Question

An experiment is performed aboard the International Space Station to verify that linear momentum is conserved during collisions in a zero-g environment. The experiment involves a 3-D completely inelastic collision of three drops of honey. At the moment just before they all collide, the masses and velocities of the drops are
m1 = 31.5 g V1 = (12.7 m/s)x
m2 = 49.9 g V2 = (12.5 m/s)y
m3 = 78.1 g V3 = (15.9 m/s)z
What is your prediction for the speed, V, of the combined honey drop after the collision?
V = _______________________ m/s

Answer 1

Answer:

The speed of the combined honey drop after the collision is 9.05 m/s.

Explanation:

Given that,

The masses and velocities of the drops are

$m_{1}=31.5\ g$

$v_{1}=12.7\ m/s$

$m_{2}=49.9\ g$

$v_{1}=12.5\ m/s$

$m_{1}=78.1\ g$

$v_{1}=15.9\ m/s$

We need to calculate the total mass

Using formula of masses

$m=m_{1}+m_{2}+m_{3}$

Put the value into the formula

$m=31.5+49.9+78.1$

$m=159.5\ g$

We need to calculate the velocity in x- direction

Using conservation of momentum

$m_{1}v_{1}=(m_{1}+m_{2}+m_{3})v_{x}$

$v_{x}=\dfrac{m_{1}v_{1}}{m_{1}+m_{2}+m_{3}}$

Put the value into the formula

$v_{x}=\dfrac{31.5\times12.7}{159.5}$

$v_{x}=2.50\ m/s$

We need to calculate the velocity in y- direction

Using conservation of momentum

$m_{2}v_{2}=(m_{1}+m_{2}+m_{3})v_{y}$

$v_{y}=\dfrac{m_{2}v_{2}}{m_{1}+m_{2}+m_{3}}$

Put the value into the formula

$v_{y}=\dfrac{49.9\times12.5}{159.5}$

$v_{y}=3.91\ m/s$

We need to calculate the velocity in z- direction

Using conservation of momentum

$m_{3}v_{3}=(m_{1}+m_{2}+m_{3})v_{z}$

$v_{z}=\dfrac{m_{3}v_{3}}{m_{1}+m_{2}+m_{3}}$

Put the value into the formula

$v_{z}=\dfrac{78.1\times15.9}{159.5}$

$v_{z}=7.78\ m/s$

We need to calculate the combined honey drop after the collision

Using formula of velocity

$v=v_{x}+v_{y}+v_{z}$

Put the value into the formula

$v=2.50i+3.91j+7.78k$

The magnitude of velocity

$v=\sqrt{(2.50)^2+(3.9)^2+(7.78)^2}$

$v=9.05\ m/s$

Hence, The speed of the combined honey drop after the collision is 9.05 m/s.