The wavelength of the four Balmer series lines for hydrogen are found to be 410.1, 434.3, 486.6, and 655.9 nm. What average percentage difference is found between these wavelength numbers and those predicted by 1 λ = R 1 nf2 − 1 ni2 ? It is amazing how well a simple formula (disconnected originally from theory) could duplicate this phenomenon.

A spaceship of triangular shape, having a length three times its width, is capable of relativistic speeds. How fast would it have to move so that to a stationary observer its length would equal its width?

a bullet of mass m and speed v is fired at an initially stationary sphere. The bullet goes through the sphere, and exits with a speed of v/3. The sphere is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the sphere.)

What were the conditions necessary to advance astronomical knowledge from Copernicus to Newton? How did they develop during the seventeenth century?

There queer gangs of young Socialists, youths and girls (Nazis),.... They strike one as strange. something primitive, like loose roving gangs of broken, scattered tribes...as if everything and everybody recoiled from the old unison, as barbarians lurking in a wood recoil out of sight�

A box of textbooks of mass 25.0 kg rests on a loading ramp that makes an angle α with the horizontal. The coefficient of kinetic friction is 0.23 and the coefficient of static friction is 0.36.

A) As the angle α is increased, find the minimum angle at which the box starts to slip. Express your answer using two significant figures.

B) At this angle, find the acceleration once the box has begun to move. Express your answer using two significant figures.

C) At this angle, how fast will the box be moving after it has slid a distance 4.9 m along the loading ramp? Express your answer using two significant figures.

6a) The work function of a clean tungsten surface is 4.50 eV. Find the speed of the fastest electrons emitted from a tungsten surface when light of 5-eV photon energy shines on the surface.

You hike up to the top of Granite Peak in the Trinity Alps to think about physics.

1. Do you have more potential or kinetic energy at the top of the mountain than you did at the bottom? Explain.
2. Do you have more, less, or the same amount of energy at the top of the mountain than when you started? (Let’s assume you did not eat anything on the way up.) Explain.
3. How has the total energy of the Solar System changed due to your hike up the mountain? Explain.
4. If you push a rock off the top, will it end up with more, less, or the same amount of energy at the bottom? Explain.
5. For each of the following types of energy, describe whether you gained it, you lost it, or it stayed the same during your hike:
   1. Gravitational potential energy
   2. Energy stored in the atomic nuclei in your body
   3. Heat energy
   4. Chemical potential energy stored in the fat cells in your body
   5. Sound energy from your footsteps
   6. Energy given to you by a wind blowing at your back

List out at least 3 uses for an RC circuit and explain how the RC would affect the use.

3. (15 pts) Consider a second-order dynamic system composed of the classical spring, mass, and damper, with spring constant k , mass m , and damping constant c .

a) Generate expressions for the undamped natural frequency ω n and the damping ratio ζ in
terms of k , m , and c .

b) If the spring constant k is increased, but m and c are unchanged, predict whether ω n will increase, decrease, or remain the same. Justify.

c) If the spring constant k is increased, but m and c are unchanged, predict whether ζ will increase, decrease, or remain the same. Justify.

In the figure, three connected blocks are pulled to the right on a horizontal frictionless table by a force of magnitude T3 = 16.0 N. If m1 = 18.3 kg, m2 = 22.0 kg, and m3 = 35.3 kg, calculate (a) the magnitude of the system's acceleration, (b) the tension T1, and (c) the tension T2.

Please answer and provide an explanation with the necessary formula. Thank you in advance,

1. A 200kg block slides down a rough inclined plane of length 2.5m inclined at 20 degrees. At the bottom of the plane the speed of the block is 3.15 m/s. Initially the block was at rest. What is the change in the internal energy of the system? What is the frictional force?

2. A sled at rest in snow seated with two children with total mass of 50kg. You pull the sled with a rope that makes an angle of 42 degrees with the horizontal. The coefficient of kinetic friction is 0.150 and the tension in the rope is 150 N. What is the speed of the sled after it has moved through 3.5m?

3. Oxygen gas has a molar mass of 32 g/mol and carbon dioxide has a molar mass of 44.05 g/mol. What is the rms speed of the oxygen molecule at 300? If the carbon dioxide molecule has the same rms speed as oxygen molecule, what is the temperature of the carbon dioxide molecule?

4. A U tube contains a liquid of unknown density. An oil of density 800 kg m/s is poured into the tube in one of the arm and the oil column is 12 cm high. The air interface is 5 cm above the liquid level in the other. What is the density of the liquid?

5. A uniform ladder of weigh 75 N leans against a frictionless vertical wall. The foot of the ladder is 2.5m away from the wall. The length of the ladder is 5m. A fireman of weigh 700 N is on the ladder at a distance of 4m along the ladder. What is the magnitude and direction of the force exerted by the floor and ladder?

n = 2.35 mol of Hydrogen gas is initially at T = 322 K temperature and p_i = 2.86×10⁵ Pa pressure. The gas is then reversibly and isothermally compressed until its pressure reaches p_f = 8.33×10⁵ Pa. What is the volume of the gas at the end of the compression process?

How much work did the external force perform?

How much heat did the gas emit?

How much entropy did the gas emit?

What would be the temperature of the gas, if the gas was allowed to adiabatically expand back to its original pressure?