🔑:## Step 1: Understanding the SetupThe apparatus for investigating the photoelectric effect consists of two electrodes: an emitting electrode (also known as the photocathode) and a collecting electrode (also known as the anode). The emitting electrode is connected to the positive terminal of a battery, and the collecting electrode is connected to the negative terminal.## Step 2: Photoelectron EmissionWhen light of sufficient frequency (and thus energy) hits the emitting electrode, it can eject electrons from the surface of the electrode. These ejected electrons are known as photoelectrons. The energy of the light is transferred to the electrons, allowing them to overcome the work function of the material (the minimum energy required for an electron to escape the surface).## Step 3: Movement of PhotoelectronsThe photoelectrons emitted from the emitting electrode travel across the gap between the electrodes. Since the emitting electrode is connected to the positive terminal of the battery and the collecting electrode is connected to the negative terminal, there is an electric field across the gap that pulls the negatively charged electrons towards the collecting electrode.## Step 4: Role of the BatteryThe battery provides the potential difference (voltage) necessary to create an electric field between the two electrodes. This electric field accelerates the photoelectrons towards the collecting electrode, ensuring that they reach it. The battery also supplies the energy needed to move the electrons against any opposing forces, such as the work function of the collecting electrode, if it has one.## Step 5: Current ProductionAs the photoelectrons reach the collecting electrode, they constitute an electric current. The current is the flow of charge (in this case, electrons) per unit time. The battery's role is crucial here because it not only facilitates the movement of electrons towards the collecting electrode but also completes the circuit by allowing electrons to flow from the negative terminal, through the external circuit, and back to the positive terminal.## Step 6: Equilibrium EstablishmentAn equilibrium is established when the rate at which photoelectrons are emitted and reach the collecting electrode equals the rate at which electrons are supplied by the battery to replace those that have been emitted. This equilibrium ensures a steady current flow. The battery maintains the potential difference necessary for the electric field to accelerate the electrons across the gap, thus sustaining the current.The final answer is: boxed{Current}

🔑:## Step 1: Calculate the energy transferred to the waterTo find the specific heat capacity of the copper sample, we first need to calculate the energy transferred to the water. The energy transferred can be calculated using the equation Q = mcΔT, where m is the mass of the water (242.3g), c is the specific heat capacity of water (4.184 J/g°C), and ΔT is the change in temperature of the water. The change in temperature of the water is 22.1°C - 18.5°C = 3.6°C.## Step 2: Apply the equation Q = mcΔT for waterSubstitute the given values into the equation to find the energy transferred: Q = 242.3g * 4.184 J/g°C * 3.6°C.## Step 3: Perform the calculation for energy transferred to the waterQ = 242.3g * 4.184 J/g°C * 3.6°C = 242.3 * 4.184 * 3.6 = 3791.49712 J.## Step 4: Calculate the energy lost by the copperThe energy lost by the copper is equal to the energy gained by the water, as energy is conserved in this closed system. Therefore, the energy lost by the copper is also 3791.49712 J.## Step 5: Apply the equation Q = mcΔT for copperFor the copper, the equation is 3791.49712 J = m_c * c_c * ΔT_c, where m_c is the mass of the copper (70.2g), c_c is the specific heat capacity of the copper (which we are trying to find), and ΔT_c is the change in temperature of the copper (103°C - 22.1°C = 80.9°C).## Step 6: Rearrange the equation to solve for the specific heat capacity of copperRearrange the equation to solve for c_c: c_c = Q / (m_c * ΔT_c).## Step 7: Substitute the values into the rearranged equationSubstitute the known values into the equation: c_c = 3791.49712 J / (70.2g * 80.9°C).## Step 8: Perform the calculation for the specific heat capacity of copperc_c = 3791.49712 J / (70.2g * 80.9°C) = 3791.49712 J / 5674.98 = 0.668 J/g°C.The final answer is: boxed{0.668}

🔑:## Step 1: Understand the Continuity EquationThe continuity equation states that for an incompressible fluid flowing through a pipe of uniform cross-sectional area, the volume flow rate (Q) remains constant. This can be expressed as Q = A1v1 = A2v2, where A1 and A2 are the cross-sectional areas at points 1 and 2, and v1 and v2 are the velocities at those points. Since the pipe has a uniform cross-sectional area, A1 = A2, which simplifies the equation to v1 = v2. However, this step is more about understanding the principle; the actual application comes when considering changes in area or flow rate, which is not the focus here.## Step 2: Apply Bernoulli's PrincipleBernoulli's Principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Mathematically, this is expressed as P1/ρ + 1/2v1^2 + gz1 = P2/ρ + 1/2v2^2 + gz2, where P1 and P2 are the pressures at points 1 and 2, ρ is the fluid density, v1 and v2 are the velocities at points 1 and 2, g is the acceleration due to gravity, and z1 and z2 are the heights of the fluid at points 1 and 2.## Step 3: Simplify Bernoulli's Equation for Horizontal PipeSince the pipe is horizontal, the change in height (z1 - z2) is zero, which simplifies Bernoulli's equation to P1/ρ + 1/2v1^2 = P2/ρ + 1/2v2^2. For a fluid accelerating due to a pressure difference, we can assume that the velocity increases as the pressure decreases.## Step 4: Determine the Relationship Between Velocity and PressureFrom the simplified Bernoulli's equation, if the velocity increases (v2 > v1), then the pressure must decrease (P2 < P1) to satisfy the equation, assuming ρ remains constant. This shows a direct relationship between the decrease in pressure and the increase in velocity.## Step 5: Implications for Pressure DistributionAs the fluid flows through the pipe and its velocity increases due to the pressure difference, the pressure within the pipe decreases. This decrease in pressure is a direct result of the conversion of potential energy (pressure) into kinetic energy (velocity) as per Bernoulli's Principle.The final answer is: boxed{v = sqrt{frac{2(P_1 - P_2)}{rho}}}

🔑:Conservative and non-conservative forces are two types of forces that can act on an object, and they differ in the way they do work on the object. Understanding the difference between these forces is crucial in physics, as it helps in predicting the behavior of objects under various conditions.Conservative Forces:A conservative force is a force that does work on an object, but the work done depends only on the initial and final positions of the object, not on the path taken. In other words, the work done by a conservative force is path-independent. Examples of conservative forces include:* Gravity: The force of gravity acting on an object is a conservative force, as the work done by gravity depends only on the initial and final heights of the object, not on the path taken.* Elastic forces: The force exerted by a stretched or compressed spring is a conservative force, as the work done by the spring depends only on the initial and final displacements of the spring, not on the path taken.* Electric forces: The force exerted by an electric field on a charged particle is a conservative force, as the work done by the electric field depends only on the initial and final positions of the particle, not on the path taken.Mathematically, a conservative force can be represented as:F = -∇Uwhere F is the force, ∇ is the gradient operator, and U is the potential energy associated with the force.Non-Conservative Forces:A non-conservative force, on the other hand, is a force that does work on an object, but the work done depends on the path taken. In other words, the work done by a non-conservative force is path-dependent. Examples of non-conservative forces include:* Friction: The force of friction acting on an object is a non-conservative force, as the work done by friction depends on the path taken by the object.* Air resistance: The force exerted by air resistance on an object is a non-conservative force, as the work done by air resistance depends on the path taken by the object.* Magnetic forces: The force exerted by a magnetic field on a moving charge is a non-conservative force, as the work done by the magnetic field depends on the path taken by the charge.Mathematically, a non-conservative force cannot be represented as the gradient of a potential energy function.Work Done by a Force:The work done by a force on an object can be used to determine whether the force is conservative or non-conservative. The work done by a force is given by the dot product of the force and the displacement of the object:W = ∫F · drIf the work done by a force is path-independent, then the force is conservative. On the other hand, if the work done by a force is path-dependent, then the force is non-conservative.Diagram:Consider a particle moving in a circular path under the influence of a force F. If the force is conservative, then the work done by the force is zero, as the particle returns to its initial position.In this case, the work done by the force can be represented as:W = ∫F · dr = 0This is because the force is conservative, and the work done depends only on the initial and final positions of the particle, not on the path taken.On the other hand, if the force is non-conservative, then the work done by the force is not zero, even if the particle returns to its initial position.In this case, the work done by the force can be represented as:W = ∫F · dr ≠ 0This is because the force is non-conservative, and the work done depends on the path taken by the particle.Equations:The work-energy theorem states that the change in kinetic energy of an object is equal to the work done by the net force acting on the object:ΔK = WIf the force is conservative, then the work done by the force can be represented as:W = Uf - Uiwhere Uf is the final potential energy and Ui is the initial potential energy.On the other hand, if the force is non-conservative, then the work done by the force cannot be represented as the difference in potential energies.In conclusion, conservative forces do work that depends only on the initial and final positions of an object, while non-conservative forces do work that depends on the path taken. The work done by a force can be used to determine whether the force is conservative or non-conservative. Mathematical equations and diagrams can be used to support this understanding and to calculate the work done by various forces.