Jack D. Ripper flipped out after missing a Must-Do-It question for the third time on his Minds On Physics assignment. Outraged by the futility of his efforts, he flings a 4.0-gram pencil across the room. The pencil lodges into a 221.0-gram Sponge Bob doll which is at rest on a countertop. Once in motion, the pencil/doll combination slide a distance of 11.9 cm across the countertop before stopping. The coefficient of friction between the doll and the countertop is 0.325. Determine the speed at which the pencil is moving prior to striking Sponge Bob.

Explanation:

Let the velocity after the 4 gram pencil strikes is v .

kinetic energy of the combination = 1/2 m v²

= .5 x ( 4 + 221 ) x 10⁻³ x v² = work done by friction

friction force acting on the combination = 225 x10⁻³x  .325 x 9.8 = .7166 N

work done by friction

= .7166 x .119 = .085 J

.5 x 225 x 10⁻³ v² = .085

v² = .085 / .1125 = .7555

v = .8692 m = 86.92 cm /s

Velocity of combination after collision = 86.92 cm /s

Let velocity of pencil before collision be V

Applying law of conservation of momentum at the time of collision ,

4 x V = 225 x 86.92

V = 4889.25 cm / s

= 48.9 m /s .