A low-friction cart of mass rolls down a straight track that makes a small angle with…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A low-friction cart of mass m rolls down a straight track that makes a small angle with the horizontal. A motion detector fixed at the top of the track continuously measures the distance s from the detector to the cart’s front bumper. The data obtained are shown below.
Time t (s): 0.00 0.20 0.40 0.60 0.80 1.00
Distance s (m): 1.200 1.115 1.030 0.945 0.860 0.775
Assume air resistance is negligible.
(The center of mass of the cart is located d = 0.12m behind the front bumper.)
(1) Using the data above, determine the cart’s average acceleration during the time interval shown. Show all algebraic steps used to extract acceleration from the displacement–time information.
(2) Explain why the cart can legitimately be treated as a point mass when calculating its acceleration in part (a).
(3) Derive an expression for the fractional error in the acceleration obtained in part (a) that arises because the detector measures the position of the front bumper rather than the cart’s center of mass. Express your answer in terms of d and the total displacement of the cart’s center of mass during the interval.
(4) For the specific data provided, evaluate the numerical value of the fractional error found in part (c) and comment on whether the object model is adequate for this experiment.