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v2 = v2o + 2a(x-xo) Note that these “kinematic equations” for constant acceleration are polynomials. Your textbook mathematically develops equations for x(t) and v(t): 1 1. You will study the motion of an object falling freely at constant acceleration g under the influence of gravity. While we will use them to describe motion, these ideas of rates and rate changes are important in many fields, including economics, biology and sociology. When you plot curves of x(t) and v(t), the slope of the x(t) curve at each t value represents the velocity at that time the slope of the v(t) curve at each time represents the acceleration of the object at that time.
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Such measurements can tell you how the velocity and acceleration vary in time. The velocity and the acceleration determined by this process are actually average values over the small interval, but are very nearly the instantaneous value at the center of the time interval.
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You can measure an instantaneous velocity by measuring the distance ∆x an object travels in a short period of time ∆t, and you can measure an instantaneous acceleration by determining two velocities that are separated by a known small time difference. If the object is accelerating, the dots won’t be evenly spaced, and the velocity won’t be constant. The slope of x(t) is constant, so v(t) is a constant, as sketched to the right. The graph of the data x(t) is also sketched. The speed is constant so the dots are evenly spaced. The figure below shows a tape with dots that represents the position of an object moving at constant speed at equal time intervals (perhaps a toy train on a track with one dot every second). In this experiment you will record the position of a falling object by a spark on a paper tape. As discussed in your textbook, instantaneous velocity and instantaneous acceleration can be expressed by the equations ∆v ∆x and a=, v= ∆t ∆t where the symbols ∆x, ∆v, and ∆t mean small intervals or changes in x, v, and t, respectively. You can then approximate its instantaneous velocity at some time by calculating the change that occurs in x between two known, closely spaced times. This involves measurement of the location of the object (the position x on some reference line) at many times. You will study the motion of an object moving in a straight line as it falls. Your TA will look for this at the beginning of lab as evidence of your preparation.īefore coming to the lab you should review from your textbook and class notes the idea of average and instantaneous velocity and acceleration, and the kinematic equations and how they relate to each other. Describe the goals of the lab and how they will be accomplished. OVERVIEW Before each lab you should carefully read this lab and write an overview of what you will do in the lab.
Acceleration due to gravity lab answers falling object manual#
ACCELERATION DUE TO GRAVITY Skills you will learn or practice: Calculate velocity and acceleration from experimental measurements of x vs t (spark positions) Find average velocities from two positions and times, and average accelerations from two velocities and times Sketch v(t) from the slope of x(t)and a(t) from the slope of v(t) Extract physical constants from polynomial and linear fits to data Use the kinematic equations to relate time, position, velocity when acceleration is constant Percent error Conceptual understanding: Linear vs polynomial equations and graphs How the equipment works as explained in the lab manual Other conceptual questions the lab manual suggests you consider.