a-construction-worker-strikes-a-nail-with-a-hammer-twice-with-the-same-initial-velocity-leftv_iright

Question

A construction worker strikes a nail with a hammer twice with the same initial velocity $\left(v_{i}\right) .$ The first time, the hammer comes to rest after hitting the nail. The second time, the hammer recoils after hitting the nail and bounces back toward the worker. Assuming the contact time in both strikes is the same, in which strike did the nail exert a greater force on the hammer?
(A) The first strike
(B) The second strike
(C) The nail exerted the same force for both strikes.
(D) Cannot be determined

Vishal Gupta · Accepted Answer

high in the given problem, mm hmm. The hammer is striking over the Neil. Then using Newton&#x27;s 2nd Law of Motion. Force exerted by the hammer over the nail. Or we can say force experienced by the hammer by but by the Neil will be given by the time rate of change of linear momentum which is taking place in the hammer. Or we can say this is final momentum of the hammer minus initial momentum divided by the time duration. Now, guess what? When the hammer comes to rest after hitting the nail, then it&#x27;s final momentum is zero. And suppose before hitting the nail the hammer was moving with the initial speed. We I so its initial momentum P. I. Uh sorry. We can say to beep even if its initial momentum P. One may be given as I am into V. I. So the force experienced by the hammer By then it will be given by zero M. B. I. Buy tea. Or we can say this is minus M. V. I by T. Here. This negative sign is for the opposite direction of force as compared with the las T. V. So if you see only for the magnitude of this force that is M V. I buy t. Now case too in case too the hammer comes back after hitting daniel with the same velocity. So we can say if its initial momentum P. Even was em into V. I. It&#x27;s final momentum peter will become minus M. Times of V. I. Because the final speed becomes -3. That&#x27;s why the final woman to means negative. So now The force experienced by we can say to be F two and initially suppose it was F one. So now this F two will be given as final momentum. P two minus pi even means this is minus envy I -2V. I divided by the same time as there is no change in the time duration, So it becomes -2 MVI By T. So if we compare it with F1, we conclude that this is too wise off a fund. So in second strike the nail exerts great greater force on hammer. In second strike the Neil will exert greater force on hammer. Hence we can see here another option. B is correct. Thank you.

Kristela Garcia · Answer

in this problem. We&#x27;re trying to determine which of these two situations inserts a greater force on the nail. So if you look at the first situation, you have a hammer coming down. We can call this an initial velocity of the O or V one as it&#x27;s given the problem and the second situation, it comes back with the same velocity. So you have a V one coming down and then everyone coming back up, and then this the fact that it&#x27;s in the opposite direction is going to be really important. So this is an impulse problem, and we know that impulse is forest times are changing time, which is equal to my change in momentum. And in this case, my mom stays the same. So it&#x27;s really just a change in velocity. So we have our force. Is our mass times change in velocity over time. Now, in this first situation, I&#x27;m just gonna go ahead and copy my equation down. In this first situation, you have a final velocity of zero. And so our force is going to be proportional to our mass. Times are in the shit velocity divided by time, and it is telling us that our time intervals are the same for both. But if you look into a second situation, we have a certain velocity going down and we have the exact same velocity coming back up. But it&#x27;s actually in the opposite direction, so we&#x27;re gonna call that negative. So if we put that information in, we get a negative V one minus. The one gives us a negative to be one. So that gives us n times negative to view one, which tells us that everything being the same, the masses being the same, the time intervals being the same, that our second situation is going to yield a force that is two times greater than the first.

Farnaz Mohseni · Answer

So in this question, frequency is given by the number of hammering per second. Have you not at every 4.6 seconds and we have something that resembles a peach frequency. So it means that if off beat frequency here is 1/4 0.6 seconds and then we have the first carpenter striking a blow every 0.75 seconds. So if one is 1/0 10.75 seconds, and then we want to find out how much time elapses between the second carpenters blows. So it means you want to find T too. And t two is a von over if too. So we need to find, too to find f two. I&#x27;m going thio use if beat if we can be if von minus of two if if one is larger than ever to or it can be if two minus of one if if two is larger than of one. So in part a, uh, they&#x27;re going to assume that if two is larger than that one, because the second corporate carpenter is hammering more rapidly than the 1st 1 so here can say f two minus F one that is a one older 0.75 is equal VON over 4.6. So if two is equal 1/4 20.6 plus 1/0 0.75 on DDE, this is equal to one point 55. So C two is 1/1 0.55 and this is equal to 0.6 feet four seconds and then in hard be, we&#x27;re going to assume that one is larger than have to. So here we have if, um one which is run over your 10.75 minus F to equal 1/4 0.6. So if it is a Ron over 0.75 minus 1/4 0.6 and this is a cult of 1.11 and then T two is one over to, which is a call to 0.9 seconds.

Keshav Singh · Answer

for this problem on the topic of energy, we&#x27;re told that a moving hammer, it&#x27;s a male and hence drives it into a war. We want to know what happens to the depth that then it will be driven if the hammer hits the nail with twice its initial speed and then with three times its initial speed. So we let the original speed off the Hama BV one, and then we will double that and then triple it. So V two is twice V one and V three is three times we won. Now let&#x27;s assume the hammer is moving with velocity V one, so it has kinetic energy. Ah, half and view one square. Now we&#x27;ll assume that the hammer comes to rest after striking the nail. Hence, all of the kinetic energy from the hammer will be transferred to the mail. In the process, work is done to the nail in, driving it into the wall so some force F is exerted onto the nail and it&#x27;s driven a distance d into the wall. So they work then is f times D. In this case, that will be D one. Now we know the force when you can. Second law is the mass times, the initial acceleration off the nail and that&#x27;s multiplied by the one. So we&#x27;ll assume the initial acceleration off the nail is the same in all three cases, but only the depth at which the natives driven to the wall changes. So if we rearrange the equation, we find the initial depth off the nail into the wall D one is equal to I am V one squared over to times F. Come on now, let&#x27;s increase the initial speed off the hammer to twice its original speed. So in this scenario, we have ah, half m. The two squared is equal to give times d to, But we know V two is twice 31 so we can write this as a half. Mm. And that&#x27;s too. We won. All squared is equal to f times D to and we can hands right this so we can bring the two squared to the front and that becomes four into a half I am V one squared. He is equal to F times D to which implies that the distance that in a will be driven to the wall in this case D to is equal to for into am the one squared over two F and so we can see that death that this is for Times D one. So that means if we double the speed off the hammer, the distance that the mayor will be driven into the wall increases by a factor off four. So D two is equal to four times the one. Now. What happens if we increase the original speed off the hammer to three times its original speak? So a half M Bt Squared is equal to F D three and we want to calculate the three. We know that the tree is three times we won. So that&#x27;s three V one. All squared is equal to F B any so this becomes nine into a half AM The one squared is equal to F Times D three, which implies that the distance that email is now driven into war, Bt is equal to I am times. We won all square over two times the force f and all of this multiplied by nine, which we can see is nine times the original distance, the one So if we triple the initial speed off the hammer, the mayor will be driven in nine times further than it originally went

Kai Chen · Answer

So is this question would happen now until we have a hammer so have restricted now is in It goes to rest in a certain time Inter broke and we won&#x27;t you know a What is the imposter Mint is and now and be what is average force acting on the nail? So let&#x27;s first to eh What is in course, So we know in court is a change of momentum. So we&#x27;re fertile topi Cuban twos And now so is it was given to the no is is opposite of the impulse That was, um that was bored to his hammer because you can certainly tell us that. So impulse committed the nail into impulsively or gives to use a hammer it would be quite opposite. So because you hear all the numbers we get also velocities we have It&#x27;s regarding the hammer in darts and nail. So we have to be very careful. Sod impulse committees now is the opposite of that. So the hammer, it&#x27;s the same m o as in it has still to be sawed em, Toby. Afterwards, it was zero, kiddo. Um, yeah, that&#x27;s just plain is a number. It is tough to the rim and before afterwards, Delta V equals fi fine on that. It&#x27;s being initial after words. It wass 20 and before it has a velocity of 7.5 meters per second. So that keeps us 12 times in 25. It&#x27;s like e kilogram meters per second. Um, yeah, so it Zen active sign here cancels the negative sign here. This is actually a positive number, and we do expect set. It will be constant because the nail initial has no impulse and then it was hit and killing our velocity. So we do expect this number to be positive and great, so this matches up with what we expect. So what is the average force acting on the nail? It&#x27;s a force again. We have Newton&#x27;s second law or equation, simply to such as us. So force is which is a wonderful mentioned over a time of contact. So we already have such a mental here. It&#x27;s 90 kilograms, Readers Percentage and Deputy is soon 0.8 2nd so it gives us, um, 11,000 YouTube so that his average force, acting anew

Farhanul Hasan · Answer

impulse is just a radio. So Delta P is what we&#x27;re after. And so does a piece of Ah, the nail will be, um, just the negative of the delta p of the hammer. That&#x27;s Ah, uh, that&#x27;s the momentum the hammer will impart on the nail. And so this will be negative. Um, m times very final AA minus. Ah, Negative. Okay, negative. M times v initial minus very final. And so that&#x27;s just the rate of change. Of that&#x27;s just a change in velocity. So would be negative. 12 kilograms times zip. Um, looks it would be the final Manus fi initial is what I meant. Uh, and so it would be on give 12 times. Ah, zero minus 8.5 meters per second. Uh, and so that gives us an impulse off 100 que je meters per second. This is part a part B F. Average force is just the impulse over the time intervals. This is 100 kilograms meters per second over eight times 10 to the negative, three seconds, eight milliseconds. And that gives us 1.3 times 10 to the four mutants

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