A rod having a mass of M = 77 grams and a length of d = 40 cm is positioned vert

Question

A rod having a mass of M= 77  grams and a length of d= 40  cm is positioned vertically on a frictionless, horizontal axle passing through its center. The rod is free to rotate about the axle, and the mass of the rod is uniformly distributed. A small cube of clay, of mass m= 12  grams , is sliding horizontally on a slick surface at a speed of v0= 2.7  m/s when hits and sticks to the very bottom tip of the rod.

Part A

What is the spin rate of the clay and rod system immediately after the collision, before the rod-clay unit has had enough time to swing upward by any significant amount?

Part B

How much kinetic energy was converted to thermal energy in this collision

Part C

After the collision, to what maximum angle, measured from vertical, does the rod (with the attached wad of clay) rotate before it momentarily comes to rest?

Explanation / Answer

A) using angular momentum conservation,

initial amgular momentum of clay rod system = final angular momentum of rod clay system

( 0 ) + ( 0.012 x 2.7 x 0.40/2) = ( I system ) w

I = ( 0.077 x 0.40^2 /12) + ( 0.012 x 0.20^2 ) = 1.51 x 10^-3 kg m^2

0.012 x 2.7 x 0.20 = 1.51 x 10^-3 x w

w = 4.30 rad/s

b) initial energy = m v^2 /2 =0.012 x 2.7^2 /2 = 0.0437 J

final energy = I w^2 /2 = 1.51 x 10^-3 x 4.30^2 /2 = 0.014 J

thernal energy = Ke difference = 0.030 J

c) final energy will completely converted into potential energy when rod is at top position.

Iw ^2 /2 = mgh

0.014 = ( 0.077 + 0.012) x 9.81 x h

h = 0.016 m   = 1.6 cm

and h = L - Lcos@

1.6 = 40 ( 1 - cos@)

@ = 16.26 deg

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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