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$\bullet$ A 5.00 kg ornament is hanging by a 1.50 $\mathrm{m}$ wire when it issuddenly hit by a 3.00 $\mathrm{kg}$ missile traveling horizontally at12.0 $\mathrm{m} / \mathrm{s} .$ The missile embeds itself in the ornament during the collision. What is the tension in the wire immediately after the collision?

$T=186.4 \mathrm{N}$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

Lectures

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So in this problem they have a five kg ornament. This argument as a matter of five kilograms and it's hanging from a thread off 1.50 meters length. This length is 1.5 centimeters. No, a bullet off mass. Three kilograms incorrectly. Grams is moving with a velocity 12.0 meters per second on embedded into this ornament. So after the collision, this new mask this bullet Lis Arnold has a mass off eight kilograms and little It has a velocity. See now because it has a velocity of on because this lamp is fixed, this most in a circular motion like a kangaroo. And because of the circular motion, there will be a centrifugal force acting on the object. Big magnet, your M V Square by our in addition, really afraid which already is already acting downwards. So this is the total downward force that is acting on this mask on has to be contacted by the stream so that tension in the string will be equal. So this this some off the gravitational force to rest the centrifugal force. So if we find the velocity, then we have the answer now, initially before the collision. The initial moment on P I is just the momentum off the bullet because the argument is not moving and it is mass times velocity, which is three into 12 which is 36 18 meters per second. Now after the moon after the collision, the ornament and the bullet more together with the velocity V hands then Windham finally would be eight kilograms. Multiply way the velocity V. This velocity is the general velocity, whether a let's call you or something So eight times we is to finally went. Um but because there are no other external forces in the horizontal direction, remember that gravity is only downwards, which is what the moment of his guns out and hand. The final moment of also must be 36 kilogram meters per second. From this we get the velocity is 36 by aid is a little 4.5 meters per second. Now that we know this, the tension we know in the spring is mg less and be square by our additional weight less the centrifugal force. We know that the mask is eight kilograms on. The gravitational acceleration is 9.8 meters per second squared unless we know that the master is again. Eight kilograms multiplied by the square would be for 15 squared. Divided by the radius would be the lender off the string, which is 1.5 meters, because when the object moves, it moves about this point as its origin. Because the string is fixed here, this point will become the origin of the circle which this object traces. Hence the radius will be 115 meters. But like this into a calculator, you can see that this is 186 Newtons. I know that because all our numbers are given after three significant digits, we have rounded it down to three significant digits.

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