Set-Up a Sequential Measurement
Add an analyzer to the experiment by:
- Break the links between the analyzer and the counters by clicking on the boxes with up and down arrow labels on the analyzer.
- Click and drag a new connection from the analyzer to empty space to create a new element. A new analyzer is one of the options.
Measure \(S_z\) twice in succession.
What is the probability that a particle leaving the first analyzer with \(S_z=\frac{+\hbar}{2}\) will be measured by the second analyzer to have \(S_z=\frac{-\hbar}{2}\)?
Try all four possible combinations of input/outputs for the second analyzer.
What have you learned from these experiments?
Try All Combinations of Sequential Measurements
In the table, enter the probability of a particle exiting the 2nd analyzer with the spin indicated in row if the particle enters the 2nd analyzer with the spin indicated in each column.
You can rotate the Stern-Gerlach analyzers to any direction you want (using spherical coordinates).
Choose an arbitrary direction (not along one of the coordinate axes) for the 1st analyzer and measure the spin along the coordinate directions for the 2nd analyzer.
face Lecture
5 min.
group Small Group Activity
30 min.
energy conservation mass conservation collision
Groups are asked to analyze the following standard problem:
Two identical lumps of clay of (rest) mass m collide head on, with each moving at 3/5 the speed of light. What is the mass of the resulting lump of clay?
face Lecture
30 min.
group Small Group Activity
30 min.
group Small Group Activity
30 min.
assignment_ind Small White Board Question
5 min.
assignment Homework
(Straightforward) Purpose: Discover that a system of two masses can be a central force system even when they are not interacting at all. Practice with center-of-mass coordinates.
Consider two particles of equal mass \(m\). The forces on the particles are \(\vec F_1=0\) and \(\vec F_2=F_0\hat{x}\). If the particles are initially at rest at the origin, find the position, velocity, and acceleration of the center of mass as functions of time. Solve this problem in two ways,
accessibility_new Kinesthetic
10 min.