n outer space, far from other objects, block 1
of mass 40 kg is at position
(7,9,0)
and block 2 of mass 1000 kg is at position
(17,13,0)
Since the z components of position are
zero, the (vector) gravitational force acting
on block 2 due to block 1 will be
(-21.359e-9,-8.54198e-9,0)
At 4.6 s after noon both blocks were at rest at
the positions given above. At 4.7 s after noon,
what is the (vector) momentum of block 2?
px,py,pz
To find the vector momentum of block 2 at 4.7 s after noon, we need to calculate it using the formula for momentum:
Momentum (p) = mass (m) × velocity (v)
However, since the problem does not provide the velocity of block 2 directly, we need to derive it. The formula for velocity can be obtained from the acceleration due to gravity:
Acceleration due to gravity (g) = gravitational force (F) / mass (m)
Since we have the gravitational force acting on block 2 due to block 1, we can find the acceleration experienced by block 2:
Acceleration (a) = F / m
Next, we can use the formula for acceleration to find the change in velocity over time:
Change in velocity (Δv) = a × time (t)
And finally, we can find the final velocity of block 2 at 4.7 s after noon by adding the change in velocity to the initial velocity:
Final velocity (v) = initial velocity (u) + Δv
Now let's calculate the momentum of block 2.
Given:
Mass of block 2 (m) = 1000 kg
Initial position of block 2 (x, y, z) = (17, 13, 0)
Final position of block 2 (x, y, z) = (? , ?, ?)
Gravitational force on block 2 due to block 1 (F) = (-21.359e-9, -8.54198e-9, 0) N
Time (t) = 4.7 s
Step 1: Calculate the gravitational acceleration on block 2.
Since the gravitational force (F) is given, we can use the formula F = m * a to solve for the gravitational acceleration (a):
a = F / m
Step 2: Calculate the change in velocity.
Using the acceleration (a) and time (t) given, we can calculate the change in velocity (Δv) using the formula:
Δv = a * t
Step 3: Calculate the final velocity.
To find the final velocity (v), we add the change in velocity (Δv) to the initial velocity (u). However, since the initial velocity is not given and we only have the initial position (x, y, z), we cannot directly calculate the initial velocity. Therefore, we'll assume the blocks were initially at rest, so the initial velocity is zero.
Step 4: Calculate the momentum.
Now that we have the final velocity (v) of block 2, we can calculate its momentum using the formula:
Momentum (p) = mass (m) * velocity (v)
Note: The position of block 2 at 4.7 s after noon is not provided in the question. Without this information, we cannot calculate the exact momentum of block 2 at that time.