See also the video files related to experiment 3 for the idea of the setup.
We measure the time required for a ball to accelerate from rest down various uniform inclines with slopes between 0 and .1. For each incline we determine the average velocity of the ball. We then plot average velocity vs. slope and determine whether the graph appears to follow a straight line. Using the asserted propositions that the ball accelerates uniformly and that the final velocity of an object which accelerates uniformly from rest is double its average velocity, we determine for each incline the average rate at which the velocity of the ball changes. We then construct a graph of the average rate of velocity change vs. incline slope. We finally determine the slope of the straight line which best fit our data points.
By timing and object as it accelerates from rest down one uniform incline, then as it travels along a second slight incline elevated just enough to keep the object moving at a uniform velocity, we test the previously asserted hypothesis that when an object accelerates uniformly from rest, its final velocity will be double its average velocity. We do this by graphing the velocity on the second ramp vs. the velocity on the first. We interpret the slope of this graph to test our hypothesis.
By timing an object as it accelerates from rest for various distances down an incline, we infer its average acceleration for various distances and average speeds. We then test to validate the hypothesis that the acceleration is in fact uniform lawn the incline.
For ramp slopes between 0 and .1, the acceleration of a cart down the slope is very nearly a linear function of ramp slope, with only a 1/2 % deviation from linearity within this range of slopes. In this experiment we determine the accelerations of the friction car corresponding to a selection of ramp slopes within this range, and plot acceleration vs. ramp slope. Since frictional forces and tabletop deviations from linearity will be very nearly the same for all trials, the slope of the graph gives us the acceleration of gravity.
Using the pendulum timer we can measure the time required for a dropped object to fall various distances from rest under the acceleration of gravity. We can calculate the acceleration for each distance and test hypothesis that the acceleration is the same for all heights.
Alternatively using the pendulum timer we can synchronize the dropping of a ball with the time required for the pendulum to complete a quarter-cycle for each of several drop distances. If the acceleration of the dropped object is uniform, then the time required for the object to drop should be proportional to the square root of the distance dropped. Since the period of the pendulum is proportional to the square root of its length, it follows that if gravity accelerates objects uniformly then the distance dropped should be proportional to the length of the synchronize to pendulum. From the associated proportionality constant, and from the proportionality constant for the pendulum period, we can determine from our data the acceleration of gravity.
In this experiment we measure the horizontal range of a ball projected horizontally from a ramp. We also measure the velocity of the ball at the end of the ramp by timing it as it rolls down the ramp from rest. Using the time required to fall to the floor we then determine the average horizontal velocity of the ball during its fall. We test the hypothesis that the horizontal velocity of the falling ball remains the same as at the instant the ball left the ramp.
Using a balance constructed from pieces of shelf standard, balanced on a knife edge and with a brass damping cylinder partially submerged in water, we investigate the rotational displacement of the balance from equilibrium in response to the addition of small weights. We then use the balance with the mass set to precisely measure the masses of various objects.
Experiment 8. Acceleration of a constant mass vs. net applied force gives a linear graph which can be extrapolated to obtain the acceleration of gravity.Using weights suspended over pulleys we observe the acceleration due to different net forces on the mass of the friction car. A graph of acceleration vs. net force can be extrapolated to a force equal to the weight of the car. Since it is this force which accelerates the car in free fall, this extrapolated acceleration will be the acceleration of gravity.
Experiment 9. The force tending to pull a pendulum back toward its equilibrium position is in the same proportion to the weight of the pendulum as the displacement from equilibrium to the length of the pendulum.By displacing a pendulum with various numbers of equal masses suspended over a pulley, we determine the nature of the relationship between the displacing force and the displacement of the pendulum.
Experiment 10. Rubber bands can be calibrated to measure force with reasonable accuracy.By pulling back a pendulum of known length and mass using two attached strings with a rubber band between them, we see that the additional force required to pull the pendulum back further and further results in a greater and greater stretch of the rubber band. By measuring the length of the rubber band vs. the displacement of the pendulum we infer and graph force vs. stretch for the rubber band. Repeating the experiment with two identical rubber bands in series, then again with the two rubber bands in parallel, we compare the forces exerted by these combinations with the force of a single rubber band. We store our calibration of the rubber bands in a convenient calibration program. We repeat this experiment for two different types of rubber bands.
Experiment 11. For any given angle, the weight of an object is completely equivalent to the resultant of two mutually perpendicular forces with one at the given angle from vertical.By suspending various masses from two perpendicular strings with inserted rubber bands, we can determine the force exerted by each string. By changing the angles of the two strings while maintaining the right angle between them, we infer at different angles the components of the weight vector for the suspended mass, and compare our results with the predictions of vector analysis.
Experiment 12. The net force on a friction car released on a ramp is proportional to the 'effective' slope of the ramp, for small slopes.For various slopes we determine the force required to prevent the friction car from rolling down a straight, slightly vibrating incline. We also determine the slope at which the car rolls down the incline at a constant velocity. A graph of acceleration vs. effective slope (effective slope is slope in excess of the constant-velocity slope) tests whether the relationship is nearly a proportionality for small slopes.
Experiment 13. The force of air resistance on a falling coffee filter is proportional to the square of the velocity of the filter (?).Under the assumption that a coffee filter dropped from a height on the order of one meter reaches its terminal velocity in a negligibly short time after covering a negligibly short distance, we compare terminal velocities of single, doubled, tripled and quadrupled coffee filters by dropping them simultaneously from various heights and adjusting the heights until all the filters reach the floor at the same time. We investigate the power-function relationship between weight and terminal velocity, and the relationship between velocity and the force of air resistance.
Experiment 14. When an object is immersed in water the water exerts a buoyant force equal to the weight of the water displaced.Using the shelf standard balance with the damping cylinder partially immersed, we compare the force required to offset a specific change in the water level on the cylinder. We determine the change in the immersed volume of the cylinder and compare the mass of an equivalent amount of water with the offsetting force.