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Chapter 8: Q11P (page 203)

(a) In Problem 5, what is the speed of the flake when it reaches the bottom of the bowl? (b) If we substituted a second flake with twice the mass, what would its speed be? (c) If, instead, we gave the flake an initial downward speed along the bowl, would the answer to (a) increase, decrease, or remain the same?

Short Answer

Expert verified

a)v=2.08ms

b)v=2.08ms

c) Speed of the bowl at the bottom will increase.

Step by step solution

01

 Step 1: Given

Mass of ice flake,

m=2.0脳10鈭�3鈥塳驳

Radius,

(r)=0.22m

02

To understand the concept

The problem deals with the law of conservation of energy. The law of conservation of energy states that, total energy of an isolated system remains constant.

Formula:

Initialtotalenergy=Finaltotalenergy

03

(a) Calculate the speed of the flake when it reaches the bottom of the bowl

According to the law of conservation of energy:

KEi+PEi=KEf+PEf

12mv2+0=0+mgr

Hence,

v=(2gr)

v=2脳0.22脳9.8

v=2.08m/s

04

(b) Calculate the speed if we substituted a second flake with twice the mass

If the mass of flake is doubled, then there would be no change in speed, because the speed of flake doesn鈥檛 depend on the mass.

Hence,

v=2.08鈥�m/s

05

(c) Figure out if the answer to (a) would increase, decrease, or remain the same if the flake is given an initial downward speed along the bowl

According to law of conservation of energy:

KEf=KEi+PEi鈭�PEf

This indicates that if initial speed is greater, the final speed must increase.

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