Asled of mass 8 kg slides along the ice. it has an initial speed of 4 m/s but
stops because of friction. how much work is done by friction?
o a. 32j
ooo
o b. -643
c. 64j
d. 32j
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As our story begins, the sled ... whose mass is 8 kg ...  is sliding along the ice at a speed of 4 m/s.

The sled's kinetic energy is (1/2 m v²) = (4 kg · 16 m²/s²) = 64 J .

After what seems like only the blink of an eye, the sled is no longer sliding.  It is stationary.  Motionless.  At Rest.  Just sitting there !  

Its speed has been reduced to zero and ... because kinetic energy is the energy of motion ... the sled's kinetic energy is now also zero.  Sixty-four Joules of energy have disappeared !

How can this be ? ! ? We know that energy is conserved.  It can never just appear out of nothing, and it can never just disappear into nothing.  If energy suddenly appears, it had to come from somewhere, and if energy suddenly disappears, it had to go somewhere.  So where did our 64 Joules of kinetic energy go ?

It went into the ice, THAT's where !  We can say that the sled did 64J of work, and melted a thin slick layer of water on the surface of the ice.  OR we can say that friction did NEGATIVE 64J of work on the sled, to cancel the 64J that it had originally, sap its kinetic energy, and bring it to rest.

I think choice-B was supposed to say "B. -64J", but somebody typed it sloppily and neglected to proofread it before posting.

The limiting angle is 7.32x10⁻⁸rad and the separation distance is 8.586x10⁹ rad m

Explanation:

Given data:

λ = 600 nm = 6x10⁻⁷m

D = 10 m

The limiting angle of resolution is equal to:

According Rayleigh expression:

L = 12.4 light year = 1.173x10¹⁷m