A clasic mechanics problom with a moving table

[anachin6000]

Homework Statement

"On a horizontal table without friction it's a cube of mass M=70 kg and on the cube it's a body of mass m1=1kg. The body m1 it's conected by a cord with an other body of mass m2=4 kg, situated at hight H=1,5 m above the table. The sistem starts from 0 velocity. What it's the displacement of the cube M by the time when the body m2 touches the table(fig. 1.5.13)?(there is no friction)"

I attached the figure.

Homework Equations

T=m1*a1
T=M*a
G2-T=m2*a2 (G is weight)
a1=a2

The Attempt at a Solution

M*a=m1*a1

h=(a1*t^2)/2
d=(a*t^2)/2
h/d=a1/a=M/m1

d=h*m1/M
But at solutions in the book says d=h*m1/(m1+m2+M).

So, can someone explain me my mistake? And also I'll be very happy if someone can give me a tip for solving the problem using the momentum.

 

[jbriggs444]

Homework Statement

"On a horizontal table without friction it's a cube of mass M=70 kg and on the cube it's a body of mass m1=1kg. The body m1 it's conected by a cord with an other body of mass m2=4 kg, situated at hight H=1,5 m above the table. The sistem starts from 0 velocity. What it's the displacement of the cube M by the time when the body m2 touches the table(fig. 1.5.13)?(there is no friction)"

I attached the figure.

Homework Equations

T=m1*a1
T=M*a
G2-T=m2*a2 (G is weight)
a1=a2

The Attempt at a Solution

M*a=m1*a1

h=(a1*t^2)/2
d=(a*t^2)/2
h/d=a1/a=M/m1

d=h*m1/M
But at solutions in the book says d=h*m1/(m1+m2+M).

So, can someone explain me my mistake? And also I'll be very happy if someone can give me a tip for solving the problem using the momentum.

I would first note that one is apparently supposed to assume that the 4 kg mass (m₂) slides down the side of cube M on massless, frictionless rails and does not sway to the side like a pendulum as cube M is pushed to one side by the force of the pulley.

What is the velocity (in the horizontal direction) of the center of mass of all three masses taken together prior to the start of the problem? What is this velocity after the end? Does this velocity change during the problem?

What does this say about the position of the center of mass during the problem?

 

[anachin6000]

Thank you!

 

[dauto]

Two mistakes.

T=M*a isn't right because the string sways

a1=a2 isn't right either because the pulley is not fixed.