Physics 221 12/5/02 name____________________

R =8.31 J/mole K N_A = 6.02x10⁺²³ molecules/mole 1cal = 4.180J

k = 1.38x10^{- 23} J/K u = 1.66x10^{- 27}kg 1 atm = 1.01x10⁵ Pa c = 3x10⁸ m/s

a_T = r a v_T = r w s = r q

1) A baseball of mass 200g is moving at 15m/s. It is hit by a bat, exactly reverses direction and rebounds with a velocity of -18m/s.

a) What average force must be delivered if the time the ball is in contact with the bat is 0.002s?

b) The batter decides to bunt the ball. What force must be delivered if ball stops on contact with the bat (assume the contact time is still 0.002s)?

c) In part a) you assumed the velocities were perpendicular to the bat. Explain how the calculations would be different if those were the x- components of velocity and the y-component of velocity is -2m/s before and after being hit by the bat (assume the x- direction is along the line between the pitcher and batter and the y- direction is up).

d) The momentum of the ball clearly changes when it hits the bat. Reconcile this with the law of conservation of momentum.

2) A sled of mass 30kg is coasting at 4m/s along level snow with a kid of mass 45kg (total mass of 75kg). The kid jumps off the back of the sled so that she finds herself sliding on the snow at 2m/s in the same direction as the sled. Assume no friction forces between the kid and the snow or between the sled and the snow during this event. There is and internal force between the kid and the sled when the kid jumps off.

a) Why can't you use conservation of energy to solve this problem?

c) What is the new velocity of the sled after she jumps off?

c) Is this an inelastic or elastic collision and how do you know?

3) At its furthest distance from the sun, Halley's comet is 5.3x10⁹ km away and is traveling at 5x10³ m/s.

a) How fast is it traveling when it is at it's closest distance to the sun, 8.8x10⁷ km? (I = mr² for an object of mass m at a distance of r, angular velocity is w = v/r)

b) Use the rules for determining the vector cross product to show that the torque (t = r x F) on the comet caused by the gravitational pull of the sun is zero.

4) An iceberg floats with a volume is 400 m³ under the surface. What are the iceberg's:

a) weight? (Hint: Volume of water displaced is 400 m³ and the density of water is 1000kg/m³.)

b) mass?

c) density (assume that the total volume of the iceberg is 444 m³ (9/10ths of the volume is under water)?

5) Brown in 1827 originally observed pollen grains of mass 2x10^-12 kg moving at average speeds in random directions around 8x10^-5m/s. What was the temperature of the water in which the grains were immersed? (This motion, called Brownian motion, was later investigated by Einstein and others and lead to our current belief in the existence of molecules.)

6) Sometimes your ears pop when going up or down a mountain.

a) What is the change in air pressure in going down 1000m in a mountain? The density of air is 1.29 kg/m³.

b) What is the additional force on your ear drum if its area is 0.0003 m²?

7) In class we talked about modeling the force holding atoms together in a solid as if the force were a kind of spring. We also found that the forces were related to potentials by F_x(x) = -¶U/¶x. Some of the potentials we looked at would not be correct because they would not give rise to thermal expansion while other potentials (the Van der Waals for example) would show expansion

a) Make two sketches, one of a potential that would not result in expansion as temperature increases, another that would.

b) Explain why the first potential you drew would not result in a solid that expanded as temperature increased but the second one would.

8) a) Explain the connection between microstates and entropy.

b) For the case of four coin toss explain how entropy is defined any why a result of two heads and two tails is more likely in a coin toss than all heads.

c) How does the example of four coins relate to thermodynamics of the molecules in this room (Hint: Label the left side of the room H and the right side T and talk about microstates and entropy.)

9) If you shake a jar of jelly beans of two different sizes, the larger jelly beans tend to appear at the top while the smaller ones tend to sink to the bottom (because the smaller beans can fall into openings which are too big for the big beans, thus packing tighter). When this happens the system goes from a disordered state to a more ordered state (small beans on the bottom, large beans on top). Why does this process not violate the second law of thermodynamics?

Bonus:

Explain the scientific meaning of chaos.

Explain the four methods of heat transfer.