We'll continue our discussion of momentum a little bit, time permitting, at least as far as figuring out how to handle collisions. A larger portion of the class will be related to homework problems, which are directly relevant for the exam, and another lab on programming.
For the homework, you should be a little bothered by #6, I'll outline 2 methods to solve this one. Number 7 should be quite mysterious, and that is OK - the technique you need to solve it is related to the experimental propagation of uncertainty - if you change one variable a little bit, how do the others change? This is related to how you move along surfaces in 3D, something you are learning or have learned in Cal III.
Number 8 requires some thought - the equilibrium spacing is where U(r) is minimum, or where dU/dr = -F = 0 and the net force is zero. Find this first. The breaking point of molecule is when you exceed the maximum restoring force implied by U(r). If you find F(r) = -dU/dr and look for its maximum, this will occur for a particular r, beyond which the force binding the atoms together is exceeded and the atoms will come apart. Mathematically, that means setting dF/dr = 0 to find the maximum, that's the radius beyond which you break the molecule. Using the result for the equilibrium spacing, you can write it in terms of only n, m, and the equilibrium radius. I might have asked this question before if you are willing to dig a little.
For the exam, the format is exactly like the last time. It will likely consist of 6 problems, of which you have to solve 4. The questions will only be on work, kinetic energy, potential energy, and conservation of energy - 2 chapters in the book. You'll have a formula sheet given like last time, and can bring 1 sheet of paper of your own. I will post HW3 solutions by Thursday morning, hopefully, to help you study.
Finally, the lab: we'll continue with coding. You have two basic tasks.
1) I assert that the sum of the first n cubes of integers (sum of i^3 from i=1 to i=n) is the square of the sum of the first n integers (square of the sum of i from i=1 to i=n). Write a program that can check this for specific values of n. Print out your code and results for n=10 and n=17. Basically: sum the integers, square the sum, and compare to the sum of the cubes of integers.
2) Write and evaluate a program to calculate the range of a projectile under only the influence of gravity (no drag forces). Verify that it gives the correct result (within a few percent numerical error) for a launch speed of 25 m/s and a launch angle of 45 degrees. (You already know how to calculate the range without a drag force ...) Note that links I gave previously, and specific folders here are highly useful. Print out your code and note your results for the conditions noted.
For the homework, you should be a little bothered by #6, I'll outline 2 methods to solve this one. Number 7 should be quite mysterious, and that is OK - the technique you need to solve it is related to the experimental propagation of uncertainty - if you change one variable a little bit, how do the others change? This is related to how you move along surfaces in 3D, something you are learning or have learned in Cal III.
Number 8 requires some thought - the equilibrium spacing is where U(r) is minimum, or where dU/dr = -F = 0 and the net force is zero. Find this first. The breaking point of molecule is when you exceed the maximum restoring force implied by U(r). If you find F(r) = -dU/dr and look for its maximum, this will occur for a particular r, beyond which the force binding the atoms together is exceeded and the atoms will come apart. Mathematically, that means setting dF/dr = 0 to find the maximum, that's the radius beyond which you break the molecule. Using the result for the equilibrium spacing, you can write it in terms of only n, m, and the equilibrium radius. I might have asked this question before if you are willing to dig a little.
For the exam, the format is exactly like the last time. It will likely consist of 6 problems, of which you have to solve 4. The questions will only be on work, kinetic energy, potential energy, and conservation of energy - 2 chapters in the book. You'll have a formula sheet given like last time, and can bring 1 sheet of paper of your own. I will post HW3 solutions by Thursday morning, hopefully, to help you study.
Finally, the lab: we'll continue with coding. You have two basic tasks.
1) I assert that the sum of the first n cubes of integers (sum of i^3 from i=1 to i=n) is the square of the sum of the first n integers (square of the sum of i from i=1 to i=n). Write a program that can check this for specific values of n. Print out your code and results for n=10 and n=17. Basically: sum the integers, square the sum, and compare to the sum of the cubes of integers.
2) Write and evaluate a program to calculate the range of a projectile under only the influence of gravity (no drag forces). Verify that it gives the correct result (within a few percent numerical error) for a launch speed of 25 m/s and a launch angle of 45 degrees. (You already know how to calculate the range without a drag force ...) Note that links I gave previously, and specific folders here are highly useful. Print out your code and note your results for the conditions noted.
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