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A 22 -g bullet strikes and becomes embedded in a 1.35 -kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is $0.28,$ and the impact drives the block a distance of 8.5 $\mathrm{m}$ before it comes to rest, what was the muzzle speed of the bullet?

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$4.3 \times 10^{2} \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

Simon Fraser University

University of Sheffield

McMaster University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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A 22 -g bullet strikes and…

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A 28 g bullet strikes and …

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'A 25-g bullet strike…

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A 5.00-g bullet is fired h…

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A $12.0-\mathrm{g}$ bullet…

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A 5.00gbullet is fired hor…

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A 5.18-g bullet moving at …

the first thing to do would be to invert momentum conservation. Initially, M V is equal to finally AM plus m be prime. Uh, the prime is what we want Ah V is what we want, but we don't know you prime So let's call this equation one and try to find the what Every prime and the way to do that is by invoking energy conservation or work energy theorem. So the work done from fiction is equal to the change in Connecticut energy, which is just 1/2 uh, M times, um, zero squared minus initial velocity squirts That's be prime squared. So this is negative 1/2 M V prime square. Ah, and that's be equal to minus minutes. Okay, times mg times Delta X Angie being the normal forest meets of Kabinda confession of kinetic friction and Delta X being the distance traveled. So that's, uh, negative signs. Cancel and you get that V prime is equal to the square root of two. And the abs cancel to you by the square. The private squared of two G. Delta Axum. It's okay. Ah, and so therefore, in one you have M V is equal to m plus big M Times Square root of two G Delta X mu subject. Okay and so V is just m plus m over small um Times square of two g Delta X turns music camp. All right, uh, therefore V is equal to small and which is 22 grams are 220.22 kilograms plus one Big M 1.35 kilograms over a 0.22 our 0.22 kilograms times to G. Two times 9.8 meters per second. Squared, UH, Times Delta X, which is pointed, are, which is 8.5 meters and times point to a, which is a confirmation of kinetic friction. Servi turns out to be 430 meters for a second.

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