Question

mi mz 7. (20 points) Consider a block of mass M on a ramp of angle 0. The block is attached by massless strings over massless, frictionless pulleys to two objects, m1 and m2, both of mass m where m< M. Assume there is no friction between the block of mass M and the ramp. Draw free-body diagrams for all three masses, keeping vectors consistent between diagrams. Label any vectors that have equal magnitude What is the acceleration of the system? mi mz

Answer 1

let tension in left string be T1 and tension in right string be T2.

let the system is moving along the direction of falling of m2.

let acceleration of the system be a .

writing force balance equation for m2:

m2*g-T2=m2*a

==>T2+m*a=m*g

==>T2=m*g-m*a…(1)

writing force balance equation for M:

T2+M*g*sin(theta)-T1=M*a

==>T2-T1-M*a=-M*g*sin(theta)…(2)

writing force balance equation for m1:

T1-m1*g=m1*a

==>T1-m*a=m*g

==>T1=m*a+m*g…(3)

substituting equation 1 and equation 3 in equation 2:

m*g-m*a-(m*g+m*a)-M*a=-M*g*sin(theta)

==>-2*m*a-M*a=-M*g*sin(theta)

==>a=M*g*sin(theta)/(M+2*m)

Tension T1 Tension T2 Acceleration Acceleration weight- m1 g-mg weight m2 g-m'g Free body diagram for m1 Free body diagram for m2 en sion T of sin(th eta) Free body diagram for M