Hi, I would like to have some help the following problem: If a 32 g arrow moving at 160km/h penetrates a block of wood suspended by a rope, what is the impulse is delivered to the block? The impulse= momentum(final)-momentum(initial). We know that momentum(initial)= 0.32 kg* 44.44m/s=14,28 N. But what is the momentum(final)?? I do not understand this concept well even after read the texbook. Can someone explain me what is going on ? Thank you B
The momentum of the system (arrow + block) after the impact should be the same as the initial arrow momentum. Calculate the speed of the system after the impact, just ignore the angular speed due to the rope and go for the linear velocity. Then calculate the momentum of the arrow _only_ after the impact. This is the final momentum to take away from the initial momentum to calculate the impulse. It goes like this, the arrow hit the block and transferred a finite amount of force through the impact (impulse). This force magnitude is equal to the delta of the arrow momentum after and before the impact. Or the impulse is equal to the momentum of the block after the impact, since the impulse force is converted to the momentum of the block.