Two boxes ( \\texttip{m1}{m1} = 51.0 {\ m kg} and \\texttip{m2}{m2} = 33.5 {\ m

Question

Two boxes ( exttip{m1}{m1} = 51.0{ m kg} and exttip{m2}{m2} = 33.5{ m kg} ) are connected by a light string that passes over a light, frictionless pulley. One box rests on a frictionless ramp that rises at 30.0^circ above the horizontal (see the figure below), and the system is released from rest.(Figure 1)

Part A.

Which way will the 51.0{ m kg} box move, up the plane or down the plane? Or will it even move at all?

Part B. Find the acceleration of each box

Two boxes ( exttip{m1}{m1} = 51.0{ m kg} and exttip{m2}{m2} = 33.5{ m kg} ) are connected by a light string that passes over a light, frictionless pulley. One box rests on a frictionless ramp that rises at 30.0^circ above the horizontal (see the figure below), and the system is released from rest.(Figure 1) Which way will the 51.0{ m kg} box move, up the plane or down the plane? Or will it even move at all? Find the acceleration of each box

Explanation / Answer

let the acceleration of the first block m1

be a hence the acceleration of second block also will be a

due to both connected by same string. hence from the figure

:: T-m1gsin30=m1a...(1)

T is tension

T-m2g=m2a....(ii) from (I) and(ii)

(m2-m1/2)g=(m1+m2)a

a=(m2-m1/2)g/(m1+m2)..

= (33.5-51/2)*9.8/(33.5+51)

=0.92781065088m/s^2

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