You are a world famous physicist lawyer defending a client...

You are a world-famous physicist-lawyer defending a client who has been charged with murder. It is alleged that your client, Mr. Lawton, shot the victim, Mr. Cray. The detective who investigated the scene of the crime, Mr. Dibny, found a second bullet, from a shot that missed Mr. Cray, that had embedded itself into a chair. You arise to cross-examine the detective. You: In what type of chair did you find the bullet? Dibny: A wooden chair. You: How massive was this chair? Dibny: It had a mass of 20 kg. You: How did the chair respond to being struck with a bullet? Dibny: It slid across the floor. You: How far? Dibny: Three centimeters. The slide marks on the dusty floor are quite distinct. You: What kind of floor was it? Dibny: A wood floor. You: What was the mass of the bullet you retrieved from the chair? Dibny: Its mass was 10 g. You: Have you tested the gun you found in Mr. Lawton's possession? Dibny: I have. You: What is the muzzle velocity of bullets fired from that gun? Dibny: The muzzle velocity is 450 m/s. With only slight hesitation, you turn confidently to the jury and proclaim, "My client's gun did not fire those shots!" (a) How are you going to convince the jury and judge? (b) Choose one part of your solution and perform a sense-making analysis. Clearly state which sensemaking analysis you’ve chosen and why.

Transcript

00:01 In this case, we will consider the collision between the bullet and the chair.

00:08 As after the collision, the miss bullet gets embedded into the chair, it means it is a case of a perfectly inelastic collision because in this collision, the both the object stick together after the collision.

00:29 Now, we take the total.

00:32 Linear momentum before the collision of a mis -bullet chair system.

00:38 Here system is consists of the bullet and the chair.

00:42 So it's totally linear moment moment before the bullet hits the chair should be equal to the total linear momentum after the bullet hit the chair.

00:54 So let initially it is m1 u1 and plus m2 u2 where m1 is m1 is the mass of the bullet u1 is the velocity of the bullet m2 is the mass of the chair u2 is the velocity of the chair initially that should be equal to after the co -mease collision the miss bullet stick gets embedded into the chair and both of them move with a common velocity so after the collision the total lead amount means means momentum will be m1 plus m2 into now as the chair is at rest, it means before collision, it means u2 is equal to zero.

01:34 Now m1 is the mass of the bullet which is given as 10 gram.

01:40 So we take is 10 upon 1 ,000 and u1 is the speed with which the bullet was moving.

01:47 It is mentioned in the problem as 450 meter per second and plus m2 is the mass of the chair and because u2 is zero and that will be m1 plus m2 into v.

02:00 Now m1 is 10 means 10 gram.

02:02 So 10 upon 1000 m2 is the mass of the chair which is 20 means which is 20 kg multiplied by v.

02:11 So if we solve it, the combined velocity of the bullet chair system after the means bullet hits and gets embedded into the chair is 0 .22 meter per second.

02:24 Now, with this velocity, there is some kinetic energy in the bullet chair system.

02:32 And that kinetic energy drags the bullet and the chair to some system and to some distance and finally they stop.

02:40 So their kinetic energy, just before the collision, just after the collision, when they start to move together, reduces to zero when the chair stops.

02:53 So it means there is a change in kinetic energy.

02:56 Energy between the moment after the collision and when the chair stops after dragging on the floor.

03:05 So that change in kinetic energy of the, means, bullet and the chair system, why the kinetic energy is reduced, why the chair stops because of the force of friction between the chair and the, means wooden floor.

03:24 It means there is some work done.

03:26 By the force of friction on the chair which reduces the kinetic energy of the chair and stop this.

03:33 So due to as the work energy principle, here we use work energy law and as per the work energy law, change in kinetic energy of the, means, bulletin chair system is equal to the work done by the force of friction.

03:50 So here change in kind means kinetic energy will be the final, the means final kinetic energy minus initial kinetic energy.

03:58 So we will just calculate because final kinetic energy is zero and initial kinetic energy will be one half.

04:07 M mass of the because kinetic energy is one of mb square but here m is the mass of the bullet plus mass of the chair.

04:16 So that will be one of m.

04:17 Mass of the bullet is 10 gram and mass of the chair is 20 gram.

04:24 Sorry, it means 20 kggy and their combined velocity.

04:27 Is 0 .22 meter per second square.

04:31 So this is 0 .48 jule.

04:35 So this is the initial kinetic energy they have just after the collision and thus kinetic energy finally drops to zero when the when the means chair stops after dragging a certain distance.

04:51 So change in kinetic energy means means energy is 0 .48 minus 0.

04:57 It means it means it means it is 0 .48 jule.

05:00 So change in kinetic energy 0 .48 is equal to work done by force of friction.

05:09 Work done by friction.

05:12 Right.

05:13 So actually this is negative because the final is zero and initially zero point means 48.

05:20 So this is negative here...