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$\bullet$ A 20.0 -kg lead sphere is hanging from …

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Problem 74 Hard Difficulty

Forensic science. Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bullet and swings upward. (See Figure 8.49.) The meas ured maximum angle of swing can be used to calculate the speed of the bullet. In one such test, a rifle fired a 4.20 g bullet into a 2.50 kg block hanging by a thin wire 75.0 $\mathrm{cm}$ long. causing the block to swing upward to a maximum angle of $34.7^{\circ}$ from the vertical. What was the original speed of this bullet?

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in this problem. We have a wooden block off math, 2.5 kilograms hanging from a wire offline, 75 centimeters. It a shot with a bullet off Mass 4.2 grams, which is 0.42 kilograms. Let's say it was morning with philosophy. The bullet gets embedded into this wooden block on. Then the whole system turns to reach an angle off 34.7 degrees. Now we want to find out the velocity off the bullet using this information. No, we simply use consideration off energy in this case. So we know that the total mass of the system wants abilities. Embryo into the pulling block is 2.5 kilograms. Place for 4.2 grams, which is 0100 for two kilograms, which is 2.50 for do we can approximate deserves to 15 So basically the mass off the bullet is negligible. In this case, now that we know this, we know that if David and blocking the velocity u this energy, it's guided. Energy is converted into a gravitational singularity when it goes up here when it is all here. So we need to find out the increase in its height now because the total length off the wire is l on. Let's say it changed by an angle, Tita. Now we know the dis distance is El Kostya, as usual on DH. Hence, this distance must be this total distance which is l minus this distance. It is l Kostya. So that's L minus. L Kostya. Now we can apply conservation of energy. We know MG hedge is half and B square, which means we is equal to squared off to the hedge. A familiar formula now in this case, our velocity issue which is equal to square it off tool. Thanks G is 9.8 as usual on hedge is this l minus L. Kostya, which can create in us l in tow one minus Kostya and we know that our l is 75 centimetres, so that 0.75 meters times one minus costs theta one minus costs 34.7. Which means by playing this inter calculator, you can see that this is 1.61 meter per second. Now that we know this, we consider the collision between they pull it on the wouldn't lock. Initially, the bullet had massed philosophy. The wooden block had zero velocity on after the collision, the whole system had velocity. U We know that initial point is equal to the final mourned him. I mean, that initial wanted was simply more. Don't pull it. Which is? It's mass 4.2 grands multiplied by its velocity. Now this must be equal to the final moment. Come off the whole total system. It is a mass. The combined mass off the public place T wouldn't lock just 2.5 kilograms. That's 4.2 into 10 for ministry the weight of the world fans. They were lost to you, which we just found out to be 1.61 meter per second. So we simply piss or sent. It's all here we is 2.5. That's 4.2 into tend Bar ministry can actually ignore this time because this is much smaller than 2.5. I said, Well, if you just put into calculator, it looks fine and this turns out to be 960 interprets it

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Problem

$\bullet$ A 20.0 -kg lead sphere is hanging from …

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Watch More Solved Questions in Chapter 8

Video Transcript

Hugh D. Young

College Physics

Christina Krawiec

Zachary Mitchell

Aspen Fenzl

Meghan Miholics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

College Physics

Christina Krawiec

Zachary Mitchell

Aspen Fenzl

Meghan Miholics

Hugh D. YoungCollege Physics

Christina Krawiec

Zachary Mitchell

Aspen Fenzl

Meghan Miholics

Hugh D. Young

College Physics