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$\bullet$ A 5.00 g bullet traveling horizontally at 450 $\mathrm{m} / \mathrm{s}$ is shot through a 1.00 kg wood block suspended on a string 2.00 $\mathrm{m}$ long. If the center of mass of the block rises a distance of 0.450 $\mathrm{cm},$ find the speed of the bullet as it emerges from the block.

391 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

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Lectures

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in this problem, we have a wooden glove off Mass. One kilogram, a bullet off masks, five grams Also its velocity. 450 meters per second. Yeah, pierces through the bullet through the wooden block on. Let's say after that go Most of the velocity still has the mass pike. Look, Lybrand's on this one kilogram block gains some velocity you during this collision and then it proceeds to swing on DH raise its height by 0.45 centimeters. Now we want to find out the velocity of the bullet. For that, we need to first find him. Velocity off the good luck now for that we use conservation of energy. If the wooden block has velocity, you on course on goes up by height Hedge. We know that the kind of unity initially is converted into the potential gravitational potential Energy. Finally, which gives us you equal to route to jihad. A familiar equation for how, what the velocity needed for an object to reach a height hedge. We started out to be squared off two times 9.8 times height age, which is 0145 centimeters 145 times standby minus two. This turns out to be 0.297 meters per second. Now that we know this, we can simply apply conservation movement because there are no other horizontal forces. In this case, the final moment is equal to initial momentum in the horizontal direction. Now the initial Wyndham is simply due to the bullet. It's mask five into 10 Power Ministry times 4 50 which is if you multiply Temper, my stated for 50 we get five times 0145 Now the finals momentum is from both the block on the bullet for the bullet in distance five dimes, 10 pound ministering to be. That's for the block. It is its mass one kilogram multiplied by its velocity 0.297 Because these two are equal, we get the equation. By then, 0.45 is equal to five times 10 part ministry times we less syrup on 297 Excuse us. We use it Will do five times 0.45 minus 0.97 divided by five times to environment Astri. This turns out to be 390 one meter per second. This is the velocity with which, and the bullet exits they would unlock. Don't that this is a valid approximation because the bullet velocity is much higher than the proof velocity of people and block, which means by the time the bullet leaves, they will and block the block wouldn't have more by a large distance.

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