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$F_{on glove}=2.9 \times 10^2N$

Giancoli 6th Edition, Chapter 6, Problem 20


Chapter 6, Problem 20 is solved.

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Transcript for this Giancoli solution

We know that the change in kinetic energy of this baseball is equal to the net force times the distance over which the force is acting; the force being provided by the glove. So we're gonna first find the force that the glove exerts on the ball and then say that the force exerted by the ball on the glove is the negative of that due to Newton's third law action reaction pairs. Anyway so we'll say that the kinetic energy is ½ 'mv' final squared minus ½ 'mv' initial squared. The final velocity being zero because the ball comes to a stop. And so we can say then that the net force times distance is negative ½ 'mv' initial squared. We'll solve for the net force by dividing both sides by 'd' and we get that the net force and there is only one force and so the net force is the force exerted by the glove on the ball is negative 'mv' initial squared over '2d'. So we'll substitute in numbers and we’ll get negative 140 grams which is 0.14 kilograms times 32 meters per second we'll square that divided by 2 times 0.25 meters and this gives negative 2.9 times 10 to the 2 newtons. In the fifth edition this number is actually 35 meters per second and you have to square that as well. And so in the fifth edition instead you're gonna get 3.4 times 10 to the 2 newtons here. Now in the end we're gonna say that the force on the glove is equal to the negative of the force on the ball. What we actually just found here was the force on the ball. So the force on the glove is gonna be positive because this force is in the same direction as the initial velocity of the ball so it's positive and it's ANSWER newtons. And again the fifth edition positive this number so force in the glove is positive ANSWER newtons for the fifth edition.