Consider the light passing from a means of refractive index n₁ to another of index n₂. Use the Fermat principle to minimize travel time and                                                                                     deduce the law of refraction: n₁sen (θ₁) = n₂sen (θ₂).

A 63.0 kg ice hockey goalie, originally at rest, catches a 0.150 kg hockey puck slapped at him at a velocity of 28.0 m/s. Suppose the goalie and the ice puck have an elastic collision and the puck is reflected back in the direction from which it came. What would their final velocities (in m/s) be in this case? (Assume the original direction of the ice puck toward the goalie is in the positive direction. Indicate the direction with the sign of your answer.)

masses m1 and m2 are stacked together on a level surface that has friction. The blocks are accelerating together to the right. There is static friction between the two blocks. Analyze the forces on each block

Three charges are placed in the following locations: Q1 of -90.0µC at the origin; Q2 of +94.5µC at (0, 40.0 cm); and Q3 of +69.6 µC at (68.0 cm, 0).

a) Determine the total electric field at “P” located at (68.0 cm, 40.0 cm).

b) A fourth charge, q4 of +52.0 µC is placed at P. Find the total force on q4.

c) Determine the total potential V at P.

d) Does q4 have any electrical potential energy at P?

e) How much work is involved to move q4 from P to a new location “S” at (136 cm, 0)? Did the electric field do the work or was an outside agent involved to get q4 from P to S?

Please be as clear and detailed as possible, explaining each step if possible

A 460 turn solenoid, 25 cm long, has a diameter of 2.2 cm. A short 2.6 cm diameter 12 turn coil is wound around the solenoid at its midpoint. What rate of change of current in the solenoid, will cause a 220

A freight company uses a compressed spring to shoot 1.90kg packages up a

The rechargeable batteries for a laptop computer need a much smaller voltage than what a wall socket provides. Therefore, a transformer is plugged into the wall socket and produces the necessary voltage for charging the batteries. The batteries are rated at 9.0 V, and a current of 272 mA is used to charge them. The wall socket provides a voltage of 120 V.

(a) Determine the turns ratio of the transformer

(b) What is the current coming from the wall socket?
I_p =

(c) Find the average power delivered by the wall socket and the average power sent to the batteries.
P_p =
P_s =

Describe a situation in your everyday life where you could use the scientific method. List all the steps of the scientific method and explain how you would apply each of the steps in that situation.

With the pressure held constant at 210 kPa , 49 mol of a monatomic ideal gas expands from an initial volume of 0.60 m3 to a final volume of 1.7 m3 .

A) How much work was done by the gas during the expansion?

B) What were the initial temperature of the gas?

C) What were the final temperature of the gas?

D) What was the change in the internal energy of the gas?

E) How much heat was added to the gas?

Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 2.1 cm . Two of the particles have a negative charge: q1 = -8.0 nC and q2 = -16.0 nC . The remaining particle has a positive charge, q3 = 8.0 nC . What is the net electric force acting on particle 3 due to particle 1 and particle 2?

A) Find the net force ΣF⃗ 3 acting on particle 3 due to the presence of the other two particles. Report you answer as a magnitude ΣF3 and a direction θ measured from the positive x axis.

Please show the process! I've tried everything I can think of.

A stretchy cord has a diameter of 0.33 mm when lying loose off the spool. Loops are made on the two ends, 75.0 cm apart from knot to knot. The cord is hung vertically with one loop over a hook and the other with a 500 g mass hanging from it. After the mass is hung from it, the distance between the marks is now 79 cm.

a. What is the Young's modulus of the cord material?

b. If the same material also comes in a cord with diameter 0.66 mm, what would be its stretched length in the same scenario as above?

An electron and a proton are a distance r = 7 × 10^-9 m apart. How much energy is required to increase their separation by a factor of 3?

Well this is pretty noobish question and I am not sure how to ask.
When We talk we don't talk in an uniform frequency. Then how can one measure frequency of ones sound/voice ?
I am asking this cause several times I've heard people to say this is his/her frequency of voice. Is this a vague term ? or it has any real meaning ?

A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 38.0 kg and diameter 80.0 cm. The power is off for 25.0 s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 160 complete revolutions.

A.) At what rate is the flywheel spinning when the power comes back on? (in rad/s)

B.) How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on? (in s)

C.) How many revolutions would the wheel have made during this time? (in rev)