What quantity must be small to ensure the validity of the Fresnel approximation (Use the second-order term of the Taylor series expansion)?

a pilot has his small airplane heading due north at 50 km/h. after two hours of flight he finds himself 40 km east and 70 km north of his starting point. find the velocity of the crosswind that is driving the plane off-course?

A 500 Kg bloack of ice at -25 degrees celsuis is placed in just enough liquid water at 100 degrees celsius to completely melt it.

A) what was the mass of the hot water?

B) what was the entropy change of the ice?

C) what was the entropy change of the hot water ?

D) what was the entroyp change of the universe ?

E) what would the finaly temperature have been if intially the liquid water was instead 100 degree celsius water vapor ?

F) for part E what waould be the entropy chnage of

i) ice ? ii) water vapor ? iii) universe ?

Hi! I have some questions I'd like to discuss regarding an experiment with the pendulum

I will have a laboratory class in which I will have to measure the period of oscillation of the swinging pendulum using an electronic stopwatch.

what method could I use to obtain the period of a physical pendulum using a stopwatch, taking care to minimise any uncertainties?

Can you help me to go through this questions?

Should you start the stopwatch at the same time as you set the pendulum swinging, or would it be better to start the pendulum swinging and begin timing later?

Will you measure the time for just one “to-and-fro” swing (i.e. one period), or the time for multiple swings and then divide the time by the number of swings to get the period?

How many measurements will you make at a particular pendulum length? Would it be better to take the average of several measurements?

What angle will you be using? Why?

What is the uncertainty in the length of the pendulum? Is it limited by the precision

of your equipment or something else?

What is the minimum length that you will be using? Why?

Derive The Dirac Equation.

A balloon is filled up completely with helium gas and left in a room with a controlled temperature of 230C. After two days of being in the same room, the balloon was found to have shrunk to half its filled-up size. However, there was no leakage of helium gas from the balloon during the two days. Explain what happened to the pressure inside the balloon due to the change in the size of the balloon. ?  Use Boyle's Law to explain your answer.

An ancient wooden club is found that contains 280g of carbon and has an activity of 7.3 decays per second.

Determine its age assuming that in living trees the ratio of ¹⁴C/¹²C atoms is about 1.3

A juniper-wood plank measuring 0.31 ft by 1 ft by 17 ft is totally submerged in water.

(a) What is its weight?

(b) What is the buoyant force acting on it?

(c) What is the size and the direction of the net force on it?

size

direction

An antelope is at a distance of 20.0 m from a converging lens of focal length 27.0 cm. The lens forms an image of the animal.
(a) If the antelope runs away from the lens at a speed of 4.10 m/s, how fast does the image move? mm/s

Three charges are placed on the y-axis. The first, with charge 8nC, sits at y=5cm. The second, with charge -14nC, is at y=0cm. The third, -10nC, is at y=−5cm.

a) What is the electric potential on the x-axis at x=10cm?

b) What is the magnitude of the electric field at x=10cm?

c) What is the electric potential at x= −10cm?

d) What is the magnitude of the electric field at x= −10cm?

Example #2A block with mass m = 5 kg sits on a surface with a coefficient of static friction sk= 0.5 and a coefficient of kinetic friction uk= 0.3. a)If you can pull on the block at any angle, what minimum force is required to break static friction and cause the block to slide? b)What is the optimal angle to pull at? c)If you pull at the optimal angle with the minimum force, what will the acceleration of the block be once static friction is broken?

A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 2.0-kg object at the origin of the coordinate system, a 6.0-kg object at (0, 2.0), and a 11.0-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin.

Please show all work! thanks!

A 80.0 cm long guitar string has mass of 75.0g and it is kept taut with force of tension equal to 800N.

 Determine: (1) speed of propagation of a transverse wave in this string, (2) frequency of the fourth harmonic (of a transverse standing wave on this string), and (3) wavelength of the fourth harmonic.

Sketch the fourth harmonic normal mode.

 How many nodes (N) and antinodes (A) are in the fourth harmonic? Label them above.

 If incident wave has the amplitude of 5.5 cm, what is the amplitude of the standing wave?

 If the reflected wave has a vertical displacement of +2.3 cm (at some time instant) at the left end of the string, what is the vertical displacement (at the same time instant) of the incident wave at the same end of the string?