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Chapter 9: Problem 24

High-speed photos of a 220 - \(\mu \mathrm{g}\) flea jumping vertically show that the jump lasts \(1.2 \mathrm{ms}\) and involves an average vertical acceleration of \(100 g .\) What (a) average force and (b) impulse does the ground exert on the flea during its jump? (c) What's the change in the flea's momentum during its jump?

Short Answer

Expert verified
The average force exerted by the ground on the flea is \(0.2156 N\), the impulse is \(0.00025872 Ns\), and the change in the flea's momentum during its jump is also \(0.00025872 Ns\).

Step by step solution

01

Conversion of Mass

First convert the mass of the flea from micrograms (\( \mu g \)) to kilograms (\( kg \)) as \( kg \) is the SI unit for mass. Using the conversion factor \(1 kg = 10^{9} \mu g\), the mass (\( m \)) of the flea in kilograms is \(220 \times 10^{-9} kg\).
02

Calculation of Force

The force \( F \) the ground exerts on the flea can be found using Newton's second law of motion \( F = m \cdot a \). Here \( a = 100g = 100 \times 9.8 ms^{-2} = 980 ms^{-2}\). The force exerted on the flea thus is \(m \cdot a = 220 \times 10^{-9} kg \times 980 ms^{-2} = 0.2156 N\).
03

Calculation of Impulse and Momentum

Impulse is the change in momentum and can also be calculated by the formula Impulse = Force \cdot time. The time given is \(1.2 ms = 1.2 \times 10^{-3} s\). Therefore, Impulse = \(0.2156 N \times 1.2 \times 10^{-3} s = 0.00025872 Ns\). This is also the change in the momentum of the flea as impulse is the change in momentum.

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Most popular questions from this chapter

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