Question

1. (30 points) A 2-kg block A is pushed up against a spring compressing it a distance r-0.1 m (i.e., the spring is unattached to the block). The block is then released from rest and slides down the 20° incline u it strikes a 1-kg sphere B that is suspended from a 1-m inextensible rope. The spring constant 800 N/m, the coefficient of friction between A and the ground i length of the spring d-1.5, and the coefficient of restitution between A and B is 0.8. As shown in fig. 1 s 0.2, the distance A slides from the unstretched 20o Figure 1: Problem 1 (a) (5 points) Determine the velocity of block A right before the impact (b) (15 points) The velocities of both particles right after the impact (c) (5 points) Show that the velocity of B at any angle o is given by 2 2g- cos(a where v, is the initial velocity of B right after collision, and v is the velocity at a general angle a, then use it to find the velocity of B at α 40° (d) (5 points) If the rope suddenly broke at α-40. The bob B will continue as a projectile til it hits a horizontal smooth platform 3-m below the initial position of B (i.e., where the first impact with A occurred). If the collision with the platform was perfectly inelastic (e-0), find the distance S that a 100 N/m spri deflect in order to stop the bob B

Answer 1

page 1

Given that massaf the block(m)ニ2k inclination ofthe plateform(e) (2d) Caufficieut af restitution betueen blodk onel pendulum loob (e)- o g llo.2 20 13 SolutHon @ work done by kll the fores chanje in Kinehc et YICHCh źky?オー.umgcorse (A4d) + w'afine(n+d) = ¼ m留.。 Solving we get Un = 2.97 m/s elocih of ac Up Camscanne

page 2

Yom canseroa ton of momen fum bekween A andB initial mementum - final memen tum multiplying equation ⓘ by D and addina in equal,one Nauo from equahon 0 we get up 1.876 yem (anseruahon of mechaniial ene Ui Scanned with CamScanner ,冫2.35 m/s

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salu on td) when rope sudiny broke 40 conseroalion of mechanical er 3 m E35-7SS3J Ihis KE uaiel to deflict the spning of ke look 2x 35-75S 71 n O. g456 m CS Scanned with CamScanner