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## Homework Statement

Two particles A and B of masses m and 2m are attached to the ends of light inextensible string which passes over smooth fixed pulley. The particles are released from rest and when particle B has moved h meters, it hits the ground and does not rebound.

(i) Find the speed of the particles just before B hits the ground

(ii) Find the direction and magnitude of the impulse that the particle B exerting on the ground

(iii) In the subsequent motion, B will rest on the ground until it is jerked into motion again. Find the period of time when B is resting on the ground before it is first jerked into motion

(iv) Find the speed when B first leaves the ground

(v) After jerked into motion, B rises up and then drops to hit the ground again. Find the distance B travels between the first hit and the second hit on the ground

(vi) The motion continues with B hitting the ground and jerked into motion indefinitely. Find the total distance traveled by B from the instance that the particles are released from rest.

## Homework Equations

v

^{2}= u

^{2}+ 2ad

v = u + at

d = u.t + 1/2 at

^{2}

ΣF = m.a

## The Attempt at a Solution

(i) acceleration of system = g/3

v

^{2}= u

^{2}+ 2ad

[itex]= \sqrt {\frac{2gh}{3}} [/itex]

(ii) Impulse on B = m . Δv = [itex] m . (0 - \sqrt {\frac{2gh}{3}}) [/itex]

[itex] = m . \sqrt {\frac{2gh}{3}}[/itex]

So the impulse on ground is downwards

(iii) Period of time when B is resting = twice the period of time for A to travel (after B hits the ground) to max. height, so:

[itex]v = u - gt[/itex]

[itex] 0 = \sqrt {\frac{2gh}{3}} - gt [/itex]

[itex] t = \sqrt {\frac{2h}{3g}} [/itex]

(iv) Speed when B leaves the ground = speed when B almost hits the ground [itex]= \sqrt {\frac{2gh}{3}} [/itex]

(v) distance of B = twice the distance when it accelerates upwards + decelerate to stop (when A hits the ground)

Distance when B decelerates to stop:

v

^{2}= u

^{2}- 2gd

0 = 2gh/3 - 2gd

d = h/3

So total distance = 4h + 2(h/3) = 14h/3

Are answer from (i) to (v) correct?

For (vi), the answer is infinite?

Thanks