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$\bullet$ A ball with a mass of 0.600 $\mathrm{kg}$ is initially at rest. It is struck by a second ball having a mass of 0.400 $\mathrm{kg}$ , initially moving with a velocity of 0.250 $\mathrm{m} / \mathrm{s}$ toward the right along the $x$ axis. After the collision, the 0.400 $\mathrm{kg}$ ball has a velocity of 0.200 $\mathrm{m} / \mathrm{s}$ at an angle of $36.9^{\circ}$ above the $x$ axis in the firstquadrant. Both balls move on a frictionless, horizontal surface. (a) What are the magnitude and direction of the velocity of the 0.600 kg ball after the collision? (b) What is the change in the total kinetic energy of the two balls as a result of the collision?

a) $53.1^{\circ}$b) $-0.0015 \mathrm{J}$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

University of Washington

Hope College

University of Winnipeg

McMaster University

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so initially as the 1400 kilogram object is moving with the velocity off Sierra 14000.250 meters and it hits a stationary object off massive 1600 kilograms. Nor that all numbers have three significant digits. From here on, I just right on one significant. I'll write it down without any significant digits, but they all have three significant digits after the collision because you don't want four kilogram mask is moving at an angle of 36.9 degrees with a velocity 012 meters per second. Let's say the other object does it want six kilogram is moving toninety kita below the X axis with our lost three. Now we want to find out the magnitude of this velocity and the angle it makes with the X axis for fighting. Now we simply used conservation of momentum in both directions. Let's say our hearts under large insects on vertical direction is white, so let's go with first white direction. Initially, the object was moving horizontally and this object was not moving, which means initial moment. And why was Cyril? But finally, let's call this object Alice, call its object object has Wyman Wyndham, Mass. Which is 014 As velocity it is you want to. I'm scientist. Just sign 36.9 degrees. And for object B, the wife wanted would be mass 016 kilogram. I'm the last to leave time scientist, but not that white component is in downward direction and hands. We have a minus sign. Using this equation, we can see recent data, which is the white 0.40 point two signed, 36.9 divided by 0.6, which turns out to be refined. Is it a Wade meter per second? Nor that I left the minus sign here because this is negative now for we ex. We simply use themoment on conservation in extraction. Initially, the moment of the next direction was just going on Object. Just mask 0.4 and velocity they want to fight. It is equal to the final moment, which is the excellent off object. There would be mass times Velocity and Scott's Tita less They want time off. Optic B would be mass Little 16 and velocity times past Tita. Now we can write. Write this instead, as we X Now from this figure, we X do we 0.25 and syrup on for minus 014 and 0.2 cost 36.9 divided by 016 which transported the 0.6%. Hence the magnitude ofthe loss TV the square root ofthe big X squared plus y squared just 0.1, Mr President. And the angle Tita is simply down in words. Off the vibe I re X It's chance out to be 53 on 13 degrees in the fourth quarter and, oh, between cities clockwise 53.13 degrees from X axis. Now for Barbie, we want to find out the initial and find finally kind of energies. The initial kinda country was simply the kind of candy off object it, which is half mask 014 and velocity squared, which is the 014 1 to 5 squared. Which is it you want? They don't want five jewels and for the final indignity is simply adding final kind of anti off Auntie's off object and after B, which are I'm smart times. Velocity squared this half and a mask and velocity is weird. I'm sorry. In the last part. Yeah, that's it. This dance or do we want? You don't want one, Jules. As you can see, there is a drop in energy changing kinda country. Initial mine is final. Would be 0.1 feel 015 Jules, this is the amount of energy last during the collision, and this usually turns into heat or something like that.

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