Physics help/?

Question

the weight of the block on the table is 476 N and that of the hanging block is 180 N. Ignore all frictional effects, and assume the pulley to be massless.
Find the acceleration of the two blocks. ?
Find the tension in the cord ?

Answer 1

This is most easily solved by looking at FBDs of each block and using F=m*a, where F is the net on each.

for the hanging block, the forces are 180-T in the direction of motion, where T is the tension

For the sliding block, the forces are T in the direction of motion.

because they are connected by a cord and the pulley is massless and frictionless, then
T=a*476/g
a=g*T/476
and
180-T=a*180/g
a=g*(180-T)/180

so

g*T/476=g*(180-T)/180
divide out g

T/476=(180-T)/180
solve for T
T*180/476=180-T
180=T*(1+180/476)
T=180*476/(180+476)

compute T and plug it in to solve for a

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