How to approach the problem
All this question is asking is: "How fast are Chuck and the ball moving away from each other?" If two objects are moving at the same speed(with respect to the ground) in the same direction, their relative speed is zero. If they are moving at the same speed, , in oppositedirections, their relative speed is . In this problem, you are given variables for the speed of Chuck and the ball with respect to the ground,and you know that Chuck and the ball are moving directly away from each other. ANSWER:
Make sure you understand this result; the concept of "relative speed" is important. In general, if two objects are moving in opposite directions(either toward each other or away from each other), the relative speed between them is equal to the sum of their speeds with respect to theground. If two objects are moving in the same direction, then the relative speed between them is the absolute value of the difference of the their two speeds with respect to the ground.
What is the speed of the ball (relative to the ground) while it is in the air?
Express your answer in terms of , , and .
How to approach the problem
Apply conservation of momentum. Equate the initial (before the ball is thrown) and final (after the ball is thrown) momenta of the systemconsisting of Chuck, his cart, and the ball. Use the result from Part A to eliminate from this equation and solve for .
Initial momentum of Chuck, his cart, and the ball
Before the ball is thrown, Chuck, his cart, and the ball are all at rest. Therefore, their total initial momentum is zero.
Find the final momentum of Chuck, his cart, and the thrown ball
What is the total momentum of Chuck, his cart, and the ball after the ball is thrown?
Express your answer in terms of , , , and .Remember that and are speeds, not velocities, and thus are positive scalars.
Assignment 4: Linear Momentum
Signed in as Mikael Lemanza
Part DWhat is the final volume ?Hint D.1
Relation between volume and temperature
Recall that, in an adiabatic process with finite changes in volume and temperature, is aconstant. As a result, . ANSWER:=
Work from an Adiabatic Expansion
In this problem you are to consider an
expansion of an ideal diatomic gas, which means thatthe gas expands with no addition or subtraction of heat.This appletshows the adiabatic compression and expansion of an ideal monatomic gas with . Itwill help you to see the qualitative behavior of adiabatic expansions, though your actual calculations willuse a slightly different . Assume that the gas is initially at pressure , volume , and temperature . In addition, assume thatthe temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is .Note that, unless explicitly stated, the variable should not appear in your answers--if needed use thefact that for an ideal diatomic gas.Part AFind an analytic expression for , the pressure as a function of volume, during the adiabaticexpansion.Hint A.1
Find the conserved quantity in an adiabatic process
Hint not displayed
Express the pressure in terms of and any or all of the given initial values , , and .
The fact that is a constant derives from the definition of an adiabatic process as one inwhich no heat flow into or out of the system occurs. Setting in the first law of