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Velocity : v(t) = d_x(t)/dt = 2At +B Acceleration : a(t) = d_v(t)/dt = 2A Experi

ID: 1530555 • Letter: V

Question

Velocity : v(t) = d_x(t)/dt = 2At +B Acceleration : a(t) = d_v(t)/dt = 2A Experiments acceleration : a_exp = 2A Newton's second law : F = ma For a frictionless ramp, the force responsible for the constant acceleration is the component of the weight parallel to the ramp. Mg sin(theta) = ma a = g sin(theta) where g is acceleration due to gravity. The angle of inclination theta can be determined from the Length (L) and height (h) of the ramp. Sin(theta) = h/L Experimentally the acceleration down the ramp can be calculated as a_exp = g(n)/L = 2A The acceleration due to gravity can then be determined by g_exp = a_exp L/h = 2A L/h Assume the track has a length L = 1.0 m, and we release a cart of known mass from five different heights.

Explanation / Answer

Given

   a exp = 2*A

and g exp = 2A(L/h), L= 0.1 m,


h (m)       A (m/s2)   a exp (m/s2)   g exp (m/s2)

0.02       0.089       0.179       2(0.179)(0.1/0.02) = 1.79

0.04       0.2       0.4       2(0.2)(0.1/0.04) = 1

0.06       0.3       0.6       2(0.3)(0.1/0.06) = 1

0.08       0.38       0.76       2(0.38)(0.1/0.08) = 0.95

0.1       0.46       0.92       2(0.46)(0.1/0.1) =0.92