Solving Physics Problems: Tips & Formulas

[dandirom]

Hi there,

I'd like some help with the formulas of these following problems. I just need some tips on how to go about answering them -- I'd like to solve them on my own though.

1.
Two rods of equal lengths and cross-sectional areas but of different materials are placed in thermal contact as shown in Figure 2. The thermal conductivity of Q is half that of P. The outer end of P
is at 0 C and that of Q is at 100 C.
What is the temperature of the interface at steady state?

2.
In two experiments with a continuous flow calorimeter to determine the specific heat capacity of a liquid, an input power of 60 W produced a rise of 10 K in the liquid. When the power was doubled, the same temperature rise was achieved by making the rate of flow of liquid three times faster. The power lost to the surroundings in each case was?




3.
A glass sphere of volume 7 l contains air at 27C and is connected to a pipe filled with mercury as shown in Figure 5 below. At the start, the mercury meniscus is level with the bottom of the sphere on both arms of the pipe. The air in the sphere is now heated and the mercury level on the right arm rises 5 mm. If the cross sectional area of the pipe is 10 cm2, what is the new temperature of the air (in C)?

4.
The distance between the double slits to the screen is 3.0 m. The slit separation is 0.2 mm, and the wavelength of incident light is 633 nm.

(i) Determine the angular displacement of the third order minima.
(ii) Determine the fringe width of the interference pattern observed on the
screen.
(iii) Estimate the theoretical maximum number of bright fringes that can be observed.
(iv) If the widths of the slits are assumed to be infinitely small and y is the distance from the central maxima on the screen, sketch a clearly labelled graph to show the variation of the intensity of the fringe pattern with y. The intensity of the waves from each slit is I0. Express the intensity in terms of I0.
(v) The slit S1 is now covered with a filter such that the light emerging from S1 is reduced by half in amplitude. Sketch on the same graph for part (iv), the new intensity pattern you would expect to observe. Label your graphs clearly.

 

[anathema]

1. To solve this problem, you will need to use the equation for thermal conductivity: Q/t = kA(T1-T2)/L, where Q is the heat transfer, t is time, k is thermal conductivity, A is cross-sectional area, T1 and T2 are temperatures, and L is length. Since the rods are in thermal contact, the heat transfer will be the same for both rods. Set up two equations using this formula for each rod and solve for the unknown temperature at the interface.

2. This problem involves using the equation for specific heat capacity: Q = mcΔT, where Q is heat transfer, m is mass, c is specific heat capacity, and ΔT is change in temperature. In the first experiment, the power lost to the surroundings can be found by subtracting the input power from the heat transfer. In the second experiment, use the fact that the same temperature rise was achieved by increasing the rate of flow of liquid three times faster to set up a ratio between the two experiments and solve for the unknown power lost to the surroundings.

3. This problem involves using the ideal gas law: PV = nRT, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature. At the start, the pressure in the sphere is equal to the atmospheric pressure and the volume is 7 liters. After heating, the volume remains constant, but the pressure increases on the right side of the pipe, causing the mercury level to rise. Use this information to solve for the new temperature of the air in the sphere.

4. This problem involves using the equations for double slit interference: d sin θ = mλ, where d is the slit separation, θ is the angle of the minima, m is the order of the minima, and λ is the wavelength. Use this equation to solve for the angular displacement of the third order minima. To find the fringe width, use the equation: β = λL/d, where β is the fringe width, λ is the wavelength, L is the distance to the screen, and d is the slit separation. To find the maximum number of fringes, use the equation: N = L/d, where N is the maximum number of fringes, L is the distance to the screen, and d is the slit separation. To sketch the intensity graph, use the equation: I = 4I0

 

[m2003]

I would first start by identifying the relevant formulas for each problem and writing them down. For problem 1, I would use the formula for thermal conductivity, Q/t = kA∆T/x, where Q is the heat transferred, t is time, k is thermal conductivity, A is cross-sectional area, ∆T is the temperature difference, and x is the distance. I would also use the formula for thermal equilibrium, Q1 = Q2, where Q1 and Q2 are the heat transferred by the two rods. By setting these two equations equal to each other, I can solve for the temperature at the interface.

For problem 2, I would use the formula for power, P = IV, where P is power, I is current, and V is voltage. I would also use the formula for specific heat capacity, c = Q/m∆T, where c is specific heat capacity, Q is heat transferred, m is mass, and ∆T is temperature change. By setting the two experiments equal to each other and solving for the power lost, I can determine the power lost to the surroundings in each case.

For problem 3, I would use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature. I would also use the formula for pressure in a column of liquid, P = ρgh, where ρ is density, g is acceleration due to gravity, and h is height. By setting the two pressure equations equal to each other and solving for temperature, I can determine the new temperature of the air in the sphere.

For problem 4, I would use the formula for the angular displacement of minima, θ = mλ/d, where θ is the angular displacement, m is the order of the minima, λ is the wavelength, and d is the slit separation. I would also use the formula for fringe width, w = λL/d, where w is the fringe width, λ is the wavelength, L is the distance to the screen, and d is the slit separation. By using these formulas, I can determine the angular displacement of the third order minima, the fringe width, and the maximum number of bright fringes that can be observed. For part (iv), I would use the equation for intensity, I = I0 cos(πy