Question

(a) In outer space, far from other objects, block 1 of mass 33 kg is at position <11, 10, 0> m, and block 2 of mass 1250 kg is located at position <20, 10, 0> m. What is the (vector) gravitational force acting on block 2 due to block 1? It helps to make a sketch of the situation. F→grav= < , , > N (b) At 4.1 seconds after noon both blocks were at rest at the positions given above. At 5.2 seconds after noon, what is the (vector) momentum of block 2? p→2= < , , > kg·m/s (c) At 5.2 seconds after noon, what is the (vector) momentum of block 1? p→1= < , , > kg·m/s (d) At 5.2 seconds after noon, which one of the following statements is true? Block 1 is moving faster than block 2. Block 2 is moving faster than block 1. Block 1 and block 2 have the same speed.

Answer 1

Answer :

block 1 of mass 33 kg is at position <11, 10, 0> m.

block 2 of mass 1250 kg is located at position <20, 10, 0> m.

1)  gravitational force acting on block 2 due to block 1

F = G*m1*m2/r^2

Fx = G*m1*m2/(x1 - x2)^2
Fy = 0 (same height)
Fz = 0 (same plane)

Fx = G*(30*1250) / (11-20)^2

put G = 6.674 08 x 10^-11 m³ kg^-1 s^-2

we get = Fx = 3.09 x 10^-8 N
Plug and chug. The Force acts towards the the Block 1 so the vector will be

F = (-Fx,0,0)

F = <-3.09 x 10^-8 , 0 , 0 > N

2) For the 2nd part you need the acceleration, g, of the block.

g = G*m2/r^2

momentum = m*v = m*g*t

momentum = < -1.1903e-8, 0, 0 > kg·m/s

3) for block 2

momentum = < -1.1903e-8, 0, 0 > kg·m/s

4) Block 1 is moving faster than block 2.