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HI

a caterpillar of mass 6*10^9 grams is used to drag a car of mass 4*10^6 grams.The caterpillar is moving at a speed of 5m/s just before the towing rope suddenly becomes tight. calculate
1,Velocity of the caterpillar immediately after the road becomes tight
2,loss in kinetic energy of the system just before the car started moving
3,The impulsive tension in the rope when it jerk into motion

Pls anwser thnks :smile:

Reply 1

The Shanus

The first one was using the principle of conservation of momentum, or PCM. So m1u1 + m2u2 = m3v3, taking it as if when the string becomes taught, they "collide", and become a single particle. So 4000kg(0) + 6000000kg(5) = (6000000+4000)kg(v). Therefore; (6000000)(5)/(6004000) = v = 4.996668887m/s.

2, Here I just did Ke (before) - Ke (after). Before: (1/2)m1(u1)^2 + (1/2)m2(u2)^2 = 2000(0) + (3000000)(25) = 75000000. After: (1/2)m3v^2= (6004000)(4.996668887^2)/2.
Therefore: Ke (before) - Ke (after) = 75000000 - (6004000)(4.996668887^2)/2 = 49966.70113 J

3, I = m(v-u). I took m to be the mass of the stationary car, as that's the one starting from rest. So
I = 4000(4.996668887) = 19986.678 Ns. (This is right, the one I put before is wrong.)

^ I sent that as part of a private message conversation with the OP, I'm not sure if I am correct, if someone could verify it, that would be great.

(edited 10 years ago)

Reply 2

tariqballe

Original post by The Shanus

The first one was using the principle of conservation of momentum, or PCM. So m1u1 + m2u2 = m3v3, taking it as if when the string becomes taught, they "collide", and become a single particle. So 4000kg(0) + 6000000kg(5) = (6000000+4000)kg(v). Therefore; (6000000)(5)/(6004000) = v = 4.996668887m/s.

2, Here I just did Ke (before) - Ke (after). Before: (1/2)m1(u1)^2 + (1/2)m2(u2)^2 = 2000(0) + (3000000)(25) = 75000000. After: (1/2)m3v^2= (6004000)(4.996668887^2)/2.
Therefore: Ke (before) - Ke (after) = 75000000 - (6004000)(4.996668887^2)/2 = 2, 49966.70113 J

3, I = m(v-u). I took m to be the mass of the stationary car, as that's the one starting from rest. So
I = 4000(4.996668887) = 19986.678 Ns. (This is right, the one I put before is wrong.)

^ I sent that as part of a private message conversation with the OP, I'm not sure if I am correct, if someone could verify it, that would be great.

pls who could verify it? :smile:

Reply 3

The Shanus

My Maths teacher came out with the same answers as me, looks good.