Two 78.5-kg hockey players skating at 6.47 m/s collide and stick together. If the angle between their initial directions was 115 ∘, what is their speed after the collision?

At the surface of a lake, the pressure is 1 atmosphere. What is the total pressure at a depth of 850m in water?

A 22.0 μF capacitor is charged by a 160.0-V power supply, then disconnected from the power and connected in series with a 0.240-mH inductor.

Calculate the energy stored in the inductor at t = 1.45 ms .

Exercise 2: Using the Relativistic Energy Momentum relationship ?² = ?²?² + ?²?⁴ and the de-Broglie relationships ? = ℏ? and ? = ℏ? with ? the angular frequency and ? the wave number, find the group ?_? and the phase velocity ?_?ℎ of the de-Broglie waves and show that their product is equal to ?².

Exercise 1: A positronium is a bound electron positron state, where the electron is rotating around a positron rather than a proton. Prove that in a positronium bound state:

a) The transition energy levels are halved compared with those of the Hydrogen Atom.

b) The electron radii are expanded to double the corresponding radii of the Hydrogen Atom.

A uniform helicopter rotor blade is 8.97 m long, has a mass of 104 kg, and is attached to the rotor axle by a single bolt. (a) What is the magnitude of the force on the bolt from the axle when the rotor is turning at 329 rev/min? (Hint: For this calculation the blade can be considered to be a point mass at its center of mass. Why?) (b) Calculate the torque that must be applied to the rotor to bring it to full speed from rest in 7.68 s. Ignore air resistance. (The blade cannot be considered to be a point mass for this calculation. Why not? Assume the mass distribution of a uniform thin rod.) (c) How much work does the torque do on the blade for the blade to reach a speed of 329 rev/min?

Water falls without splashing at a rate of 0.400 L/s from a height of 3.60 m into a 0.530-kg bucket on a scale. If the bucket is originally empty, what does the scale read 3.40 s after water starts to accumulate in it?

1. Three identical resistors are connected in parallel to a single battery. The current through the resistors must be...

a. one-third of the current through the battery.
b. the same for the resistors as for the battery.
c. different for each resistor.
d. higher for one resistor and lower for the other two.

2. A 6Ω and a 12Ω resistor are connected in series with a 36 volt battery,. How many Joules per second are dissipated by the 12Ω resistor.

a. 14 watts
b. 24 watts
c. 48 watts
d. 64 watts

3. Six identical resistors are connected in series with a battery. The number of joules per second supplied by the battery is then determined. If a seventh resistor is added (in series) the number of joules per second supplied by the battery:

a. increases
b. decreases
c. stays the same
d. changes, but may increase or decrease

A 90 kg student jumps off a bridge with a 10-m-long bungee cord tied to his feet. The massless bungee cord has a spring constant of 390 N/m. You can assume that the bungee cord exerts no force until it begins to stretch.

How far below the bridge is the student's lowest point?

How far below the bridge is the student's resting position after the oscillations have been fully damped?

In February 1955, a paratrooper fell 370 m from an airplane without being able to open his chute but happened to land in snow, suffering only minor injuries. Assume that his speed at impact was 60 m/s (terminal speed), that his mass (including gear) was 71 kg, and that the magnitude of the force on him from the snow was at the survivable limit of 1.2

1) A 0.490 kg soccer ball is kicked and hits a 2.45 kg stationary tether ball hanging from a 1.49 m tether resulting in a perfectly elastic collision. If the tether ball swings out at a maximum angle of 45.4°, what was the soccer ball's velocity before the collision?
2) A 5.27 g pellet is shot horizontally from a BB gun at a speed of 15.2 m/s into a 21.1 g wooden block. The wooden block is attached to a spring and lies on a frictionless table. If the collision is inelastic and the spring constant k = 20.0 N/m, what is the maximum compression of the spring?

The takeoff speed for an Airbus A320 jetliner is 82 m/s . Velocity data measured during takeoff are as follows: t(s) vx(m/s) 0 0 10 23 20 46 30 69

What is the jetliner's acceleration during takeoff, in g's?

At what time do the wheels leave the ground?

For safety reasons, in case of an aborted takeoff, the length of the runway must be three times the takeoff distance. What is the minimum length runway this aircraft can use?

A cylinder of volume 0.240 m³ contains 10.1 mol of neon gas at 21.6°C. Assume neon behaves as an ideal gas

(g) Compute ΔU − W.

(i) Compute Q, the thermal energy transfer.