Question

In outer space, far from other objects, block 1 of mass 55 kg is at position <10,5,0> m, and block 2 of mass 900 kg is at position <22,5,0 > m.

At 4.6 seconds after noon both blocks were at rest at the positions given above. At 4.9seconds after noon, what is the (vector) momentum of block 2?

At 4.9seconds after noon, what is the (vector) momentum of block 1?

At 4.9seconds after noon, which one of the following statements is true?

Block 1 is moving faster than block 2.

Block 1 and block 2 have the same speed.    

Block 2 is moving faster than block 1.

Answer 1

Suppose block 1 (m₁ = 55 kg) and block 2 (m₂ = 900 kg) are placed at point A(10,5,0) and point B(22,5,0) respectively in the coordinate system where the origin is denotedby O(0,0,0).

Then,

Seperation between m1 and m2,

It is clear that line joining these blocks is parallel to the x axis and the gavitational force acts along the x axis. The magnitute of the atttractive gravitational force between these two blocks is,

For m1 the force acts along the positive x axis and hence its acceleration will be along that axis. The acceleration of m1 is given by,

At t=4.6 s, block 1 was at rest. Then at t=4.9 s its velocity will be,

Then the momentum of block 1 is,

Similarly the acceleration of m2 acts along the negative x axis and given by,

It is clear that at t=4.9 s, block 1 ismoving faster than block 2. But observe that momentums of these two block are exactly same and opposite as they started from rest.