You are given a copper bar of dimensions 3 cm × 5 cm × 8 cm and asked to attach leads to it in order to make a resistor. If you want to achieve the smallest possible resistance, you should attach the leads to the opposite faces that measure.

A) 3 cm × 5 cm.

B) 3 cm × 8 cm.

C) 5 cm × 8 cm.

D) Any pair of faces produces the same resistance.

Answer:

21.5 °C.

Explanation:

Given:

α = −5.00 × 10−4 °C−1

To = 4°C

Ro = 217 Ω

Rt = 215.1 Ω

Rt/Ro = 1 + α(T - To)

215.1/217 = 1 + (-5 × 10^−4) × (T - 4)

-0.00876 = -5 × 10^−4 × (T - 4)

17.5 = (T - 4)

T = 21.5 °C.

The temperature on a spring day can be calculated by using the relationship between temperature and resistance. Given the initial resistance, the change in resistance and the temperature coefficient of resistivity for carbon, the spring day temperature can be deduced to be 21.51 °C.

The change in temperature can be determined by using the equation ΔR = R0αΔT, where ΔR is the change in resistance, R0 is the initial resistance, α is the temperature coefficient of resistivity and ΔT is the change in temperature. The initial resistance of the carbon resistor is given as 217.0 Ω, the resistance on a spring day was 215.1 Ω, so the change in resistance ΔR is 215.1 - 217.0 = -1.9 Ω. The temperature coefficient for carbon is given as -5.00×10-4 C-1, and α is -5.00×10-4 C-1. We can rearrange the above equation to solve for ΔT: ΔT = ΔR / (R0 * α) = -1.9 Ω / (217.0 Ω * -5.00×10-4 C-1) = 17.51 C.

Thus, the temperature on the spring day would be the winter day temperature plus the calculated change in temperature: T_spring = T_winter + ΔT = 4.00 °C + 17.51 °C = 21.51 °C.

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Answer:

The coefficient of kinetic friction between the puck and the ice is 0.11

Explanation:

Given;

initial speed, u = 9.3 m/s

sliding distance, S = 42 m

From equation of motion we determine the acceleration;

v² = u² + 2as

0 = (9.3)² + (2x42)a

- 84a = 86.49

a = -86.49/84

|a| = 1.0296

[tex]F_k = \mu_k N[/tex] = ma

where;

Fk is the frictional force

μk is the coefficient of kinetic friction

N is the normal reaction = mg

μkmg = ma

μkg = a

μk = a/g

where;

g is the gravitational constant = 9.8 m/s²

μk = a/g

μk = 1.0296/9.8

μk = 0.11

Therefore, the coefficient of kinetic friction between the puck and the ice is 0.11

Answer:

The magnetic field intensity at the point P, equidistant from the wires is

9.566 x  [tex]10^{-5}[/tex] T

Explanation:

The magnetic field intensity can be obtained by resolving the vertical and horizontal components of the magnetic field. The step by step calculation is contained in the pictures attached;

Answer:

t=63s

tempersture gradient -2.36 x 10⁴

Explanation:

Answer:

0.28 ft

Explanation:

We are given that

Strength=m=[tex]36ft^2/s[/tex]

Distance between source and sink=15 ft

Distance between the sink of the source and origin=[tex]a=\frac{15}{2}[/tex] ft

Uniform velocity, U=12 ft/s

We have to find the length of the oval.

Formula to find the half length of the body

[tex]\frac{l}{a}=(\frac{m}{\pi Ua}+1)^{\frac{1}{2}}[/tex]

Where a=Distance between sink of source and origin

U=Uniform velocity

m=Strength

l=Half length

Using the formula

[tex]\frac{l}{\frac{15}{2}}=(\frac{36}{\pi\times 12\times \frac{15}{2}}+1)^{\frac{1}{2}}[/tex]

[tex]l=\frac{2}{15}(\frac{36}{\pi\times 12\times \frac{15}{2}}+1)^{\frac{1}{2}}[/tex]

[tex]l=0.14[/tex]

Length of oval=[tex]2l=2(0.14)=0.28 ft[/tex]

Answer:

The time required to penetrate the 40 cm clay layer is 126.82 years

Explanation:

Given:

Hydraulic gradient = 1 [tex]\frac{cm}{cm}[/tex]

Permeability of clay [tex]K = 1 \times 10^{-8}[/tex] [tex]\frac{cm}{sec}[/tex]

Time required to penetrate 40 cm clay layer,

  [tex]= \frac{40}{K}[/tex]

  [tex]= \frac{40}{1 \times 10^{-8} }[/tex]

  [tex]= 40 \times 10^{8}[/tex] sec

But we have to find time in years,

  [tex]= \frac{40 \times 10^{8} }{24 \times 60 \times 60 \times 365}[/tex] years

  [tex]= 126.82[/tex] years

Therefore, the time required to penetrate the 40 cm clay layer is 126.82 years

Answer:

its a

Explanation:

Answer:

[tex] m = \rho V[/tex]

Since we have an ball we can consider this like a sphere and the volume is given by [tex] V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (1.69cm)^3 = 20.218 cm^3 = 0.00002022 m^3[/tex]

The density for the copper is approximately [tex] \rho = 8940 kg/m^3[/tex]

So then the mass is :

[tex] m =8940 kg/m^3 * 0.00002022m^3 = 0.1808 Kg[/tex]

And now we have everything in order to replace into the formula for F, like this:[tex] F = 0.1808 Kg *9.8 m/s^2 + 0.884 kg/s * 0.093 m/s= 1.772 +0.975 N = 2.747 N[/tex]And that would be the final answer for this case.

Explanation:

For this case if we assume that we have a damping motion the force action on the vertical direction would be:

[tex] F = mg + bv[/tex]

Where F represent the upward force on the copper ball

m represent the mass

g = 9.8 m/s^2 represent the gravity

b = 0.884 kg/s represent the proportionality constant

v = 9.3 cm/s = 0.093 m/s represent the velocity

We can solve for the mass from the following expression:

[tex] m = \rho V[/tex]

Since we have an ball we can consider this like a sphere and the volume is given by [tex] V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (1.69cm)^3 = 20.218 cm^3 = 0.00002022 m^3[/tex]

The density for the copper is approximately [tex] \rho = 8940 kg/m^3[/tex]

So then the mass is :

[tex] m =8940 kg/m^3 * 0.00002022m^3 = 0.1808 Kg[/tex]

And now we have everything in order to replace into the formula for F, like this:[tex] F = 0.1808 Kg *9.8 m/s^2 + 0.884 kg/s * 0.093 m/s= 1.772 +0.975 N = 2.747 N[/tex]And that would be the final answer for this case.

Answer:

A) vᵣ = 1.2 m/s

B) vₜ = 0.4π m/s = 1.257 m/s

C) aᵣ = - 1.2π m/s² = - 3.771 m/s²

D) aₜ = 7.2 m/s²

Explanation:

Given,

θ' = 3 rad/s

r = 0.4 θ

Note that

θ' = (dθ/dt) = 3 rad/s

θ" = (d²θ/dt²) = (d/dt) (3) = 0 rad/s²

r' = (dr/dt) = (d/dt) (0.4θ) = 0.4 (dθ/dt) = 0.4 × θ' = 0.4 × 3 = 1.2 m/s

r" = (d²r/dt²) = 0.4 (d²θ/dt²) = 0 m/s²

A) Radial component of the velocity of P at the instant θ=π/3rad.

From the kinematics of a particle in a plane,

vᵣ = r' = 1.2 m/s

B) Transverse component of the velocity and acceleration of P at the instant θ=π/3rad.

vₜ = rθ' = (0.4 θ) (3) = 1.2 θ = 1.2 (π/3) = 0.4π m/s = 1.257 m/s

C) Radial component of the acceleration of P at the instant θ=π/3rad.

aᵣ = r" - r(θ'²) = 0 - (0.4θ)(3²) = - 3.6θ = - 3.6 (π/3) = - 1.2π m/s² = - 3.771 m/s²

D) Transverse component of the acceleration of P at the instant θ=π/3rad

aₜ = rθ" + 2r'θ' = (0.4θ)(0) + (2)(1.2)(3) = 0 + 7.2 = 7.2 m/s²

Hope this Helps!!!

The response requires understanding rotational kinematics and dynamics to determine the velocity and acceleration of a particle moving along a spiral guide, involving calculus and principles of rotational motion.

The question pertains to kinematics in the context of rotational and spiral motion. In particular, it involves the motion of a particle along a spiral guide with a given radial dependency on the angle turned through (in radians). To find the velocity and acceleration of the particle, one must apply the equations of motion that relate linear and angular quantities and consider any given geometric relationships and constraints, such as the provided relationship between radial distance and angular position. To solve the tasks posed, one would typically employ differential calculus and the principles of rotational dynamics including tangential and radial components of velocity and acceleration.

For example, the velocity of the particle can be found by taking the time derivative of the radial position r, which in turn depends on the angular velocity ω. The acceleration would then be found by differentiating the velocity with respect to time or by explicitly using the tangential and radial acceleration components for rotational motion, which are related to ω and its time derivative (angular acceleration).

Answer:

[tex]CPP=52mm \ Hg[/tex]

Explanation:

Cerebral Perfusion Pressure is obtained by subtracting IntraCranial Pressure(ICP) from the Mean Arterial Pressure(MAP). Adequate cerebral perfusion requires a minimum goal of [tex]70mm \ Hg[/tex]. MAP is obtained using the formula:-

[tex]MAP=\frac{(diastolic \ blood \ pressure\times2)+\ systolic \ blood \ pressure)}{3}\\\\MAP=\frac{2\times60+90}{3}\\\\MAP=70mm \ Hg\\CPP=MAP-ICP\\CPP=70-18\\CPP=52mm \ Hg[/tex]

Answer:

Voltage= 9.4 V

Current= 1.3 A

Explanation:

Equivalent resistance will be the sum of two resistors hence

[tex]R_{equ}[/tex]=2+7.2=9.2Ω

From Ohm's law, V=IR where I is current, R is equivalent resistance and V is voltage

Terminal voltage will be given by V=e-Ir where r is internal resistance, I is current and e is electromotive force.

From Ohm's law, current is given by dividing emf of the battery by the equivalent resistance hence

[tex]I=\frac {e}{R_{equ}}\\I=\frac {12}{9.2}=1.304347826A\approx 1.3A[/tex]

This is the current through external resistor

Terminal voltage will be given by V=e-Ir hence V=12-(1.3*2)=9.4 V

Final answer:

The terminal voltage across the 7.2
Ω resistor when connected to a 12.0 V battery with 2.0
Ω internal resistance is approximately 9.392 V, and the current flowing through the resistor is approximately 1.304 A.

Explanation:

The student is asking about the calculation of terminal voltage and current through a resistor when connected to a battery that has internal resistance. This is a problem related to the topic of electrical circuits in Physics.

To find the current through the 7.2
Ω resistor, use Ohm's law which states that V = IR, where V is voltage, I is current, and R is resistance. Since the battery has an internal resistance, we need to consider the total resistance in the circuit which is the sum of the internal resistance and the resistance of the 7.2
Ω resistor.

Total resistance (Rtotal) = Internal resistance (r) + External resistance (R) = 2.0
Ω + 7.2
Ω = 9.2
Ω

Using Ohm's Law, the current (I) through the circuit can be calculated as follows:
I = V / Rtotal = 12.0 V / 9.2
Ω = 1.304
A (approximately).

To find the terminal voltage (Vterminal) across the 7.2
Ω resistor when the current is flowing, we account for the voltage drop across the internal resistance:
Vterminal = emf - I × r = 12.0 V - (1.304
A × 2.0
Ω) = 12.0 V - 2.608 V = 9.392 V (approximately).

The terminal voltage across the 7.2
Ω resistor when it is connected to the battery is 9.392 V, and the current flowing through the resistor is 1.304
A.

Answer:

Total drag force is 88.74 N

Rate of heat transfer over the entire plate per unit width is 26451.6 W

Explanation:

The rate of heat transfer over the entire plate per unit width can be obtained by applying the Newton's law of cooling. The pictures attached are step by step solution to the question;

Answer:

(a) L = 149.2 cm

(b) d = 0.033 cm

Explanation:

Note that the resistivity of copper is

[tex]\rho = 1.72\times 10^{-8}~{\rm \Omega . m} = 1.72\times 10^{-6}~{\rm \Omega.cm}[/tex]

and the mass density of copper is

[tex]d = 8.96~{\rm g/cm^3}[/tex]

We will use the following formula to relate the resistance to other parameters

[tex]R = \frac{\rho L}{A} = \frac{\rho L}{\pi r^2}[/tex]

If all the copper with 1.15 g is used, then

[tex]m = dV\\1.15 = 8.96 \times (L\pi r^2)\\L\pi r^2 = 0.128[/tex]

Back to the resistance:

[tex]0.3 = \frac{1.72\times 10^{-6} L}{\pi r^2}\\L = \pi r^2 (1.74\times 10^5)\\L = \frac{0.128}{L}(1.74\times 10^5)\\L = 149.2~{\rm cm}[/tex]

Then, the diameter is

[tex]149.2\times \pi r^2 = 0.128\\r = 0.0165~{\rm cm}\\d = 2r = 0.033~{\rm cm}[/tex]

Explanation:

As we all know that the atom mainly composed of two parts, Nucleus at the center and the electrons dancing around it. And, yes there is a vast distance between nucleus and the electrons and it's about ten billionth of a meter. So the question is if there is such an empty space then why not our body just move through the chair and fall?  So the answer is, it's all due to the forces. Just like the cracking of lightning through the void, specks of electrons and nuclei are constantly interacting through the force called electromagnetic forces. During each interaction there is an exchange of energy particles called photons. So the each photon swapped is equals to the push or pull or the forces exerted across the emptiness. So these forces enable us to sit on chair or to do other things.

Answer:

d. Test the rods one pair at a time in each possible end‑to‑end orientation until finding a pair that repels; the leftover rod is unmagnetized.

Explanation:

Repulsion is the surest test of magnetisation . If two objects repel each other , they must be magnets . If two objects attract each other , they may not be magnets. In later case , one may be non - magnet. So the last test will help us identify the unmagnetised rod.

The textbook would not likely suggest 'Physics ability is less likely than math to reflect real biological differences' as an explanation for identical physics scores between genders. This because research shows academic abilities aren't influenced by biological gender differences but rather other factors like sociocultural influences, teaching methods, and individual variance.

The statement that would not be an explanation for finding the almost identical distribution of physics scores between male and female students, based on information provided in a textbook, is a. Physics ability is less likely than math to reflect real biological differences.

This claim implies there is a biological basis for differing abilities in physics between genders. However, research has largely debunked this concept, showing that abilities in academic subjects are not influenced by biological gender differences. Instead, other factors like sociocultural influences, teaching methods, and individual variance play a significant role.

Options b, c, and d all refer to sociocultural aspects such as the way physics is taught, the societal concept of gender roles, and the equality of the society. These, not inherent biological differences, could explain identical distributions of physics scores between genders.

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Answer:

w = 0.189 rad/ s

Explanation:

This exercise we work with the conservation of the moment, the system is made up of the merry-go-round and the child, for which we write the moment of two instants

Initial

         L₀ = I₀ w₀

Final

          [tex]L_{f}[/tex] = I w

         L₀ = L_{f}

         I₀ w₀ = I_{f} w

         .w = I₀/I_{f}   w₀

The initial moment of inertia is

        I₀ = 500 kg. m2

The final moment of inertia

         [tex]I_{f}[/tex] = 500 + m r²

         I_{f} = 500 + 20 1.5

         I_{f} = 530 kg m²

Initial angular velocity

         w₀ = 0.20 rad / s

Let's calculate

          w = 500/530 0.20

          w = 0.189 rad / s

Answer:

(c) 10.29 J

(d) 113.19 J

(e) 113.19 J

(f) 10061 N/m

Explanation:

15 cm = 0.15 m

Let g = 9.8 m/s2

(c) The work done by gravitational force is the product of gravity force and the distance compressed

[tex]E_p = mgx = 7*9.8*0.15 = 10.29 J[/tex]

(d) By using law of energy conservation with potential energy reference being 0 at the maximum compression point. As the ball falls and come to a stop at the compression point, its potential energy is transferred to elastic energy, which is the work that the mattress does on the ball:

[tex]E_p = E_e[/tex]

[tex]E_e = mgh[/tex]

where h = 1.5 + 0.15 = 1.65 m is the vertical distance that it falls.

[tex]E_e = 7*9.8*1.65 = 113.19 J[/tex]

(e) Before the compression, the potential energy of the mattress is 0. After the compression, the potential energy is 113.19J. So it has increased by 113.19J due to the potential energy transferred from the falling ball.

(f) [tex]E_e = 113.19 = kx^2/2[/tex]

[tex]k0.15^2/2 = 113.19[/tex]

[tex]k = 10061 N/m[/tex]

Answer:

(C) Wg = 113.2J

(D) Wm = 10.3J

(E) E = 1/2kx² + mgh where h is the height above the mattress and x is the compressed distance in the mattress.

(F) k = 457N/m.

Explanation:

See attachment below.

Answer:

Friction acts in the opposite direction to the motion of the truck and box.

Explanation:

Let's first review the problem.

A moving truck applies the brakes, and a box on it does not slip.

Now when the truck is applying brakes, only it itself is being slowed down. Since the box is slowing down with the truck, we can conclude that it is friction that slows it down.

The box in the question tries to maintains its velocity forward when the brakes are applied. We can think of this as the box exerting a positive force relative to the truck when the brakes are applied. When we imagine this, we can also figure out where the static friction will act to stop this positive force. Friction will act in the negative direction. Or in other words, friction will act in the opposite direction to the motion of the truck and box. This explains why the box slows down with the truck, as friction acts to stop its motion.

Final answer:

The frictional force acting on the box in a decelerating truck acts forward, towards the direction of the truck's original motion. This occurs as a result of trying to prevent the box from slipping backward by opposing its tendency to remain in motion, illustrating key concepts from Newton's laws of motion.

Explanation:

When the truck brakes and slows down at a constant acceleration, the box inside does not slip due to the frictional force acting on it. The direction of the frictional force on the box will be forward, towards the direction of the truck's original motion.

This might initially seem counterintuitive, but it's essential to understand that the frictional force is what keeps the box from sliding backward as the truck decelerates. According to Newton's first law of motion, an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.

In this case, the frictional force acts as that external force, opposing the box's tendency to remain in motion while the truck slows down.

Friction, in physics, acts opposite to the direction of motion and is necessary for stopping the movement of objects. Since the truck is decelerating, the box tries to maintain its state of motion (Newton's first law), but the frictional force acts forward relative to the truck to prevent the box from slipping backward.

This example beautifully demonstrates the role of friction in everyday phenomena, aligning with concepts like Newton's laws of motion and the interaction between surfaces in contact.

Answer:

h = 4.281 m

Explanation

Given Data,

Weight of disk = 2kg

Speed of water jet (V) = 10 m/s

diameter of water jet = 25 mm

Cal. the velocity of the water jet as function height by applying Bernoulli's  eqtn of water surface to the jet

[tex]\frac{P}{\rho } +\frac{V^{2}}{2} + gz[/tex] = Constant

[tex]\frac{V_{0}^{2}}{2} + g(0) = \frac{V^{2}}{2} + g[/tex]

[tex]V=\sqrt{V_{0}^{2}-2gh}[/tex]

Relation between  [tex]V_{0}[/tex] & V

[tex]m=\rho V_{0}A_{0}[/tex]

[tex]\rho VA=\rho V_{0}A_{0}[/tex]

[tex]VA= V_{0}A_{0}[/tex]

Momentum

[tex]F_{w}+F_{d}= \frac{\partial }{\partial t}\int_{cv} w\rho dA + \int_{cs} w\rho V dA[/tex]

[tex]-mg = w_{1}[-\rho VA] +w_{2}[\rho VA][/tex]

[tex]w_{1}[/tex] = V

[tex]w_{2}[/tex] = 0

[tex]mg = \rho V^{2}A[/tex]

[tex]mg = \rho VV_{0} A[/tex]

[tex]mg = \rho VV_{0} A_{0}[/tex]

[tex]mg = \rho V_{0} A_{0} \sqrt{V_{0} ^{2}-2gh }[/tex]

Solving for h

[tex]h = \frac{1}{2g}[V_{0}^{2}-\frac{mg}{\rho V_{0}A_{0}}][/tex]

g is gravitational acc.

[tex]= \frac{1}{2\times 9.81}[10^{2}-(\frac{2\times 9.81}{999\times10\times\frac{\Pi }{4}\times(0.025)^{2}})^{2} ][/tex]

[tex]= \frac{1}{19.62}[100-(\frac{19.68}{4.9038})^{2}][/tex]

[tex]= \frac{100-16.0078}{19.62}[/tex]

h = 4.281 m

h of disk on which it remains stationary.

Answer: The statement is TRUE.

Explanation: The Newton's third law states that a body that experiments an external force responds with an opposite force with same magnitude. Therefore, the statement is true.

Answer:

Explanation:

electric potential of electron

= k Qq / r

= - 9 x 10⁹ x 1.4 x 10⁻¹⁵ x 1.6 x 10⁻¹⁹ / ( 1.2 x 10⁻² )

= - 16.8 x 10⁻²³ J

If v be the escape velocity

1/2 m v² = potential energy of electron

= 1/2 x 9.1 x 10⁻³¹ x v² = 16.8 x 10⁻²³

v² = 3.69 x 10⁸

v = 1.92 x 10⁴ m /s

Answer:

[tex]F=800N[/tex]

Explanation:

The average force is defined as the mass of the body multiplied by its average velocity over the contact time. According to the third Newton's law,  the magnitude of the average force exerted on the wall by the ball is equal to  the magnitude of the average force exerted on the ball by the wall. Thus:

[tex]F=m\frac{v_f-v_i}{t}\\F=0.80kg\frac{25\frac{m}{s}-(-25\frac{m}{s})}{0.05s}\\F=800N[/tex]

Answer:

800 N

Explanation:

Force: This can be defined as the product of mass and acceleration. The S.I unit of force is Newton(N).

From the question,

F = m(v-u)/t ....................... Equation 1

Where F = force exerted on the wall by the ball, m = mass of the ball, v = final velocity, u = initial velocity, t = time.

Note: Assuming the direction of the initial motion to be negative

Given: m = 0.80 kg, v = 25 m/s ( bounce back), u = -25 m/s, t = 0.05 s

Substitute into equation 1

F = 0.8[25-(25)]/0.05

F = 0.8(50)/0.05

F = 0.8(1000)

F = 800 N

Answer:

1.6*10⁻¹⁹ J = 1 eV

Explanation:

        [tex]\Delta U_{e} = e*\Delta V[/tex]

        ⇒ [tex]\Delta U_{e} = e*\Delta V = 1.6e-19 C* 1.0 V = 1.6e-19 J = 1 eV[/tex]

Explanation:

Below is an attachment containing the solution.

Answer: [tex]V_{\epsilon}\propto \frac{d\phi_{B}}{dt}[/tex]

Explanation:

A direct proportionality means a linear relationship between two variables and rate of change means an application of derivatives. Hence, the mathematical model is:

[tex]V_{\epsilon}\propto \frac{d\phi_{B}}{dt}[/tex]

Faraday's Law of Induction, primarily focused on Physics, reveals that the induced electromotive force in a coil is proportional to the rate of change of magnetic flux through the coil and is also dependent on the number of coil turns.

Understanding Faraday's Law of Induction

Faraday's Law of Induction is a critical concept in electromagnetism, underlying the working principles of various electrical devices. The induced electromotive force (emf) is directly proportional to the time rate of change of magnetic flux. In simpler terms, when the magnetic environment of a circuit changes, an emf is induced. Faraday's Law is given by the equation EMF = -N(ΔΦ/Δt), where 'N' represents the number of turns in a coil, and (ΔΦ/Δt) is the rate of change of magnetic flux over time. This equation highlights three main factors influencing the induced EMF:

The negative sign in Faraday's Law is a reflection of Lenz's Law, which indicates that the induced emf always works to oppose the change in magnetic flux that produces it.

Explanation:

When copper rod is heated , its length increases

The increase in length can be found by the relation

L = L₀ ( 1 + α ΔT )

here L is the increased length and L₀ is the original length

α  is the coefficient of linear expansion and ΔT is the increase in temperature .

The increase in length = L - L₀ = L₀ x α ΔT

Substituting all these value

Increase in length = 27.5 x 1.7 x 10⁻⁵ x 35.9

= 1.87 x 10⁻² m

Answer:0.01678325m

Explanation:

Original length(L1)=27.5m

Temperature rise(@)=35.9°C

Linear expansivity(α)=0.000017

Length increase(L)=?

L=α x L1 x @

L=0.000017 x 27.5 x 35.9

L=0.01678325m

Answer:

(d) 14.7 J.

Explanation:

Using the equation,

W = mghsin∅.................  equation 1

Where W = work  done on  the cart by the force of gravity, g = acceleration due to gravity, h = height, ∅ = angle between the displacement and the force of gravity.

Given: m = 2 kg, g = 9.8 m/s², h = 1.5 m, ∅ = 30°

Substitute into equation 1

W = 2(9.8)(1.5)sin30

W = 2×9.8×1.5×0.5

W = 14.7 J.

The right option is (d) 14.7 J

The work done by gravity on a 2-kg cart rolling down a 1.5 m, 30° incline is 14.7 J, corresponding to option (d).

When an object slides down an inclined plane, the work done by gravity can be calculated using the formula W = mgh, where W is the work done, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s2), and h is the vertical height. The vertical height can be determined from the incline's length and the angle of inclination using the sine function (h = l · sin(θ)). For a 2-kg cart rolling a distance of 1.5 m down a 30° incline, the work done by gravity would be W = m · g · l · sin(θ) = 2 kg · 9.8 m/s2 · 1.5 m · sin(30°) = 2 · 9.8 · 1.5 · 0.5 = 14.7 J, which corresponds to option (d).

Answer:

The minimal vertical distance from the level of the person’s eye is 2.55 cm.

Explanation:

Given;

height of the person = 1.9 m

his eyes are 5.1 cm below the top of his head

If top of his head is the same distance from the mirror as his eyes is from the mirror, then the top of the mirror must be half of his eyes level.

Therefore, the minimal vertical distance from the level of the person’s eye is ¹/₂ x 5.1 cm = 2.55 cm

The minimal vertical distance of the mirror from the level of the person’s eye is 2.55 cm.

Answer:

The partial pressure of H2 is 0.375 atm

The partial pressure of Ne is also 0.375 atm

Explanation:

Mass of H2 = 1 g

Mass of Ne = 1 g

Mass of Ar = 1 g

Mass of Kr = 1 g

Total mass of gas mixture = 1 + 1 + 1 + 1 = 4 g

Pressure of sealed container = 1.5 atm

Partial pressure of H2 = (mass of H2/total mass of gas mixture) × pressure of sealed container = 1/4 × 1.5 = 0.375 atm

Partial pressure of Ne = (mass of Ne/total mass of gas mixture) × pressure of sealed container = 1/4 × 1.5 = 0.375 atm

The partial pressures of H2 and Ne in the mixture under ideal gas behavior are approximately 1.278 atm and 0.128 atm respectively. This is calculated using their mole fractions and the total pressure.

In this scenario, we're essentially dealing with ideal gas behavior. The partial pressure of a gas in a mixture can be determined by the mole fraction of the gas times the total pressure. The moles of each gas can be calcuated using the equation: moles = mass/molar mass. The molar masses of H2, Ne, Ar, and Kr are approximately 2 g/mol, 20 g/mol, 40 g/mol, and 84 g/mol, respectively.

For example, moles of H2 ≈ 1.000 g / 2 g/mol = 0.5 mol. Likewise, moles of Ne = 1.000 g / 20 g/mol = 0.05 mol, moles of Ar = 1.000 g / 40 g/mol = 0.025 mol, and moles of Kr = 1.000 g / 84 g/mol = 0.012 mol. The total moles of gas = 0.5 mol + 0.05 mol + 0.025 mol + 0.012 mol = 0.587 mol.

The mole fraction of H2 = 0.5 mol / 0.587 mol = 0.852. Therefore, the partial pressure of H2 = 0.852 * 1.5 atm = 1.278 atm. Applying the same calculations for Ne, the mole fraction of Ne = 0.05 mol / 0.587 mol = 0.085. Therefore, the partial pressure of Ne = 0.085 * 1.5 atm = 0.128 atm.

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