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Category > Management Posted 29 Jan 2018 My Price 3.00

leaky bucket

Another leaky bucket

 

Consider the setup in Problem 16, but now let the sand leak at a rate proportional to the bucket’s acceleration. That is, dm/dt = b. Note that  is negative, so dm is also.

(a) Find the mass as a function of time, m(t).

(b) Find v(t) and x(t) for the times when the bucket contains a nonzero amount of sand. Also find v(m) and x(m). What is the speed right before all the sand leaves the bucket (assuming it hasn’t hit the wall yet)?

(c) What is the maximum value of the bucket’s kinetic energy, assuming it is achieved before it hits the wall?

(d) What is the maximum value of the magnitude of the bucket’s momentum, assuming it is achieved before it hits the wall?

(e) For what value of b does the bucket become empty right when it hits the wall?

Problem 16

Leaky bucket

At t = 0, a massless bucket contains a mass M of sand. It is connected to a wall by a massless spring with constant tension T (that is, independent of length).18 See Fig. 4.43. The ground is frictionless, and the initial distance to the wall is L. At later times, let x be the distance from the wall, and let m be the mass of sand in the bucket. The bucket is released. On its way to the wall, it leaks sand at a rate dm/dx = M/L. In other words, the rate is constant with respect to distance, not time. Note that dx is negative, so dm is also.

(a) What is the kinetic energy of the (sand in the) bucket, as a function of the distance from the wall? What is its maximum value?

(b) What is the magnitude of the momentum of the bucket, as a function of the distance from the wall? What is its maximum value?

Answers

Maurice Tutor
(5)
Status NEW Posted 29 Jan 2018 11:01 PM My Price 3.00

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