Links to document. http://imgur.com/xR63w0X http://i60.tinypic.com/2cm0kz.jpg Th

Question

Links to document.

http://imgur.com/xR63w0X

http://i60.tinypic.com/2cm0kz.jpg

This homework will help to prepare you for the activity we will do in lab next week. Please complete it prior to coming to lab. 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. Find the acceleration of mass M in terms of g, M, and m values. Mass M is released from rest at some point to the left of the position x_0. The velocity of mass M is measured at points x_0 and x_1 as shown in the figure. Find the acceleration of M in terms of the distance d = x_1 - x_0, and the measured velocities v_0 and v_1 at points x_0 and x_1 respectively. A student performs the experiment and measures the distance between photogates: d = 50 plusminus 0.1 cm, the times measured by photogates: t_0 = 0.052 plusminus 0.001 s and t_1 = 0.035 plusminus 0.001 s, and the cart's length: s = 10 plusminus 0.05 cm. Find the acceleration a of the cart and estimate the uncertainty in a. The student repeats the measurements and obtains more values of the acceleration : Calculate the best estimate of a and the random uncertainty of these results (dont forget to include die very first value from part c). Compare the estimated uncertainty of one measurement (c) and the random uncertainty (d). Figure 1: Mass and pulley arrangement

Explanation / Answer

a) Force on M = mg

Acceleration = mg/M

b)

So at x0,

v0^2 = 0 + 2*mg/m*x0

v1^2 = 0 + 2*mg/M*x1

x0 = 0 + 1/2*mg/M*t0^2

t0^2 = 2*x0*M/mg

Similarly

t1^2 = 2*x1*M/mg

Hence

Acceleration = v1-v0/(t1-t0)

Put in the values and compute

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