Useful physical constants: g = 9.80 m/s2

1. At a baseball game in a large stadium with seats surrounding the outfield, a batter hits a “home run” up into the seats. The ball lands at a height above the height at which it was hit.

The ball is hit with an initial velocity of 43.0 m/s at an angle of 40.0 ̊ above the horizontal, and it takes 5.00 s to land. Ignore the effect of air resistance throughout this problem.

a. Decompose the ball’s initial velocity, v0, into its x- and y- components, v0x and v0y. Calculate the numerical value of both components. Choose the +y-direction to be upward and the +x-direction to be downrange. Show your work.

b. What is the baseball’s total horizontal displacement, from hit to landing? Show your work.

c. What is the maximum vertical displacement that the ball reaches during its trajectory? Show your work completely.

1. The potential energy of an object attached to a spring is 2.80 J at a location where the kinetic energy is 1.50 J.1.50 J. If the amplitude ?A of the simple harmonic motion is 20.0 cm, calculate the spring constant k and the magnitude of the largest force Fspring, max that the object experiences.

k = ??? N/m

F spring, max = ??? N

2. The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader–a physicist, naturally–immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.37 m. She sets the pendulum swinging, and her collaborators carefully count 104 complete cycles of oscillation during 208 s. What is the result?

acceleration due to gravity = ??

An object with a high density can be floated on an object with a low density in a fluid with a density if the volumes of the objects are right. What is the condition for such a stack having neutral buoyancy, in terms of masses and volumes of the blocks and the density of the water? Express the condition mathematically.

So I know the basic gist is that fusion power's main issue is sustaining the fusion. I also know that there are two methods. The Torus method and the laser method. The torus magnetically contains plasma and heats it with radiation and accelerates the plasma around to make strong enough collisions that protons fuse. The laser method uses 192 lasers and focuses it on tiny frozen hydrogen pellets and aims to initiate fusion each time pellets are dropped.

The though struck me when we could sorta combine the two designs together. The torus doesn't have to worry about making fusion happen at a specific location but it has issues in that the plasma is unevenly heated and leaks. On the other hand, the laser design is extremely complicated in the level of precision needed and would have to repeat this for every pellet. This lead me to think to make something precise and contained at the same time.

I see that particle colliders are able to direct two beams of protons and have them collide at a specific spot with a very precise energy. Couldn't we tune the energy of the two beams of protons to the energy required for them to fuse? We have the ability to smash them into bits, surely we have the ability to have them fuse. (I'm thinking about the type of collider that circles two beams in opposite directions)

It would be at much lower energies than normal colliders and would be very precise and it would be possible to fuse at a specific location that has greater leeway because for protons that missed collision, they'd just circle around again! Thus protons would efficiently be used and very little would be wasted. There wouldn't be problems of plasma leakage because we are focusing them in a thin tight beam.

It seems that this idea has girth, or I feel this way at least, can someone back me up by offering some calculations on how to calculate the efficiency? How would I go about calculating the two circling beams of protons and at what specific velocity would be needed? etc.

Using the currently accepted values of the cosmological parameters, and assuming the validity of the CDM Model (what Ryden calls the Benchmark Model), (a) determine the total baryonic mass in the observable universe (that is, within the particle horizon). Express your answer in solar masses, and also in number of baryons, and finally in joules. (b) Do the same for the total amount of dark matter, expressed in solar masses. (c) Calculate the total energy of CMB photons in the observable universe.

1. X-rays are scattered from a target at an angle of 35.4° with the direction of the incident beam. Find the wavelength shift of the scattered x-rays.

nm

2. (a) If the wavelength of an electron is 4.61 ✕ 10⁻⁷ m, how fast is it moving?
km/s

(b) If the electron has a speed equal to 8.30 ✕ 10⁶ m/s, what is its wavelength?
m

A spherical shell of radius 2.84 cm and a sphere of radius 7.97 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the spherical shell\'s angular speed to the sphere\'s angular speed be?

A raft is made of 10 logs lashed together. Each is 32.0 cm in diameter and has a length of 6.50 m. How many people (whole number) can the raft hold before they start getting their feet wet, assuming the average person has a mass of 65.0 kg? Do not neglect the weight of the logs. Assume the density of wood is 600 kg/m³

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 25.0

As the electrons are accelerated through the second anode, the gain in kinetic energy is 2.0 x 10-15 J, and the speed of the electrons as they enter the region between the plates is 6.6 x 107 m/s. The electrons are moving to the right as they pass between the plates. The plates are 2.0 cm long, 1.0 mm apart, and as the electrons pass between the plates, the potential difference is 450 V. Determine the time it takes to pass the region between the plates. Determine the electric field strength between the plates. Determine the acceleration of the electron in the region between the deflection plates. Determine the vertical component of the velocity of the electrons when they emerge from the region between the plates. Determine the vertical displacement of the electrons as they are deflected.

When a mass m is attached to a spring it exerts a force W = mg on the spring and the length of the spring is changed by delta x. If the single spring is replaced with a) two identical springs in series, what happens to delta xseries compared to the case of a single spring? b) If the single spring is replaced by two identical springs in parallel, what happens to delta xparallel compared to the case of a single spring?

See figure above. Assume all springs are identical, i.e. have the same spring constant k, length, mass, etc. Answer questions a) and b) by stating if delta x increases, decreases or remains unchanged and compare it to the single spring case, i.e. what are delta xseries and delta xparallel in terms of delta x for the single spring case? Hint: Draw a force diagram of the system remembering that the net force on the mass must be zero when it is in equilibrium.

The figure is second from last page of this website: http://www.pa.msu.edu/courses/2015summer/PHY251/labfiles/exp9.pdf

A specific type of ideal gas has a specific heat capacity at constant pressure (c_p=c_v+R) that is a function of temperature T, such that c_p=0.48T+885, where c_p has units of J/kg/K and T has units of K. The gas, which is initially at T1 = 314 K and P1 = 1x10⁵ Pa, undergoes a reversible adiabatic process such that its final temperature is T2 = 772 K. Calculate the pressure of the gas (in Pa) in this final state. Assume the following ideal gas constant: R = 287 J/kg/K. Recall that ds = c_pdT/T – RdP/P

A 50.2-kg skateboarder starts out with a speed of 1.96 m/s. He does 100 J of work on himself by pushing with his feet against the ground. In addition, friction does -279 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 7.11 m/s. (a) Calculate the change (PEf - PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give the absolute value.

Two trains, A and B, travel in the same direction on the same set of tracks. A starts at rest at position d, and B starts with velocity v0 at the origin. A accelerates with acceleration a, and B decelerates with acceleration –a. What is the maximum value of v0 (in terms of d and a) for which the trains don’t collide? Make a rough sketch of x vs. t for both trains in the case where they barely collide.

Two boats are heading away from shore. Boat 1 heads due north at a speed of 2.81 m/s relative to the shore. Relative to Boat 1, Boat 2 is moving 31.5° north of east at a speed of 1.50 m/s. A passenger on Boat 2 walks due east across the deck at a speed of 1.29 m/s relative to Boat 2. What is the speed of the passenger relative to the shore?