A mass m is attached to a cord passing through a smallhole in a frictionless, ho

Question

A mass m is attached to a cord passing through a smallhole in a frictionless, horizontal surface. The mass is initiallyorbiting with speed vi in a circle of radiusri. The cord is then slowly pulled from below,and the radius of the circle decreases to r. (Use r_i forri, v_i for vi, m,and r as appropriate in your equations below.) (a) What is the speed of the mass when theradius is r?
v = 1

(b) Find the tension in the cord as a function of r.
T = 2

(c) How much work W is done in moving m fromri to r? (Note: The tensiondepends on r.)
W = 3


(d) Obtain numerical values for v, T, andW when r = 0.125 m,m = 40.0 g,ri = 0.300 m, and vi =1.35 m/s. v = 4 m/s T = 5 N W = 6 J (a) What is the speed of the mass when theradius is r?
v = 1

(b) Find the tension in the cord as a function of r.
T = 2

(c) How much work W is done in moving m fromri to r? (Note: The tensiondepends on r.)
W = 3


(d) Obtain numerical values for v, T, andW when r = 0.125 m,m = 40.0 g,ri = 0.300 m, and vi =1.35 m/s. v = 4 m/s T = 5 N W = 6 J v = 4 m/s T = 5 N W = 6 J

Explanation / Answer

a) initial angular momentum = m*rivi final angular momentum = m*rv angular momentum conservation: m*rivi = mrv v = rivi/r b) T = mv2/r =m*ri2vi2/r3 c) W = final energy - initial energy = mv2/2 -mvi2/2 = mvi2/2*(ri2/r2 - 1) d) v = 3.24 m/s T = 3.36 N W = 0.1735 J

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