Answer to Question #92188 in Mechanics | Relativity for Krishna

Question

In a system, a pulley is attached to a block of mass 5M. Also, the pulley contains a chord on both sides, attached with a block of mass M on one side and with a pulley further attached to a mass 2M on the other side. There is no friction anywhere. Find the initial acceleration of block of mass 5M

Answer 1

Let’s consider a block of mass 5M. It’s equation of movement will be next:

$$5Ma ⃗=5Mg ⃗-T_1 ⃗-T_2 ⃗,$$

where T1 and T2 are tension forces of the chord on the left and right of the pulley respectively. 

$T_1=Mg$ , as the chord is directly attached to the block of M mass.

$T_2 ⃗=1/2 * 2Mg ⃗=Mg ⃗$ , as the chord goes through the pulley with block of 2M mass. By the golden rule of mechanics, in this case the effort done by this block is divided by two.

Now, let’s rewrite the equation of movement for the block of 5M mass:

$$5Ma ⃗=5Mg ⃗-Mg ⃗-Mg ⃗,$$ $$5Ma ⃗=3Mg ⃗,$$ $$5a ⃗=3g ⃗,$$ $$a ⃗=3/5*10=6m/s^2.$$

Answer:  a ⃗=6 m/s^2.