A mass M on a frictionless horizontal surface is connected to mass m by a massle

Question

A mass M on a frictionless horizontal surface is connected to mass m by a massless string passing over a massless pulley as shown in the figure below. (a) Find the acceleration of mass M in terms of g. M, and m values (b) Mass M is released from rest at some point to the left of the position ro. The velocity of mass M is measured at points ro and r as shown in the figure. Find the acceleration of M in terms of the distance d = z1-z0, and the measured velocities to and vi at points zo and zi respectively. (c) A student performs the experiment and measures the distance between photogates: d = 50 ± 0.1 cm, the times measured by photogates: to = 0.052 ± 0.001 s and ti-0.035 ± 0.001 s, and the cart's length: 8-10 ± 0.05 cm. Find the acceleration a of the cart and estimate the uncertainty in a. (d) The student repeats the measurements and obtains more values of the acceleration : 5.15 4.22 4.63 ·3.92 m, 4.58 m. 4.27 Calculate the best estimate of a and the random uncertainty of these results (dont forget to include the very first value from part c) e) Compare the estimated uncertainty of one measurement (c) and the random uncertainty (d) Xo Figure 1: Mass and pulley arrangement

Explanation / Answer

a)Let acceleration be a and tension in rope be T

from free body diagram of m,we get

mg-T=ma

From free body diagram of M,we get

T=Ma

Or, mg-Ma=ma

mg=(M+m)a

a=mg/(m+M)

b)distnace between xo and x1 =d= x1-xo

velocity at xo=vo

velocity at x1=v1

v12=vo2+2*a*d

a=(v12-vo2)/2d

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