A boy stands on a diving board and tosses a stone into a swimming pool. The stone is thrown from a height of 2.50 m above the water surface with a velocity of 4.00 m/s at an angle of 60.0

II. Dimensions Involving Derivatives When we do dimensional analysis, we do something analogous to stoichiometry, but with multiplying instead of adding.

Part A) Consider the diffusion constant that appears in Fick’s first law: J = −D dn dx. In this expression, J represents a flow of particles (the number of particles per unit area per second), n represents a concentration of particles (the number of particles per unit volume), and x represents a distance. We can assume that they have the following dimensionalities: [J] = 1 L 2T , [n] = 1 L 3 , [x] = L.

1. What is the dimensionality of dx? Explain. (Hint: Remember from calculus that dx is just an infinitessimally small portion of x.)

2. Based on part (A), what is the general rule for the dimensionality of any differential? That is, given any physical quantity, Z, how does the dimensionality of dZ compare to that of Z?

3. Given any two physical quantities, Y and Z, what is the dimensionality of the derivative dY dZ in terms of [Y ] and [Z]?

Part B) Einstein discovered a relation that expresses how D depends on the parameters of the system: the size of the particle diffusing (R), the viscosity of the fluid it is diffusing in (η), and the thermal energy parameter (kBT). Assume that we can express D as a product of these three quantities to some power, like this: D = (kBT) a (η) b (R) c .

1. Rewrite the equation above in terms of M, L, and T, by substituting in your answer for the dimensionality of D from question 4 above, and the dimensionalities of the other constants, which are: [kBT] = ML2 T

2 , [η] = M LT , [R] = L 2. By “balancing” M, L, and T on each side of the expression above, determine three equations in terms of a, b, and c that will guarantee that D will have the correct dimensionality.

3. Solve these equations and write an expression for how D depends on the three parameters. (The correct equation has a factor of 1/6π that cannot be found from dimensional analysis.)

A positive point charge Q1=2.8×10−5C is fixed at the origin of coordinates, and a negative point charge Q2=−4.1×10−6C is fixed to the x axis at x=+2.0m. Find the location of the place(s) along the xx axis where the electric field due to these two charges is zero.

. How does the appearance of the diode change when the maximum voltage is above or below the threshold

1. How might you demonstrate the existence of an electrical force? Explain
2. How might you demonstrate the existence of a magnetic force? Explain

Then for each circuit component tested, write a brief analysis of the component. Explain how you know whether it is "ohmic" or not. Report anything else you find interesting. If it is "ohmic," then attach the additional V –vs- I plot and report here the value of the resistance, as a confidence interval. Attach more paper if needed.

Testing Ohms Law

Component 1: Lamp

Component 2: Resistor

Component 3: LED

Component 4: Diode

1a. A 747 airplane starts from rest and reaches a takeoff velocity of 78.0 m/s due west in 5.50 s. Assuming a constant acceleration, how far has it traveled before takeoff? Please explain.

b. Use the component method of vector addition to find the resultant of the following two vectors (magnitude and angle): (show the calculations) A=21.0 km, 26 degree south of west B=38.0km, 30 degrees east of south

What's the speed of water wave?

I'm asking about constant number.

A rope of negligible mass is stretched horizontally between two supports that are 2.81 m apart. When an object of weight 4190 N is hung at the center of the rope, the rope is observed to sag by 39.6 cm. What is the tension in the rope?

A = 3, B = 9, C = 18. A (1.25+A) kg bowling ball is hung on a (2.50+B) m long rope. It is then pulled back until the rope makes an angle of (12.0+C) degrees with the vertical and released. Find the speed of the ball is at the lowest point. Give your answer in m/s and with 3 significant figures.

To what height would a 3.0 kg object have to be raised such that its gravitational potential energy would equal the kinetic energy it would possess if it were moving at 3.0 m/s?

1 Why is it cooler to wear a white shirt than a black shirt on a hot, sunny day?

2 On a hot day in your hot kitchen, you decide to work with the refrigerator door open in an attempt to have the refrigerator cool the room. Which of the following best describes the result of this decision? Explain your answer.

a It will cool the room very effectively

b It will cool the room, but inefficiently

c It will not change anything

d It will actually warm the room

3 Consider standing on a bathroom scale. How will the reading of the scale compare if you stand on one leg instead of two?

a It will show less

b It will show more

c It will show the same

4 Consider standing on a bathroom scale. What does a bathroom scale show?

a Mass

b Density

c Force

d Pressure

The hunt for Red October is on! (Remember the 1990 Sean Connery

why isn't it accurate to say static friction is the force that keeps objects from moving? describe a counter example like a box on a table