = L/2

The perpendicular distance at that point, r = (L/2) sinθ

Therefore, the torque acting on the pendulum at that point,

τ = Iα

where I is the moment of inertia of the pendulum and α is the angular acceleration.

mg (L/2 sinθ) = (mL²/3)α

1/2 gsinθ = 1/3 Lα

Therefore,

α = (3g/2L) sinθ

For smaller values of θ, we can take sinθ = θ

So, α = (3g/2L) θ

We know that α = θ''

where θ is the angular displacement.

Therefore,

θ'' = (3g/2L) θ

So, ω = √3g/2L

Therefore, the equation of motion of the pendulum can be written as,

θ = θ₀ cos(ωt)

θ = θ₀ cos [(√3g/2L) t]

So, time period of the pendulum,

T = 2[tex]\pi[/tex]/ω

T = 2[tex]\pi[/tex]/(√3g/2L)

2[tex]\pi[/tex]/(√3g/2L) = 1

(√3g/2L) = 2[tex]\pi[/tex]

Therefore, length of the rod,

L = 3g/8[tex]\pi[/tex]²

L = 0.37 m

Hence,

The length of the pendulum rod is 0.37 m.

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Attaching the image file here.

Answer:

- E = 11.55J

- Q = 0.17C

- E' = (1/4)E

Explanation:

- To calculate the amount of energy stored in the capacitor, you use the following formula:

[tex]E=\frac{1}{2}CV^2[/tex]

C: capacitance = 3800.0*10^-6F

V: potential difference = 78.0V

[tex]E=\frac{1}{2}(3800.0*10^{-6}C)(78.0V)^2=11.55J[/tex]

The energy stored in the capacitor is 11.55J

- If the electrical energy stored in the capacitor is 6.84J, the charge on the capacitor is:

[tex]E=\frac{1}{2}QV\\\\Q=\frac{2E}{V}\\\\Q=\frac{2(6.84J)}{78.0V}=0.17C[/tex]

The charge on the capacitor is 0.17C

- If you take the capacitor as a parallel plate capacitor, you have that the energy stored on the capacitor is:

[tex]E=\frac{1}{2}CV^2=\frac{1}{2}(\frac{\epsilon_oA}{d})V^2=\frac{1}{2}\frac{\epsilon_oAV^2}{d}\\\\[/tex]

A: area of the plates

d: distance between plates

If the distance between plates is increased by a factor of 4, you have:

[tex]E'=\frac{1}{2}\frac{\epsilon_oAV^2}{(4d)}=\frac{1}{4}\frac{\epsilon_oAV^2}{2d}=\frac{1}{4}E[/tex]

Then, the stored energy in the capacitor is decreased by a a factor of (1/4)

Answer:

(a) 62.3 N

(b) 1.89 N

(c) 0.430 kg m²

Explanation:

(a) Find the acceleration of block B.

Δy = v₀ t + ½ at²

1.80 m = (0 m/s) (2.00 s) + ½ a (2.00 s)²

a = 0.90 m/s²

Draw a free body diagram of block B.  There are two forces:

Weight force mg pulling down,

and tension force Tb pulling up.

Sum of forces in the -y direction:

∑F = ma

mg − Tb = ma

Tb = m (g − a)

Tb = (7.00 kg) (9.8 m/s² − 0.90 m/s²)

Tb = 62.3 N

(b) Draw a free body diagram of block A.  There are three forces:

Weight force mg pulling down,

Normal force N pushing up,

and tension force Ta pulling right.

Sum of forces in the +x direction:

∑F = ma

Ta = ma

Ta = (2.10 kg) (0.90 m/s²)

Ta = 1.89 N

(c) Draw a free body diagram of the pulley.  There are two forces:

Tension force Tb pulling down,

and tension force Ta pulling left.

Sum of torques in the clockwise direction:

∑τ = Iα

Tb r − Ta r = Iα

(Tb − Ta) r = I (a/r)

I = (Tb − Ta) r² / a

I = (62.3 N − 1.89 N) (0.080 m)² / (0.90 m/s²)

I = 0.430 kg m²

The tension force that the rope exerts on block B is 62.3 N, the tension force that the rope exerts on block A is 1.89 N, and the moment of inertia of the pulley for rotation about the axle on which it is mounted is [tex]\rm 0.430 \; kg\;m^2[/tex].

Given :

a) First, determine the acceleration of the B block.

[tex]\rm s = ut + \dfrac{1}{2}at^2[/tex]

[tex]\rm 1.8 = \dfrac{1}{2}\times a\times (2)^2[/tex]

[tex]\rm a = 0.9\; m/sec^2[/tex]

Now, apply Newton's second law of motion in order to determine the tension force that the rope exerts on block B.

[tex]\rm \sum F=ma[/tex]

[tex]\rm mg-T_b=ma[/tex]

[tex]\rm T_b = m(g-a)[/tex]

[tex]\rm T_b = 7\times (9.8-0.9)[/tex]

[tex]\rm T_b = 62.3\;N[/tex]

b) Now, again apply Newton's second law of motion in order to determine the tension force that the rope exerts on block A.

[tex]\rm \sum F=ma[/tex]

[tex]\rm T_a=ma[/tex]

[tex]\rm T_a = 2.1\times 0.9[/tex]

[tex]\rm T_a = 1.89\;N[/tex]

c) The sum of the torque in order to determine the moment of inertia of the pulley for rotation about the axle on which it is mounted.

[tex]\rm \sum \tau = I\alpha[/tex]

[tex]\rm T_br-T_ar = I\alpha[/tex]

[tex]\rm I = \dfrac{(T_b-T_a)r^2}{a}[/tex]

Now, substitute the values of the known terms in the above expression.

[tex]\rm I = \dfrac{(62.3-1.89)(0.080)^2}{0.90}[/tex]

[tex]\rm I = 0.430 \; kg\;m^2[/tex]

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Answer:

The force experienced  is 0.6 N

Explanation:

Given data

length of wire L= 2 m

current in wire I= 0.6 A

magnetic field B= 0.5

The force experienced can be represented as

[tex]F= BIL[/tex]

[tex]F= 0.5*0.6*2\\\F= 0.6 N[/tex]

Answer:

5. The amount of work is the same for both.

Explanation:

Work done is a measure of change in kinetic energy of each egg

For both egg , the initial speed and mass are same , so they have equal initial Kinetic energy

For both egg , the final speed is 0 and mass are same , so they have equal final Kinetic energy which is 0.

So work done is same for both eggs since they have same change in kinetic energy.

Answer:  If you are traveling at a speed of 60mph, you will go 220 feet.

Explanation: 60mph is a mile a minute. 5280 feet in a mile, 60 seconds in a minute. Divide to find that is 88 feet per second. Multiply by the number of seconds.

Answer:

T = 15,576 N

Explanation:

The speed of a wave on a string is given by

        v = √ T /ρ rho

also the speed of the wave is given by the relationship

       v = λ f

we substitute

     λ f = √ T /ρ

T = (lam f)² ρ

let's find the wavelength in a string, fixed at the ends, the relation that gives the wavelength is

       L= λ/2 n

       λ= 2L / n

we substitute

      T = (2L / n f)²ρ rho

let's calculate

      T = (2 1.20 / 2 590) 0.022

      T = 15,576 N

Answer:

6.44 s

Explanation:

Given:

v₀ = 119 m/s

v = 233 m/s

a = 17.7 m/s²

Find: t

v = at + v₀

(233 m/s) = (17.7 m/s²) t + (119 m/s)

t = 6.44 s

Answer:

D

Explanation:

The power equation is P= V^2/R

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As a result of the given scenario, power delivered from the battery to combination decreases. The correct option is D.

A resistor is a two-terminal passive electrical component that uses electrical resistance as a circuit element.

Resistors are used in electronic circuits to reduce current flow, adjust signal levels, divide voltages, and bias active elements.

A resistor is a component of an electronic circuit that limits or regulates the flow of electrical current. Resistors can also be used to supply a fixed voltage to an active device such as a transistor.

The current through resistors is the same when they are connected in series. The battery voltage is divided among resistors.

Adding more resistors to a series circuit increases total resistance and thus lowers current. However, in a parallel circuit, adding more resistors in parallel creates more options while decreasing total resistance.

Thus, the correct option is D.

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