An experiment it. performed using the apparatus above. A small disk of mass m1 o

Question

An experiment it. performed using the apparatus above. A small disk of mass m1 on a frictionless table is attached to one end of a string. The string posses through a hole in the table and an attached narrow, vertical plastic tube. An object of mass m2 is hung at the other end of the string. A student holding the tube makes the disk rotate in a circle of constant radius r. while another student measures the period P. Derive the equation that relates P and m2. The procedure is repeated, and the period P is determined (or four different values of m2, where m1 = 0.012 kg and r = 0.80 m. The data, which are presented below, can be used to compute an experimental value for g. What quantities should be graphed to yield a straight line with a slope that could be used to determine g ? On the grid below, plot the quantities determined in part (b). label the axes, and draw the best-fit line to the data. You may use the blank rows above to record any values you may need to calculate. Use your graph to calculate the experimental value of g.

Explanation / Answer

something wrong with the diagram software so cant draw a diagram.

consider mass m2. The tension is pulling it up whereas its weight m2g acts downwards.

Since the mass is not moving, T = m2g. This tension must be the same throughout the string and hence, a force m2g is providing the centripetal force for this motion.

Thus, m2g = m1r2

But = 2/P

Thus, m2g = m1r (2/P)2

Thus, 2/P = (m2g/m1r) and P = 2(m1r/m2g).

(b) for a straight line, the equation must be of the form y = mx + c or y = mx.

There should be no square root. Thus, we square both sides of our answer to get:

P2 = 42(m2g/m1r).

This is in the form y = mx where y = P^2, x = m2 and m = 42g/(m1r).

Thus, if you plot P^2 on the y axis and m2 on the x-axis, the gradient will give you 42g/(m1r).

you can then solve for g as you know m1 and r.

(c) and (d) I guess its hard to explain here. Try and get back if you need help. Will scan a paper and send you in few days if needed.

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