A flatbed truck is carrying a 20-kg crate up a sloping road. The coefficient of static friction between the crate and the bed is 0.40, and the coefficient of kinetic friction is 0.30. What is the maximum angle of slope that the truck can climb at constant speed if the crate is to stay in place

Answer:

t = 7.5 s

Explanation:

The distance traveled by the car at the time of meeting of the two cars must be the same. First, we calculate the distance traveled by the police car. For that we use 2nd equation of motion. Here, we take the time when police car starts to be reference. So,

s₁ = Vi t + (0.5)gt²

where,

s₁ = distance traveled by police car

Vi = Initial Velocity = 0 m/s

t = time taken

Therefore,

s₁ = (0 m/s)(t) + (0.5)(9.8 m/s²)t²

s₁ = 4.9 t²

Now, we calculate the distance traveled by the car. For constant speed and time to be 1 second more than the police car time, due to car starting time, we get:

s₂ = Vt = V(t + 1)

where,

s₂ = distance traveled by car

V = Velocity of car = (100 km/h)(1000 m/1 km)(1 h/ 3600 s) = 27.78 m/s

Therefore,

s₂ = 27.78 t + 27.78

Now, we know that at the time of meeting:

s₁ = s₂

4.9 t² = 27.78 t + 27.78

4.9 t² - 270.78 t - 27.78 = 0

solving the equation and choosing the positive root:

t = 6.5 s

since, we want to know the time from the moment car crossed police car. Therefore, we add 1 second of starting time in this.

t = 6.5 s + 1 s

t = 7.5 s

Given that,

Mass of trackler, m₁ = 100 kg

Speed of trackler, u₁ = 2.6 m/s

Mass of halfback, m₂ = 92 kg

Speed of halfback, u₂ = -5 m/s (direction is opposite)

To find,

Mutual speed immediately after the collision.

Solution,

The momentum of the system remains conserved in this case. Let v is the mutual speed after the collision. Using conservation of momentum as :

[tex]m_1u_1+m_2u_2=(m_1+m_2)V\\\\V=\dfrac{m_1u_1+m_2u_2}{(m_1+m_2)}\\\\V=\dfrac{100\times 2.6+92\times (-5)}{(100+92)}\\\\V=-1.04\ m/s[/tex]

So, the mutual speed immediately after the collision is 1.04 m/s but in opposite direction.

Answer:

work = 1728

Power = 134

Explaination:

by using the formula,

Work(W)= Force(F)×Distance(D)

Power(P)= Work(W)/Time taken(T)

Answer:

3 m

Explanation:

PE = mgh

120 J = (4 kg) (10 m/s²) h

h = 3 m

The book is 3m high from the ground.

The energy by virtue of its position is called the potential energy.

PE = mgh

where, g = 9.81 m/s²

Given is the mass of book m =4kg and the potential energy P.E = 120J, then the height is

120 J = (4 kg) (10 m/s²) h

h = 3 m

Thus, the book is 3m high from the ground.

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Answer:

24.7°C

Explanation:

Heat lost by brass = heat gained by aluminum and water

-q = q

-mCΔT = mCΔT + mCΔT

-(50 g) (0.380 J/g/°C) (T − 200°C) = (50 g) (0.900 J/g/°C) (T − 20°C) + (160 g) (4.186 J/g/°C) (T − 20°C)

-(19 J/°C) (T − 200°C) = (45 J/°C) (T − 20°C) + (670 J/°C) (T − 20°C)

-(19 J/°C) (T − 200°C) = (715 J/°C) (T − 20°C)

-19 (T − 200°C) = 715 (T − 20°C)

-19T + 3800°C = 715T − 14300°C

18100°C = 734T

T = 24.7°C

Answer:

a) The planet experiences a centripetal force towards its star

b) The universal attractive force (Gravitational force)

c)None of these choices are true.

Explanation:

This problem raise several claims, let's review some aspects of circular motion

            F = m a

the centripetal acceleration is

            a = v² / r

where v is the speed (modulus of velocity) that is constant and r is the radius

The direction of the acceleration is perpendicular to the motion.

Let's review the different claims

Part a) the orbital velocity is constant

The correct statement is: The planet experiences a centripetal force towards its star

Part b) what is the centripetal force

The correct statement: The universal attractive force (Gravitational force)

Part c) which statement is true

1) False. There can be no tangential force

2) False. There is a centripetal force that creates the movement, but there is no centrifugal force because the system is accelerated and there is no tangential force because the movement is circular.

3) False. There is no tangential force

4) True none is true

5) False. There is a force because movement has acceleration

Answer:

A) correct answer is C,   B)   correct answer is b  and C) The correct answer is b

Explanation:

In the exercises of geometric optics, the equation of the constructor tells us the location of the image.

        1 / f = 1 / p + 1 / q

where f is the focal length of the cornea-crystalline system, p and q are the distances to the object and the image.

In this case, the distance to the image on the retina is constant, about 3 cm. Therefore depending on the distance to the object) p = the focal length must change

        1 / q = 1 / f 1 / p

let's apply this expression to our case

A) indicates that the tree is at a medium distance

so that the image is formed on the retina THE SAME AS

correct answer is C

B) The squirrel is at a smaller distance (p ') than the tree (p), therefore if we substitute in the equation above we find that q must decrease. Consequently the image is in front of the retina

The mountain is very far, suppose in infinity, so the image is BEHIND THE RETINA

therefore the correct answer is b

C) The squirrel is very close so the curvature of the lens INCREASES, resulting in a DECREASE in the focal length

The correct answer is b

Answer:

It can be said to be reliable although it is not valid

Explanation:

This is because Reliability means an indicator of consistency, A measure should produce similar or the same results consistently if it measures the same quantity. So does the thermometer measures over 5days but it is not valid because it deviates from the real value

Answer:

The  pressure difference is  [tex]\Delta P = 1.46 *10^{5}\ Pa[/tex]

Explanation:

From the question we are told that

   The  density is  [tex]\rho = 1250 \ kg/m^3[/tex]

   The  speed at location 1  is  [tex]v_1 = 9.93 \ m/s[/tex]

    The  diameter at location 1 is  [tex]d_1 = 11.1\ cm = 0.111 \ m[/tex]

     The  diameter at location 2 is  [tex]d_1 = 16.7\ cm = 0.167 \ m[/tex]

     The  height at location 1 is  [tex]h_1 = 8.89 \ m[/tex]

       The  height at location 2  is  [tex]h_2 = 1 \ m[/tex]

Generally the cross- sectional area at location 1 is mathematically represented as

       [tex]A_1 = \pi * \frac{d^2}{4}[/tex]

=>     [tex]A_1 = 3.142 * \frac{ 0.111^2}{4}[/tex]

=>     [tex]A_1 = 0.0097 \ m^2[/tex]

Generally the cross- sectional area at location 2 is mathematically represented as

           [tex]A_2 = \pi * \frac{d_1^2}{4}[/tex]

=>     [tex]A_2= 3.142 * \frac{ 0.167^2}{4}[/tex]

=>     [tex]A_2 =0.0219 \ m^2[/tex]

From continuity formula

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

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

=>      [tex]v_2 = \frac{0.0097 * 9.93}{0.0219 }[/tex]

=>      [tex]v_2 = 4.398 \ m/s[/tex]

Generally according to Bernoulli's theorem

     [tex]P_1 + \rho * g * h_1 + \frac{1}{2} \rho * v_1^2 = P_2 + \rho * g * h_2 + \frac{1}{2} \rho * v_2^2[/tex]

=>   [tex]P_2 - P_1 = \frac{1}{2} \rho (v_1 ^2 - v_2^2 ) + \rho* g (h_1 - h_2)[/tex]

=> [tex]\Delta P = \frac{1}{2}* 1250* (9.93 ^2 - 4.398^2 ) + 1250* 9.8 (8.89- 1)[/tex]

=> [tex]\Delta P = 1.46 *10^{5}\ Pa[/tex]

Answer:

Explanation:

With the help of expression of  time period of pendulum we can calculate the height of the branch . The swinging tire can be considered equivalent to swinging bob of a pendulum . Here length of pendulum will be equal to height of branch .

Let it be h . Let the time period of swing of tire be T then from the formula of time period of pendulum

[tex]T = 2\pi\sqrt{\frac{l}{g} }[/tex]  where l is length of pendulum .

here l = h so

[tex]T = 2\pi\sqrt{\frac{h}{g} }[/tex]  

[tex]h = \frac{T^2g}{4\pi^2}[/tex]

If we calculate the time period of swing of tire , we can calculate the height of branch .

The time period of swing of tire can be estimated with the help of a stop watch . Time period is time that the tire will take in going from one extreme point to the other end and then coming back . We can easily estimate it with the help of stop watch .

Explanation:

Distance = speed × time

d = (600 km/hr) (2 hr)

d = 1200 km

Answer:

The angle through which the wheel turned is 947.7 rad.

Explanation:

initial angular velocity, [tex]\omega _i[/tex] = 33.3 rad/s

angular acceleration, α = 2.15 rad/s²

final angular velocity, [tex]\omega_f[/tex] = 72 rad/s

angle the wheel turned, θ = ?

The angle through which the wheel turned can be calculated by applying the following kinematic equation;

[tex]\omega_f^2 = \omega_i^2 + 2\alpha \theta\\\\\theta = \frac{\omega_f^2\ -\ \omega_i^2}{2\alpha } \\\\\theta = \frac{(72)^2\ -\ (33.3)^2}{2(2.15)}\\\\\theta = 947.7 \ rad[/tex]

Therefore, the angle through which the wheel turned is 947.7 rad.

Answer:

Transverse

Explanation:

It's tranverse because the water molecules are moving repeatedly up and down vertically when the waves move horizontally across the waters surface.

Answer:

5) 4.00, 2.00, 1.0

Explanation:

wave equation is given as;

F₀ = V / λ

Where;

F₀ is the fundamental frequency = first harmonic

Length of the string for first harmonic is given as;

L₀ = (¹/₂) λ  

λ  = 2 L₀

when L₀ = 1

λ  = 2 x 1 = 2m

when L₀ = 2m

λ  = 2 x 2 = 4m

For First harmonic, the wavelength is 2m, 4m

For second harmonic;

L₁ = (²/₂)λ  

L₁ = λ

When L₁ = 1

λ  = 1 m

when L₁ = 2

λ  = 2 m

For second harmonic, the wavelength is 1m, 2m

Thus, the wavelength that could represent harmonics present on both strings is 4m, 2m, 1 m

Answer:

Advertising, events and experiences, and personal selling all become more important in the maturity stage.

Explanation:

In the growth stage, demand has its own momentum through word of mouth and interactive marketing. hope this helps you :)

Answer:

the answers d

A Carnot heat engine and an irreversible heat engine both operate between the same high-temperature and low-temperature reservoirs. They absorb the same energy from the high-temperature reservoir as heat. The irreversible engine cannot absorb the same energy from the high-temperature reservoir as heat without violating the second law of thermodynamics, therefore the correct option is E.

It is a theoretical engine assumed to have the maximum efficiency among all engines out there in the universe.

No other engine can have greater efficiency than the Carnot engine.

The Carnot engine work on the principle of the Carnot cycle which assume that the heat and work tranfer processes are reversible in nature. there is no loss due to the friction of the piston.

As we know from the second law of thermodynamics that no other engine can have greater efficiency than the Carnot engine.

Thus, the irreversible engine cannot absorb the same energy from the high-temperature reservoir as heat without violating the second law of thermodynamics, therefore the correct option is E.

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Answer:

Initial state    Final state

     3           ⇒        2

     3           ⇒        1

     2          ⇒         1

Explanation:

For this exercise we must use Bohr's atomic model

         E = - 13.606 / n²

where is the value of 13.606 eV is the energy of the ground state and n is the integer.

The energy acquired by the electron in units of electron volt (eV)

          E = e V

          E = 12.5 eV

all this energy is used to transfer an electron from the ground state to an excited state

        ΔE = 13.6060 (1 / n₀² - 1 / n²)

the ground state has n₀ = 1

       ΔE = 13.606 (1 -  1/n²)

        1 /n² = 1 - ΔE/13,606

         1 / n² = 1 - 12.5 / 13.606

         1 / n² = 0.08129

          n = √(1 / 0.08129)

          n = 3.5

 since n is an integer, maximun is

         n = 3

because it cannot give more energy than the electron has

From this level there can be transition to reach the base state.

Initial state    Final state

     3           ⇒        2

     3           ⇒        1

     2          ⇒         1

The possible quantum-jump transitions by which the excited atom emits a photon are :

Initial state    Final state

    3          --->       2

    3          ---->      1

    2          ---->      1

Given data :

Potential difference through which an electron accelerates = 12.5 V

Energy acquired by the the electrons = 12.5 eV  ( e * 12.5 )

The Model we will use to determine the possible quantum jump transition is  Bohr's atomic model

 E = - 13.606 / n²    

where ; n = integer

energy at ground state = 13.606 eV

The energy acquired by the electrons ( 12.5 eV )  is used to move the electron from its ground state to an excited state.

Therefore

ΔE = 13.606 * (1 / n₀² - 1 / n²)  ---- ( 1 )  

where n₀ = 1

Back to equation ( 1 )

ΔE = 13.606 (1 -  1/n²)   -- ( 2 )

Resolving equation ( 2 )

1 / n² = 0.08129

n = 3.5 .    Therefore the maximum integer = 3  

Hence The collision between the electron and the hydrogen atom will undergo three ( 3 ) transition to reach the base state.

In Conclusion The possible quantum-jump transitions by which the excited atom emits a photon are :

Initial state    Final state

    3          --->       2

    3          ---->      1

    2          ---->      1

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Answer:

What is the intensity is 1.3349 × 10⁻⁷ w/m²

Explanation:

Given that;

λ = 582 nm = 582 × 10⁻⁹

R = 75.0 cm = 0.75 m

d = 0.640 mm = 0.000640 m

a = 0.434 mm = 0.000434 m

I₀ =  4.40×10⁻⁴ W/m²

y = 0.710 mm  = 0.00071 m

Now to get our tanФ we say

tanФ = y/R =  0.00071 / 0.75 = 0.0009466  

Ф is so small

∴ tanФ ≈ sinФ

So

∅ = 2πdsinФ / λ

we substitute

∅ = ( 2π × 0.000640 × 0.0009466  ) /  582 × 10⁻⁹

=  6.54 rad

Now

β = 2πasinФ / λ

we substitute

β = ( 2π × 0.000434 × 0.0009466  ) /  582 × 10⁻⁹

β = 4.435 rad

I = I₀ cos²(∅/2) [(sin(β/2))/(β/2)]²

we substitute

I = 4.40×10⁻⁴ cos(3.27)² [ (sin(2.2175)) / (2.2175) ]²  

= 4.40×10⁻⁴ × 0.9967 × 0.0003044

= 1.3349 × 10⁻⁷ w/m²

Answer:

allows for better thermal equilibrium

Explanation:

Due to the cone shape, most of the liquid will be closer to the bottom than the top.  The large surface area of the bottom allows for faster heating.

Answer:

16.26 cm in front of the mirror

Explanation:

Using,

1/f = 1/u+1/v....................... Equation 1

Where f = focal focal length of the concave mirror, u = object distance, v = image distance.

make v the subject of the equation

v = fu/(u-f)................... Equation 2

Note: The focal length of a concave mirror is positive

Using the real- is- positive convention

Given: f = 22/2 = 11 cm, u = 34 cm.

Substitute into equation 2

v = (34×11)/(34-11)

v = 374/23

v = 16.26 cm.

The image will be formed 16.26 cm in front of the mirror.

Answer:

9 Ω

Explanation:

The following data were obtained from the question:

Resistor 1 (R1) = 3 Ω

Resistor 2 (R2) = 3 Ω

Resistor 3 (R3) = 3 Ω

Resistor 4 (R4) = 3 Ω

Resistor 5 (R5) = 3 Ω

Resistor 6 (R6) = 3 Ω

Resistor 7 (R7) = 3 Ω

Resistor 8 (R8) = 3 Ω

Resistor 9 (R9) = 3 Ω

Resistor 10 (R10) = 3 Ω

Resistor 11 (R11) = 3 Ω

Resistor 12 (R12) = 3 Ω

Equivalent Resistance (R) =.?

From the above diagram,

Resistor 1, 2, 3, 4, 5 and 6 are in series connection and in parralle connections with Resistor 7, 8, 9, 10, 11 and 12 which are also in series connection.

Thus we shall determine the equivalent resistance of Resistor 1, 2, 3, 4, 5 and 6

This is illustrated below:

Resistance Ra = R1 + R2 + R3 + R4 + R5 + R6

Ra = 3 + 3 + 3 + 3 + 3 + 3

Ra = 18 Ω

Next, we shall determine the equivalent resistance of Resistor 7, 8, 9, 10, 11 and 12.

This is illustrated below:

Resistance Rb = R7 + R8 + R9 + R10 + R11 + R12

Rb = 3 + 3 + 3 + 3 + 3 + 3

Rb = 18 Ω

Thus, Ra and Rb are in parallel connections. The equivalent resistance between A and B can be obtained as shown below :

Ra = 18 Ω

Rb = 18 Ω

Equivalent resistance R =?

1/R = 1/Ra + 1/Rb

1/R = 1/18 + 1/18

1/R = 2/18

1/R = 1/9

Invert

R = 9 Ω

Therefore, the equivalent resistance between A and B is 9 Ω.

Answer:

98 N.

Explanation:

Given data: mass= 10 kg,      gravity= 9.8 m/s2

required: tension in the cord=  ?

solution:

formula of tension= mass x gravity

by putting values of mass and gravity, we get

tension= 10 x 9.8

tension= 98 N.  Ans

If the mass of the object which is attached with both ends of cord is 10 kg, so the tension which is a opposite force of weight is 98 N.

Answer:

To find out the area of the hot filament of a light bulb, you would need to know the temperature, the power input, the Stefan-Boltzmann constant and Emissivity of the Filament.

Explanation:

The emissive power of a light bulb can be given by the following formula:

E = σεAT⁴

where,

E = Power Input or Emissive Power

σ = Stefan-Boltzmann constant

ε = Emissivity

A = Area

T = Absolute Temperature

Therefore,

A = E/σεT⁴

So, to find out the area of the hot filament of a light bulb, you would need to know the temperature, the power input, the Stefan-Boltzmann constant and Emissivity of the Filament.

Answer:

The velocity of a rotating object and the centripetal force exerted on it are proportional to each other. Centripetal force is equal to mv /r. If the velocity increases, the centripetal force increases as well.

Explanation:

The velocity has the direct effect on the centripetal force. Hence, increasing the velocity, centripetal force also increases or vice - versa.

The given problem is based on the basic concept of centripetal force and fundamentals involved in the centripetal force. The centripetal force is a center seeking force which comes to play, when any object undergoes the rotational motion around the circular path.

The mathematical expression for the centripetal force is given as,

[tex]F= \dfrac{mv^{2}}{r}[/tex]

Here,

m is the mass of an object.

v is the velocity of an object undergoing the motion around the circular path.

r is the radius of curvature.

From the concept of centripetal force, the velocity of a rotating object and the centripetal force exerted on it are proportional to each other. Centripetal force is equal to mv /r. If the velocity increases, the centripetal force increases as well.

Thus, we can conclude that the velocity has the direct effect on the centripetal force. Hence, increasing the velocity, centripetal force also increases or vice - versa.

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A.30cm

B.282.7cm/s

C.26655cm/s²

Explanation:

A. Maximum displacement= Amplitude= 0.3m

B.mum velocity=

2πAf= 2π x 1.5x30 =282.7cm/s

C. Maximum acceleration

= ( angular velocity)² A= (2πf)² A

=( 2 x 3.142 x 1.5)² x 30

2665.5cm/s²

Answer:

3.0 m/s²

Explanation:

Given:

v₀ = 8.0 m/s

v = 14 m/s

t = 2.0 s

Find: a

v = at + v₀

14 m/s = a (2.0 s) + 8.0 m/s

a = 3.0 m/s²

Answer:

The resistor to be hooked up must be 9900 [tex]\Omega[/tex]

Explanation:

Recall how resistors in parallel combine to render an equivalent resistor:

[tex]\frac{1}{R_e} =\frac{1}{R_1} +\frac{1}{R_2}[/tex]

So we need to find which resistor (R2) we need to combine in parallel with resistor R1 (100 [tex]\Omega[/tex]) in order to obtain an equivalent resistor Re (99 [tex]\Omega[/tex]) :

[tex]\frac{1}{99} =\frac{1}{100} +\frac{1}{R_2}\\\frac{9900\,R_2}{99} =\frac{9900\,R_2}{100} +\frac{9900\,R_2}{R_2}\\100\,R_2= 99\,R_2+9900\\R_2=9900\,\,\Omega[/tex]

Answer:

32.13 N

Explanation:

Given that

mass of the crate, m = 3 kg

angle of inclination, = 35°

coefficient of static friction, = 0.3

To solve this, we can assume that the minimum force is F Newton, then use the formula

mgsinA = coefficient of static friction * [F + mgcosA]

=>3 * 9.8 * sin35 = 0.3 * [F + 3 * 9.8 * cos35]

=> 29.4 * 0.5736 = 0.3 * [F + 29.4 * 0.8192]

=> 16.86 = 0.3 [F + 24.08]

=> 16.86 = 0.3F + 7.22

=> 16.86 - 7.22 = 0.3F

=> 0.3F = 9.64

=> F = 9.64/0.3

=> F = 32.13 N

Therefore, the Force that must be applied is 32.13 N

The  net force that must be applied is  9.8 N.

The minimum force required is Fnet.

Fnet = -Ff + mgsinθ

But Ff = μN = μmgcosθ

Fnet = - μmgcosθ + mgsinθ

Where;

m = 3.00 kg

μ =  0.300

θ = 35.0o

Substituting values;

Fnet = mgsinθ - μmgcosθ

Fnet = (3 × 10 × sin 35.0o) - (3 × 0.300  × 10 × cos  35.0o)

= 17.2 - 7.4

Fnet = 9.8 N

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Answer:

The speed stays constant after the force stops pushing.

Explanation:

Speed always stays constant when the force stops pushing it.

Answer:

The correct answer is:

doesn't change (d)

Explanation:

The total energy in a system is the sum of Kinetic and Potential energies in a system, assuming that energy is not lost to an external procedure. Now, let us define what potential and kinetic energies are:

Potential Energy: this is energy at rest or stored energy

Kinetic Energy: this is energy in motion

In a simple harmonic motion of a mass-spring system, there is no dissipative force, hence the total energy is equal to the potential and kinetic energies. The total energy is not changed rather, it varies between potential and kinetic energies depending on the point at which the mass is. The kinetic energy is greatest at the point of lowest amplitude (highest velocity) and lowest at the point of greatest amplitude (lowest velocity), while potential energy is greatest at the point of highest amplitude (lowest velocity) and lowest at the point of smallest amplitude ( highest velocity). However, at every point, the sum of kinetic and potential energies equals total energy.