A father (weight W = 858 N) and his daughter (weight W = 372 N) are spending the day at the lake. They are each sitting on a beach ball that is just submerged beneath the water (see the figure). Ignoring the weight of the air in each ball, and the volumes of their legs that are under the water, find (a) the radius of father's ball and (b) the radius of daughter's ball

A hot-air balloon stays aloft because hot air at atmospheric pressure is less dense than cool air at the same pressure. The volume of a balloon is V = 1000.0 m3,

and the surrounding air has a temperature T0 which is 10.0 degrees C. The density of air at 10.0 degrees C and atmospheric pressure is p0=1.23 kg m-3.

a. What must the temperature T of the air in the balloon be for it to lift a total load of M plus the mass of the hot air? Express your answer only in terms of the variables defined above and any needed physical constants.

b. If this happens when T = 80.2◦C, what is the mass M in kilograms?

c. What is the density of the air inside the balloon in kgm−3?

An amusement park ride consists of a cylindrical chamber of radius R that can rotate. The riders stand along the wall and the chamber begins to rotate. Once the chamber is rotating fast enough (at a constant speed), the floor of the ride drops away and the riders remain "stuck" to the wall. The coefficients of friction between the rider and the wall are us and uk. 1. Draw a free body diagram of a rider of mass m after the floor has fallen away. 2. Is the rider on the wall accelerating? If so, in what direction? Should our FBD be balanced? 3. Write Newton's second law in the vertical direction. 4. Write Newton's second law in the horizontal direction. 5. If the ride takes a time T to go through one full revolution, what is the speed of the rider on the wall of the ride? 6. Assume that the ride is spinning just fast enough to keep the rider on the wall. Using the equations found in questions #3 and #4, calculate the minimum velocity to keep the rider suspended. 7. You get on the ride and notice another rider beside you who has twice your mass. If the ride is going just fast enough to keep you suspended, will the person beside you have a problem on the ride? 8. After a rider gets sick on the ride, the operator hoses down the walls of the ride, which reduces the coefficient of friction by half. What happens to the minimum velocity required for the rider to remain suspended?

A uniform solid ball of m=4.0 kg and radius r rolls smoothly down a ramp. The ball starts from rest. The ball descends a vertical height of 6.0 m to reach the bottom of the ramp. What is its speed at the bottom?

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?