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

Given data:

Mass of the banana, m = 0.50 kg

Initial speed of the banana, $v_{i} = 4 m / s$

Maximum height reached by the banana, $h = h_{f} - h_{i} = 0.8 m$

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:

$W = ∆ E_{m e c h} + ∆ E_{t h}$

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,

$W = ∆ E_{m e c h} + ∆ E_{t h}$

In this case, W = 0 Then,

$0 = ∆ E_{m e c h} + ∆ E_{t h} 0 = ∆ K E + ∆ P E + ∆ E_{t h} 0 = \frac{1}{2} m v_{f}^{2} - \frac{1}{2} m v_{i}^{2} + m g (h_{f} - h_{i}) + ∆ E_{t h} 0 = 0 - \frac{1}{2} (0.50) {(4)}^{2} + (0.50) (9.8) (0.8) + ∆ E_{t h} ∆ E_{t h} = 0.08 J$