Week 4 (Sep. 2, 3, 5)
Reading: PSE Chap 3, Vectors
Topics: One-dimensional kinematics, vector algebra
No quiz this week.
Week 4 exercises:
Accelerating object: An object starts from rest at the origin and moves along the x-axis with a constant acceleration of 4 m/s^2. What is its average velocity as it goes from x=2 to x=8 meters? Plot the position, velocity, and acceleration versus time for this object. Accelerating car: A car, initially at rest travels 20 meters in 4 seconds along a straight line with constant acceleration. What is its acceleration? Make a plot of the position, velocity and acceleration of this car. Accelerating truck: How far does a truck travel in 6 seconds if its initial velocity is 2 m/s and its acceleration is 2 m/s^2 in the forward direction?
Classroom exercises: As a reminder, these are some of the problems we worked out in class…
No quiz this week.
Week 4 exercises:
- Ramp laboratory experiment
- Set up a ramp. Measure the angle of the ramp with respect to the horizontal desktop.
- Roll a small steel ball down the ramp. Record the time the ball takes to roll 10, 20, 30, 40, etc. cm down the ramp. Be sure to record experimental uncertainty.
- Repeat this procedure for at least three different ramp angles.
- Make a plot of the distance (ordinate) as a function of time (abscissa) using graphical analysis software. Label your plot appropriately.
- Put the data from all three data sets on the same graph; for each data set perform a power-law fit to the data. Does your fit match your expectations?
- Using the kinematic equations we've learned this week, determine the acceleration of the ball from your graphs. How does the acceleration depend on the ramp angle? Make a plot.
Classroom exercises: As a reminder, these are some of the problems we worked out in class…
- Finding average velocities from displacement vs. time plots
- Finding the time of flight and height of a ball thrown upwards.
- 1-d kinematic equations: the connection between geometry (area under velocity vs time plots), algebra (kinematic equations relating position, velocity and acceleration), and calculus (integrating acceleration to find velocity and again to find position).