Incline Plane Lab PHYS 253 Kevin Hamilton January 16, 2019 1 Theory Figure 1 We know from our experiences in reality that when we roll a ball down a hill, the ball will roll down the hill and continuously accelerate, or speed up, if unhindered. Now, we will be able to actually make measurements of the acceleration. First, however, we will need to find the angle at which the inclined plane sits with respect to the horizontal surface. We can do this by measuring the height from the table at two different points along the plane, hl and fig. These two measurements will be separated by some distance, which we call l. If we look at Figure 1, we see two smaller triangles formed within the larger triangle, both of which have the same angle, 6, between the inclined plane and the surface. If we remember some basic trigonometry, we can nd that angle based off of our measurements. OPP h? hl ) = = (1) ADJ l Note that we are measuring the angle within the small triangle, but that angle is the same that is labeled to the right side of Figure 1. Lastly, in order to get the actual angle, we take the inverse tangent of both sides. tan\"? 1' } :9 = tan'1 L2 l L1 (2) This equation gives us a measurement for the angle between ti = inclined plane and the table. We can then use this measurement to relate our acceleration that we measure to the value of g, the acceleration due to gravity. If we look at Figure 2 on the next page, we recognize that as physicists, we can define our coordinate systems in a way that is convenient for us to describe the motion of the ball, and so the sisdirection lies parallel to the inclined plane We can then consider our basic kinematic equations for position and velocity. v(t) = on + at (3) l alt) = :50 + not + but? (4)