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Giancoli 6th Edition, Chapter 6, Problem 19

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Transcript for this Giancoli solution

The change in kinetic energy of this arrow is gonna be equal to the work done on it. And the work done on it is the net force times the distance over which the force is acting. The change in kinetic energy is ½ 'mv' final squared minus ½ 'mv' initial squared. But the arrow starts from rest so this term is 0. So we can say then ½ 'mv' final squared equals the net force times distance and 'vf' is what we're trying to solve for. So we'll multiply by two and divide by 'm' canceling those times this by two and divide by 'm' as well. And also square root both sides and we'll end up with the final speed is the square root of 2 times the net force times distance over 'm.' And substituting in numbers we get square root of 2 times 110 newtons times 0.78 meters divided by the mass of 0.088 kilograms always need mks units there so convert those grams to kilograms. And this gives ANSWER meters per second.

For the fifth edition you actually get the same answer 44 meters per second as well but you get it a different way and you say that the force exerted on the arrow was 95 newtons and is exerted over a distance of 0.8 meters and the mass is instead 0.08 kilograms or 80 grams. And the answer still is ANSWER meters per second for the fifth edition. In either case this is ANSWER kilometers per hour which is a nicer unit to visualize that's pretty fast.

Comments

How does kinetic energy equal the force net? What is the relationship between the two?

Hi there, and thanks for the good question. Here's the relationship:

The change in the Kinetic Energy is equal to the Net Force times the Distance.

It's important to notice how this differs from your comment. Kinetic energy does not equal the force net. Kinetic energy doesn't even equal force net times distance. But rather,

The Change in the Kinetic Energy is equal to the Net Force times the Distance.

Hope this helps,
Shaun