A block weighing 259 g slides along a frictionless track at a speed 6.1 cm/s. It then attaches to a spring-bumper with an electromagnetic device so that the block attaches to the bumper. The bumper has a mass of 130 g, and the spring has a stiffness of 1540 kg/s² and an equilibrium length of 10.6 cm. After the spring compresses and returns to its original length, the magnet turns off and the block launches off again, conserving energy.

(a) How fast is the block just after it attaches to the paddle?


(b) What is the maximum compression of the spring before the block turns around?


(b) How fast is the block moving after it launches off the paddle?

A charge of 4.85 mC is placed at each corner of a square 0.100 m on a side.

a. Determine the magnitude of the force on each charge. (N)

b. Determine the direction of the force on each charge. Assume that the positive x-axis is directed to the right. (degrees above x-direction)

Calculate the magnitude of the force between two point charges of +1.6×10^-19 C and -1.6×10^-19 C, for a range of distances, from r = 0.090 nm to r = 0.18 nm in 0.010 nm steps.

Plot the results on a graph of magnitude of force F versus distance r. You must label the graphs with axis labels including units, and a title. Also choose an appropriate scale of the graph to show the data.

Hint: use a spreadsheet, Logger Pro, or write some computer code to do this for you. You must try to do this type of problem on the computer, as writing this out by hand/doing repetitive calculations is just too time-consuming.

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 12-m-high hill, then descends 20m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.5m and that a loaded car will have a maximum mass of 450kg . For safety reasons, the spring constant should be 15% larger than the minimum needed for the car to just make it over the top.

A) What spring constant should you specify?

B) What is the maximum speed of a 360kg car if the spring is compressed the full amount?

Choose true or false for each statement regarding concave mirrors.
true false  A concave mirror produces an enlarged real image when the object is placed far beyond its focal point (Region 1).
true false  If an object is placed 4.1 cm from a concave mirror with f = 4 cm, then its image will be reduced and virtual.
true false  If an object is placed 7.9 cm from a concave mirror with f = 4 cm, then its image will be enlarged and real.

Choose true or false for each statement regarding convex mirrors.
true false  A convex mirror produces a reduced real image when the object is placed between the mirror and its focal point (Region 3).
true false  If an object is placed 7.9 cm from a convex mirror with f = 4 cm, then its image will be reduced and real.
true false  If an object is placed 3.9 cm from a convex mirror with f = 4 cm, then its image will be reduced and real.

Choose true or false for each statement regarding the sign conventions for mirrors.
true false  The focal length f is positive for convex mirrors.
true false  Virtual images appear behind a mirror and have a positive value for the image distance.
true false  The magnification m is negative for upright images.

A hot-air balloon is ascending at the rate of 13 m/s and is 73 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

1. The solution for the finite potential well is

   		a combination of sine and cosine functions
   		a combination of exponential functions
   		a combination of exponential functions and sine and/or cosine functions
   		a third degree polynomial

An electron of kinetic energy 0.972 keV circles in a plane perpendicular to a uniform magnetic field. The orbit radius is 26.9 cm. Find (a) the electron's speed, (b) the magnetic field magnitude, (c) the circling frequency, and (d) the period of the motion.

A particle with an initial linear momentum of 3.72 kg · m/s directed along the positive x-axis collides with a second particle, which has an initial linear momentum of 7.44 kg · m/s, directed along the positive y-axis. The final momentum of the first particle is 5.58 kg · m/s, directed 45.0° above the positive x-axis. Find the final momentum of the second particle.

If 200 g of water is contained in a 300g aluminum calorimeter at 20

Then answer the following questions about each unit:

What is the name of the unit that you found, and how is it commonly used? How do you convert an everyday quantity (mass of a candy bar, the volume of a soda can, length of a soccer field, etc.) into that unit?

On average, a lightning flash on Earth transfers about 30 C is transferred across 1 GV.

Suppose that, in a single lightning flash, 27.7 C of charge is transferred through a potential difference of 2.44 GV. If all this energy could be used to accelerate a car of mass 1,427 kg car from rest, what speed would the car reach, in m/s?

NOTE: 1000 m/s is 2237 miles per hour!

List the three phases of matter in order of the distance between the particles. List the properties of each phase. Explain what causes matter to change states.

The muon is a subatomic particle with the same charge as an electron but with a mass that is 207 times greater: m?=207me. Physicists think of muons as "heavy electrons." However, the muon is not a stable particle; it decays with a half-life of 1.5 ?s into an electron plus two neutrinos. Muons from cosmic rays are sometimes "captured" by the nuclei of the atoms in a solid. A captured muon orbits this nucleus, like an electron, until it decays. Because the muon is often captured into an excited orbit (n>1), its presence can be detected by observing the photons emitted in transitions such as 2?1 and 3?1.
Consider a muon captured by a carbon nucleus (Z=6). Because of its large mass, the muon orbits well inside the electron cloud and is not affected by the electrons. Thus the muon "sees" the full nuclear charge Ze and acts like the electron in a hydrogen-like ion.

Part 1: What is the orbital radius of a muon in the n=1 ground state? Note that the mass of a muon differs from the mass of an electron? Solving for r₁

Part 2: What are the speed of a muon in the n=1 ground state? Solving for v₁

Part 3: What is the wavelength of the 2?1 muon transition? solving for lambda

Part 4: How many orbits will the muon complete during 1.5 ?s? Solve for N