# Acceleration Due to Gravity

2131 Words9 Pages
Acceleration Due to Gravity Introduction In this lab you will measure the acceleration due to gravity near the earth’s surface with two experiments: first, by determining the time for a steel ball to fall a known vertical distance (free fall), and then second, by measuring the velocity of a cart at various points as it glides down a slightly inclined and nearly frictionless air track (slow fall). Equipment Part 1: Free-Fall • Free-fall apparatus (steel plate, drop mechanism) • Electronic Timer • Steel Ball Part 2: Slow-Fall • Air Track • Electronic Timer (may be different brand/model than in Part 1) • Gliding Car • Laser Photogate Background: Free Fall Acceleration Under the constant acceleration of gravity near the Earth’s surface,…show more content…
When an object slides down an incline, there are three forces acting upon it: the normal force, (N) of the incline pushing up on the object, the weight of the object (W), and any frictional forces (Ffr). Figure 2 illustrates these forces. The dashed lines indicate the components of the object’s weight along and perpendicular to the incline. Any net force in the x-direction will cause the object to slide along the incline. Summing the x-components of the forces shown in Figure 2, we find that W x " F fr = ma x ! 2 Acceleration Due to Gravity Physics 117/197/211 Figure 2: Free-body diagram of an object sliding down an inclined plane When the frictional force is very small, as will be the case in this lab, it can be neglected, so that W x = ma x The x-component of the object’s acceleration is then ! ( mg sin " ) = g sin " W ax = x = m m For a fixed inclination angle, θ, measurement of the acceleration down the incline permits g to be determined experimentally. Note that because the acceleration is constant we can appeal to the familiar ! kinematics equations to describe the motion of the object as it moves down the incline. r r r 1r r = r0 + v 0 t + at 2 r r r2 v = v 0 + at For this lab, we are interested in ax, the acceleration of the object along the incline, so all positions, ! velocities, and accelerations will be associated with the x-direction. To further simplify the experiment, the ! initial