Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bury itself just below the surface. What would have to be the mass of this asteroid, in terms of the earth's mass M , for the day to become 26.0% longer than it presently is as a result of the collision? Assume that the asteroid is very small compared to the earth and that the earth is uniform throughout.

What are the challenges for laser therapy of dental caries? Estimate the absorption coefficient and ablation threshold of enamel and dentin for the 1.057-µm radiation of the Nd:YLF laser. What would be the advantage of using the 800-nm radiation from the Ti:sapphire laser?

A large cubic thermal reactor, moderated and reflected by an infinite reflector of water, is fueled with
235U at a concentration of (10)^-4 g/cm3.
(a) Calculate the critical dimensions of the core.
(b) Compute the critical dimensions if the reactor is bare.
Assume that the system is at room temperature.

2. Using the Michelson-Morley experiment as an example, explain why classical mechanics was unable to explain natural phenomena.

3. Using at least one of Einstein's "thought-experiments", explain how special relativity addresses how it is possible for observers in two different inertial reference frames to “disagree” about time and distance intervals.

In preparation for this problem, review Conceptual Example 7. A space traveler whose mass is 101 kg leaves earth. What are his (a) weight and (b) mass on earth and (c) weight and (d) mass in interplanetary space where there are no nearby planetary objects?

Include written explanation and picture diagram.

Communication satellites are often placed in geosynchronous orbits, which means that the satellite always appears in the same location relative to a receiver on the ground. This requires among other things that the rotational speed at which the satellite orbits the planet is the same as the rotational speed at which the planet spins on its axis. Consider a planet with mass = 4.32 × 1024 kg and radius = 5.43 × 106 m and rotational period 25.0 hours.

A uniform plastic block floats in water with 40.0 % of its volume above the surface of the water. The block is placed in a second liquid and floats with 20.0 % of its volume above the surface of the liquid.

What is the density of the second liquid?

In a fixed source/detector spectro-fluorometer, what can be done to increase the sensitivity of the optical emission signal?

A 0.454-kg block is attached to a horizontal spring that is at its equilibrium length, and whose force constant is 25.0 N/m. The block rests on a frictionless surface. A 5.80×10−2-kg wad of putty is thrown horizontally at the block, hitting it with a speed of 8.96 m/s and sticking. How far does the putty-block system compress the spring?

You are give a system about which two things are known: the relation between pressure,

volume and temperature, and the heat capacity at constant volume (α is a constant) PV^3=αT; CV =A(V)T

Please
(a) Find the derivative of entropy with respect to volume at fixed T

(b) Show that the coefficient A(V ) in the specific heat is independent of V

(c) Find S(T,V) in terms of the (assumed known) value S0 of the entropy at a given temperature and volume T0, V0, S0 = S(T0, V0).

(d) Find the heat capacity at constant pressure

Consider a case in which we have an Einstein solid that is neither at high or low temperature. In this case, we cannot use either the N>>q or q>>N approximation. In this case both N and q are >> 1. Derive an expression for the chemical potential then discuss how this more general result differs from and/or could correlate to the low and high temperature cases.

Thermodynamics

Choices: True or False.

If velocity is zero then acceleration must be zero too.

If speed is constant then acceleration is zero.

If velocity is constant then speed must be constant too.

If speed changes then velocity must change too.

Object slows down if it's acceleration is negative.

If speed is constant then velocity must be constant too.

A spring with force constant k = 175 N/m is attached to the ground. On top of the spring a 1.30 kg metal pan is attached. The combination could be used as a scale, but we are going to do something more interesting. We place a metal ball with mass 0.250 kg on the tray and then the tray is pushed down 0.150 m below its equilibrium point and released from rest (take this as t = 0).

a) At what time does the ball lose contact with the metal pan? Carefully consider direction and remember that ω is in rad/s.

b) How high above the equilibrium point is the pan at this time?

c) How fast is the ball moving at the time it loses contact with the pan?

A small block with mass 0.0550 kg slides in a vertical circle of radius 0.0740 m on the inside of a circular track. There is no friction between the track and the block. At the bottom of the block's path, the normal force the track exerts on the block has magnitude 3.40 N Part A What is the magnitude of the normal force that the track exerts on the block when it is at the top of its path?