Question

For the arrangement shown in the figure blocks a and b are plzced on the smooth horozontal surface. The free end p of the thread is being pulled by a constant force 1 N . Find the acceleration of free end p.

Answer 1

Answer:

Given,In an arrangement shown in the fig.Finding the tension in the rope and acceleration of the masses m1 and m2 and pulley. m1

Answer 2

a1 = F / (m1 + 3m2/4) and a2 = 3F / (4m1 + 3m2)

Explanation:

From top to bottom, let us assume that the lengths of the strings are l1​, l2​, l3, and l4​.

So total length = l1​ + l2 ​+ l3 ​+ l4. Let it be L.

After the pull, the move will be such that:

l1​-y, l2-y+x, l3​-y+x, and l4​-y+x

Now, the total length will be l1​-y + l2-y+x + l3​-y+x + l4​-y+x.

Since the total length does not change:

We have l1​-y + l2-y+x + l3​-y+x + l4​-y+x = l1​ + l2 ​+ l3 ​+ l4.

Solving, we get: y = 3x/4

Now, let a1 and a2 be the acceleration. Then a1 = d²x/dt² and a2 = d²y/dt²

Hence we get a1/a2 = 3/4

acceleration = F/ m1 + m2

So a1 = F / (m1 + 3m2/4) and a2 = 3F / (4m1 + 3m2)