Download Analysis of a Freely-Falling Body: Determining the Acceleration due to Gravity and more Papers Physics in PDF only on Docsity! 1 EXPERIMENT: ANALYSIS OF A FREELY-FALLING BODY Part I: Dependence of Speed and Position on Time OBJECTIVES • to verify how the distance of a freely-falling body varies with time • to investigate whether the velocity of a freely-falling body increases linearly with time • to calculate a value for g, the acceleration due to gravity APPARATUS A Behr Free-Fall Apparatus and Spark Timing System will be used. BEHR FREE FALL SYSTEM THEORY In this experiment a brass cylinder is dropped and a record of its free fall is made. Before the measurement, the cylinder is suspended at the top of the stand with the help of an electromagnet. When the electromagnet is turned off, the cylinder is released and starts to fall. Simultaneously, the spark timer starts to send evenly-spaced, high-voltage pulses through two wires which are stretched along the cylinder’s path. At the time of each pulse a spark goes through the wires and the cylinder, leaving a mark on the special paper tape that lies between the cylinder and one of the wires. The time interval between two adjacent sparks, τ, is 1/60 of a second. 2 Measuring the distances between any two marks, ∆y, and knowing the times between the corresponding sparks, ∆t, it is possible to calculate the average velocity during this interval using the formula v = ∆y ∆t (1) If ∆t is small enough, we can assume that the velocity at any instant within this interval is approximately equal to this average velocity. In general, for the motion of a body with a constant acceleration a, the velocity v is given by the equation v = at + vo, (2) where vo is the velocity of the cylinder at t = 0. Since in our case the brass cylinder is falling freely, a = -g, (3) where g=9.81 m/s2 is the magnitude of the acceleration due to gravity. Therefore it follows from (2) that for a freely-falling body v = v0 − gt . (4) Thus g can be determined from a plot of v vs. t since the slope of any velocity versus time graph is just the acceleration. The obtained value of g can then be compared with the known value of the acceleration due to gravity. The position of the cylinder, y, as a function of time is given by the standard equation for an object that is undergoing constant acceleration. If at time = 0 the object has height yo and velocity vo, then this equation looks like y = y0 + v0t − 1 2 gt 2 . (5) PROCEDURE Using the free fall apparatus, drop the brass cylinder and record on spark tape the location of the falling cylinder at a series of equally spaced time intervals, τ = 1/60 s. The quantities needed to analyze the motion are the position (y), velocity (v) and time (t) of the points on your spark tape. The choices of t = 0 and y = 0 are arbitrary and do not necessarily refer to your first or last data points. However, as your object falls the position y must decrease (becoming negative if necessary). After you have performed the experiment, tape the paper strip to your lab table. Label the points on your tape, starting with the point AT THE BOTTOM OF THE OBJECT’S FALL as #31 and label them in DESCENDING numerical order. Make sure that point #31 is the last actual data point and not the point where the brass cylinder is stuck in the putty and simply sparking. NOTE: Point #1 will not necessarily correspond to your very first point, but the very first points are somewhat ambiguous anyway. It does not matter if you do not use some of the first points. Next, put a ruler
