An oxygen molecule has a "diameter" of about $3 \text{\AA}$. Calculate the average oxygen gas free path ($l) and the average time between collisions$\tau$ at NTP.

In large compressors, the gas is frequently cooled while being compressed to reduce the power consumed by the compressor. Explain how cooling the gas during a compression process reduces the power consumption.

An ideal gas starts with pressure $p_{1}$ and volume $V_{1}$. Draw a pV diagram showing the process in which the gas undergoes an isothermal process during which the volume is halved, then an isochoric process during which the pressure is halved, followed by an isobaric process during which the volume is doubled. Label each of the three processes.

A 20.00-kg lead sphere is hanging from a hook by a thin wire 2.80 m long and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.00-kg steel dart that embeds itself in the lead sphere. What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision?

A small wooden block with a mass $0.800 \textrm{ kg}$ is suspended from the lower end of a light cord that is $1.60 \textrm{ m}$ long. The block is initially at rest. A bullet with a mass $12.0 \textrm{ g}$ is fired at the block with a horizontal velocity $v_{0}$. The bullet strikes the block and becomes embedded in it. After the collision the combined object swings on the end of the cord. When the block has risen to a vertical height of $0.800 \textrm{ m}$, the tension in the cord is $4.80 \textrm{ N}$. What was the initial speed $v_{0}$ of the bullet?

Three objects, A, B, and C, have $x$ and $y$ components of velocity that vary with time as shown in given figure. What is the direction of the net force acting on (a) object $A$.(All of the nonzero slopes have the same magnitude.)

Block B (mass 4.00 kg) is at rest at the edge of a smooth platform, 2.60 m above the floor. Block A (mass 2.00 kg) is sliding with a speed of 8.00 m/s along the platform toward block B. A strikes B and rebounds with a speed of 2.00 m/s. The collision projects B horizontally off the platform. What is the speed of B just before it strikes the floor?

A uniform cube with mass 0.500 kg and volume 0.0270 $\mathrm{m}^{3}$ is sitting on the floor. A uniform sphere with radius 0.400 m and mass 0.800 kg sits on top of the cube. How far is the center of mass of the two-object system above the floor?

Two figure skaters, one weighing $625 \mathrm{~N}$ and the other $725 \mathrm{~N}$, push off against each other on frictionless ice.
(a) If the heavier skater travels at $1.50 \mathrm{~m} / \mathrm{s}$, how fast will the lighter one travel?
(b) How much kinetic energy is "created" during the skaters' maneuver, and where does this energy come from?

Two figure skaters, one weighing $625 \mathrm{~N}$ and the other $725 \mathrm{~N}$, push off against each other on frictionless ice.
(b) How much kinetic energy is "created" during the skaters' maneuver, and where does this energy come from?

Three objects, A, B, and C, have $x$ and $y$ components of velocity that vary with time as shown in given figure. What is the direction of the net force acting on object $B$, (All of the nonzero slopes have the same magnitude.)

O A basketball rolls across a floor without slipping, with its center of mass moving at a certain velocity. A block of ice of the same mass is set sliding across the floor with the same speed along a parallel line. (i) How do their energies compare? (a) The basketball has more kinetic energy(b) The ice has more kinetic energy. (c) They have equal kinetic energies. (ii) How do their momenta compare? (a) The basketball has more momentum. (b) The ice has more momentum. (c) They have equal momenta. (d) Their momenta have equal magnitudes but are different vectors. (iii) The two objects encounter a ramp sloping upward. (a) The basketball will travel farther up the ramp. (b) The ice will travel farther up the ramp. (c) They will travel equally far up the ramp.

A local ice hockey team has asked you to design an apparatus for measuring the speed of the hockey puck after a slap shot. Your design is a 2.00-m-long, uniform rod pivoted about one end so that it is free to rotate horizontally on the ice without friction. The 0.800-kg rod has a light basket at the other end to catch the 0.163-kg puck. The puck slides across the ice with velocity $\vec{v}$ (perpendicular to the rod), hits the basket, and is caught. After the collision, the rod rotates. If the rod makes one revolution every 0.736 s after the puck is caught, what was the puck’s speed just before it hit the rod?

A sphere with radius $R=0.200$ m has density $\rho$ that decreases with distance $r$ from the center of the sphere according to $\rho=3.00 \times 10^3 \mathrm{~kg} / \mathrm{m}^3-\left(9.00 \times 10^3 \mathrm{~kg} / \mathrm{m}^4\right) r$.
(b) Calculate the moment of inertia of the sphere for an axis along a diameter.