a ping pong ball weighing 2 oz. with a contant velocity of V=8j+6k ft/sec. A gust of wind exerts a force of F=.5t i oz. on the ball. Determine the magnitude and direction of th ball after .5 sec

It is well known that the Lagrangian of a classical free particle equal to kinetic energy. This statement can be derived from some basic assumptions about the symmetries of the space-time. Is there any similar reasoning (eg. symmetry based or geometrical) why the Lagrangian of a classical system is equal kinetic energy minus the potential energy? Or it is just because we can compare the Newton's equations with the Euler-Lagrange equation and realize how they can match?

What are the reciprocal and direct lattice structures of a (100) plane of a FCC structure? What are the lattice constants of these direct and reciprocal lattices, provided that the standard lattice constant of the original FCC lattice is a?

A positive point charge Q1 = 1.6 ? 10-5 C is fixed at the origin of coordinates, and a negative charge Q2 = -5.5 ? 10-6 C is fixed to the x axis at x = +2.0 m. Find the location of the place(s) along the x axis where the electric field due to these two charges is zero. (Enter the locations in order from -x to +x. If there is only 1 location, enter 0 in the second box.)

A convex mirror has a focal length of ?35 cm. Where is the image if the image is upright and three-fourths the size of the object?

Consider a long cylindrical charge distribution of radius R = 15 cm with a uniform charge density of ? = 14 C/m3. Find the electric field at a distance r = 31 cm from the axis.

Consider the Oort clound to consist of a large number of comets at a distance from the Sun where the period of a circular orbit around the Sun would be a million years.

A. What is the radius of this orbit?

B. If a comet in this orbit is perturbed, so that its new orbit has an aphelion at its original orbital radius, but now a perihelion at 0.3AU, how long will it take to reach its perihelion?

Suppose a supernova explosion emits 10^(51) ergs spread over a year. How far away from Earth would a typical supernova have to be to be as bright as our Sun if the Sun emits 10^(33) ergs/sec? Chinese observers record seeing a supernova 1000 years ago that appeared 10 times less bright than the Sun. How far away was this supernova?

Question: Particles of charge +65, +48, and ?95 ?C are placed in a line (Figure 1) . The center one is L = 35cm from each of the others.

Part A: Calculate the net force on the left charge due to the other two. Enter a positive value if the force is directed to the right and a negative value if the force is directed to the left.

Part B: Calculate the net force on the center charge due to the other two. Enter a positive value if the force is directed to the right and a negative value if the force is directed to the left.

Part C: Calculate the net force on the right charge due to the other two. Enter a positive value if the force is directed to the right and a negative value if the force is directed to the left.

Living cells "pump" singly ionized sodium ions, Na+, from the inside of the cell to the outside to maintain a membrane potential ?Vmembrane=Vin?Vout= -71mV It is calledpumping because work must be done to move a positive ion from the negative inside of the cell to the positive outside, and it must go on continuously because sodium ions "leak" back through the cell wall by diffusion.

a) How much work must be done to move one sodium ion from the inside of the cell to the outside?

B )At rest, the human body uses energy at the rate of approximately 93W to maintain basic metabolic functions. It has been estimated that 24{\rm \\%} of this energy is used to operate the sodium pumps of the body. Estimate?to one significant figure?the number of sodium ions pumped per second.

Consider n equal positively charged particles each of magnitude Q/n placed symmetrically around a circle of radius a. (a) Calculate the magnitude of the electric field at a point a distance x from the center of the circle and on the line passing through the center and perpendicular to the plane of the circle. (Use any variable or symbol stated above along with the following as necessary: ke.) E = (b) Now consider a ring of radius a that carries a uniformly distributed positive total charge Q. Recall the calculation of the electric field at point a point a distance x from the center of the ring and on the line passing through the center and perpendicular to the plane of the ring. Explain why the result in part (a) is identical to the result for the ring.

write down all the physical principles about resistances and currents in simple circuits containing resistors. also write down all the physical principles about resistances and currents in simple ciruits contaning resistors connected in parallel

A geologist searching for oil finds that the gravity at a certain location is 2 parts in 10⁷ smaller than average. Assume that the location contains oil and the oil is located 3100 m below the Earth's crust. Estimate the size of the deposit. Take the density of rock to be 3100 kg/m³ and that of oil to be 1200 kg/m³.
_____________kg

Two airplanes in a show are performing an act called a near miss, in which they start over opposite ends of the show (in the air), head directly toward one another, and then roll at the last second to avoid collision. Suppose the roll is supposed to happen in front of the announcer

Industrial processes often require the damping of vibrations.

Consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of 35200 N/m. This workbench is used when creating products that involve highly unstable chemicals. According tp specifications, the acceleration of the manufacturing equipment must be held to less than 14.4 m/s² for the manufacturing process to proceed safely. The amplitude of vibrations are expected to remain under 0.472 mm throughout. Given that the workbench and manufacturing equipment comine to 5.25 kg, find the maximum acceleration expected of the equipment and workbench. (Ignore the mass of the springs.)

_________ m/s²

Using shock absorbers, you decided to damp the oscillations applying one shock absorber to each spring. These shock absorbers apply a velocity-dependent drag force F=bv that opposes the motion of the bench. For proper damping you decide that the motion of the bench should drop to half-amplitude within 0.367 seconds. (In other words, within 0.367 seconds the amplitude of motion should drop b a factor of one-half.) When purchasing shock absorbers, what damping coefficient b should you specify to your industrial equipment supplier? (Assume that b² < mk, that is, underdamping.)

____________ kg/s