A mass ??? rests on a smooth horizontal table and is attached by two inelastic strings to masses ?1?? and ?2?? with (?1 > ?2) which is hung over 2 smooth pulley at opposite edges of the table. Find the acceleration of the system and the tension in the string.

Explore the Balmer series of atomic transitions for a hydrogen atom. Assume the shortest wavelength possible occurs when the atom is ionized or when n = ∞ . What is the longest and shortest wavelengths possible?
What is the frequency, wavelength and energy of the longest wavelength?
longest λ = ___________ nm

frequency = _________ Hz

energy = _________ eV

Shortest λ = ___________ nm

Design a structure using primitive material so that 1000W store fire can keep the internal temperature to at least 17°C W/a -40°C outside temperature, of at least 1000ft^2 floor area?

The simplest model of a polymer involves a sequence of bonds of fixed length λ, where each bond can make any angle with the previous bond. This is called the freely-jointed chain model. Here will will study it in 3D. We start at the origin. Then we choose an angle θ randomly between 0 and 2π. We make a step of length λ at an angle of θ top the +x direction. We then repeat, making N steps in total. We can measure the size of the polymer by finding the end to-end-vector R and squaring it. We then take the square root of this to get the root-mean-square size. We will set λ = 1 Note that this model is “off-lattice" or continuum, we are not using any lattice.

You should: (1) Plot an example walk of say 100 steps.

(2) Generate walks between say 10 and 10^6 steps and make a log-log plot of the root mean square size versus total number of steps. You may need to average over several walks for each length to get good data.

Your friend claims he can throw a baseball straight up with a speed of 80 mi/h. You do not
believe him, so you design an experiment that will enable you to calculate the speed of a thrown
ball. You attach a 0.5-kg block to a vertical spring. The block hangs a distance of 0.05 m below
the relaxed position. Your friend stands directly beneath the hanging block and throws the
baseball straight up. He releases the ball at a distance of 2.4 m below the hanging block. You
design the experiment so that the ball sticks to the block after the collision. You observe that the
block-baseball combination rises a distance of 0.18 m after the collision.
 Do you believe that your friend can throw a baseball with a speed of 80 mi/h?

(a) (15 pts) A net force is applied to a mass m that is initially at rest on a level frictionless surface. The force varies with position and is given by F(x)=Ax3/2. The force is applied tothemassfrompositionsx=0tox=d. Aftertheforcestopsacting,the mass then slides throughalevelfrictionpatchwithcoefficientoffriction µk.

How far does the mass travel through the friction patch before coming to rest? Put your answer in terms of m,g,d, µk,and A.

(b) (5 pts) Now, suppose that instead of the position-varying force acting on the mass, a time-varyingnetforceF(t)=At3/2 acted on the block from time st =0tot =t1. After the time-varying force stopped acting, then the block went through the same friction patch. For this new scenario, what would be your approach to solving this problem? Briefly explains using equations and/or technical words. Be specific to earn full credit. Solving part (b) is not required for full credit.

A Boeing 747 "Jumbo Jet" has a length of 64.4 m. The runway on which the plane lands intersects another runway. The width of the intersection is 23.6 m. The plane decelerates through the intersection at a rate of 5.50 m/s2 and clears it with a final speed of 46.9 m/s. How much time is needed for the plane to clear the intersection?

In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth's atmosphere, 104 km above sea level, a pion is created.The pion has a total energy E of 1.92 × 10⁵ MeV and is traveling vertically downward. In the pion's rest frame, the pion decays 35.0 ns after its creation. At what altitude above sea level, as measured from Earth's reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV.

a 4.2 g coin sliding to the right at 21.4 cm/s makes an elastic head-on collision with a 12.6g coin that is initially at rest. after the collision, the 4.2g coin moves to the left at 10.7cm/s.
a. find the final velocity of the other coin in cm/s
b. find the amount of kinetic energy transferred to the 12.6g coin

Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (⁴He) from gold-197 nuclei (¹⁹⁷Au). The energy of the incoming helium nucleus was 7.38 ✕ 10⁻¹³ J, and the masses of the helium and gold nuclei were 6.68 ✕ 10⁻²⁷ kg and 3.29 ✕ 10⁻²⁵ kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.)

(a)

If a helium nucleus scatters to an angle of 129° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus.

⁴He speed ___ m/s ¹⁹⁷Au velocity ___ m/s ¹⁹⁷Au direction ___° counterclockwise from the +x-axis

(b)

What is the final kinetic energy (in J) of the helium nucleus?

A "pulse oximeter" operates by using light and a photocell to measure oxygen saturation in arterial blood. The transmission of light energy as it passes through a solution of light-absorbing molecules is described by the Beer-Lambert law
I = I010−εCL or log10II0= −εCL,

which gives the decrease in intensity I in terms of the distance L the light has traveled through a fluid with a concentration C of the light-absorbing molecule. The quantity ε is called the extinction coefficient, and its value depends on the frequency of the light. (It has units of
m2/mol)>

Assume the extinction coefficient for 660-nm light passing through a solution of oxygenated hemoglobin is identical to the coefficient for 940-nm light passing through deoxygenated hemoglobin. Also assume that 940-nm light has zero absorption (ε = 0) in oxygenated hemoglobin and 660-nm light has zero absorption in deoxygenated hemoglobin. If 32.8% of the energy of the red source and 76.5% of the infrared energy is transmitted through the blood, what is the fraction of hemoglobin that is oxygenated?

= %

A person hears a siren as a fire truck approaches and passes by. The frequency varies from 480Hz on approach to 400Hz going away. What is the speed of the truck if the speed of sound in air is 343m/s?