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Chapter 8: Q97P (page 211)

A 0.50 kgbanana is thrown directly upward with an initial speed of4.00 m/sand reaches a maximum height of 0.80 m. What change does air drag cause in the mechanical energy of the banana-Earth system during the ascent?

Short Answer

Expert verified

The change is caused by the air drag in the mechanical energy of the banana-Earth system during the ascent.is equal to 0.08 J.

Step by step solution

01

Given data:

Mass of the banana, m = 0.50 kg

Initial speed of the banana,vi=4m/s

Maximum height reached by the banana, h=hf-hi=0.8m

02

To understand the concept:

Using the formula for workdone on a system by external force, find thechange caused by the air drag in the mechanical energy of the banana-Earth system during the ascent.

Formula:

W=∆Emech+∆Eth

03

Calculate what change the air drag causes in the mechanical energy of the banana-Earth system during the ascent:

Work done on a banana-Earth system by external force is given by,

W=∆Emech+∆Eth

In this case, W = 0 Then,

0=∆Emech+∆Eth0=∆KE+∆PE+∆Eth0=12mvf2-12mvi2+mg(hf-hi)+∆Eth0=0-12(0.50)(4)2+(0.50)(9.8)(0.8)+∆Eth∆Eth=0.08J

Since

∆Emech+∆Eth=0∆Emech=-∆Eth∆Emech=∆Eth

Therefore,

∆Emech=0.08J

Hence, the change caused by the air drag in the mechanical energy of the banana-Earth system during the ascent is equal to 0.08 J.

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