10. Huy is angry for getting a 99 out of 100 on the final, and takes it out on a

Question

10. Huy is angry for getting a 99 out of 100 on the final, and takes it out on a 5 kg piece of Styrofoam sitting on a table. She throws her physics book (which has a mass 3 kg) at a speed of 10 m/s at the Styrofoam, which becomes lodged inside. The Styrofoam with the book inside slides 2 m to the end of the table and then fly off, hitting the floor 1.5 m below. If the coefficient of friction between the Styrofoam and the table is 0.2, how far from the base of the table does the Styrofoam with the book inside land?

Explanation / Answer

Start with conservation of mementum

mv = (m + M)v

3(10) = (3 + 5)(v)

v = 3.75 m/s

Then friction reduced some of that velocity before it leaves the table

The work by friction is equal to the change in KE

(umgd) = .5mv2 - .5mv2

(.2)(8)(9.8)(2) = (.5)(8)(3.75)2 - (.5)(8)(v)2

v = 2.49 m/s

Then we need to find how long it take to fall the 1.5 m

d = vot + .5at2 for the fall

(1.5) = 0 + (.5)(9.8)(t)2

t = .553 sec

Finally, the distance is from d = vt

d = (2.49)(.553) = 1.38 m

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