Week 4
Topics: One-dimensional kinematics, vector algebra
Week 4 exercises:
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?
- 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. Do a power-law fit to your data. Label your plot appropriately. Do this for each of the three ramp angles. Put the data from all three data sets on the same graph.
- 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 of acceleration versus ramp angle. Does this make sense? Explain.
- 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).