Answer to Question #230322 in Mechanics | Relativity for haro

Question

the blocks on the horizontal table

are in contact with one another. The first block is connected to a massless

string that passes over a massless and frictionless pulley and then is fastened to

a hanging object of mass M.

a) Assuming the surface of the table as frictionless

i) determine the acceleration of the system.

ii) find the tension in the string.

iii) find the interaction forces between M1 & M2.

Answer 1

Solution.

$M_1;$

$M_2;$

i)$M_2a=M_2g-T_2;$

$M_1a=T_1;$

$T_1=T_2;$

$M_2a=M_2g-M_1a;$

$M_2a+M_1a=M_2g;$

$a(M_2+M_1)=M_2g;$

$a=\dfrac{M_2g}{M_1+M_2};$

ii)$T_1=\dfrac{M_1M_2g}{M_1+M_2};$

iii)$F_1=M_1a=\dfrac{M_1M_2g}{M_1+M_2};$

$F_2=M_2(g-a)=M_2(g-\dfrac{M_2g}{M_1+M_2})=\dfrac{M_1M_2g}{M_1+M_2};$

Answer: i)$T_1=\dfrac{M_1M_2g}{M_1+M_2};$

ii)$T_1=\dfrac{M_1M_2g}{M_1+M_2};$

iii)$F_1=\dfrac{M_1M_2g}{M_1+M_2};$

$F_2=\dfrac{M_1M_2g}{M_1+M_2}.$