A mass m is attached to a cord passing through a small hole in a frictionless, h

Question

A mass m is attached to a cord passing through a small hole in a frictionless, horizontal surface (Fig. P11.49). The mass is initially orbiting with speed vi in a circle of radius ri. The cord is then slowly pulled from below, and the radius of the circle decreases to r. (Use ri, vi, m, and r as appropriate in your equations below.)

(a) What is the speed of the mass when the radius is r?
v =

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

(c) How much work W is done in moving m from ri to r? (Note: The tension depends on r.)
W =

(d) Obtain numerical values for v, T, and W when r = 0.105 m, m = 50.0 g, ri = 0.300 m, and vi = 1.50 m/s.

Explanation / Answer

a) Since the angular momentum is conserved

m*vi*ri = m*v*r

so v = vi*ri / r

b) tension of the cord

T = mv^2/r = m*(vi*ri/r)^2/r = m(vi*ri)^2/r^3

c) Kinetic energy of the puck

K = mv^2/2 = m*(vi*ri/r)^2/2 = 0.5*m*(vi*ri)^2/r^2

so work done by the hand

W = K-Ki = 0.5*m*(vi*ri)^2*(1/r^2-1/ri^2)

d) v = 4.29 m/s

T = 8.75 N

W = 0.40 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.