Please explain steps in detail for easy understanding. The pucks are tied togeth
ID: 2178310 • Letter: P
Question
Please explain steps in detail for easy understanding.The pucks are tied together with a string of length and negligible mass. At time t = 0, a constant force of magnitude F begins to pull to the right on the center point of the string. At time t, the moving pucks strike each other and stick together. At this time, the force has moved through a distance d, and the pucks have attained a speed v.
(a) What is v in terms of F, d, , and m?
v =
(b) How much of the energy transferred into the system by work done by the force has been transformed to internal energy? (Use the following as necessary: m, t, F, d, and .)
?K =
Explanation / Answer
This is same as Sherwood Energy/Momentum approach.
dCM = d -l/2
The force on the system is constant leads to a constant acceleration of the center of mass of the system during the time interval t = 0 to t = t.
For constant acc. of the center of mass starting from rest, its avg. vel. over time interval of interest is half the final vel.
t = dCM /vavg = (d -l/2)/v/2 = (2d-l)/v
By using Impulse theorem momentum function.
we get F((2d-l)/v) = (2m)(v-0) =2mv
==> F [(2d-l)] = 2mv2
==> v = (F [(2d-l)]/2m)
The conservation energy of the system reduces to
K +Eint = W + Q + TMV
on the right side onlyt W repreents Work done and other represents tansfer of energy which we don't consider
so K +Eint = W
(1/2) (2m)(v2) + Eint = Fd
==> Eint = Fd - m [(F [(2d-l)]/2m)]
= Fd - (F/2) (2d-l) = Fl/2
and K = mv2 = F(2d-l)/2 and Eint = Fl/2