Question

A spacecraft is separated into two parts by detonating the explosive bolts that hold them together. The masses of the parts are 1200 kg and 1800kg; the magnitude of the impulse on each par from the bolts is 300 N s. With what relative speed do the twe twe parts separate because of the detonation?

Answer 1

Answer:

Explanation:

Given that,

A space ship is separated into two part

Mass of first part

M1 = 1200kg

Mass of second part

M2 = 1800kg

Magnitude of impulse on each part is

I = 300Ns

We want to find the relative velocity at which the two parts separate

Now,

Impulse is give as

I = ft = mv - mu

Since the body is considered to be at rest before detonation

Then, I = mv

So for first part

I = M1•V1

V1 = I / M1

V1 = 300 / 1200

V1 = 0.25m/s

Also, for second part

V2 = —I / M2

V2 = —300 / 1800

V2 = —0.167 m/s

NOTE: the negative sign is due to the fact that the two bodies are moving away from each other.

The relative speed of the two masses because of detonation is

V = V1 — V2

V = 0.25 — (—0.167)

V = 0.25 + 0.167

V = 0.417 m/s

The relative speed of the two masses because of detonation is 0.417 m/s

Answer 2

Answer:

(1) $\frac{5}{12} m/s$

(2)  $-\frac{5}{12} m/s$

Explanation:

Lets say two parts went left and right, one with 1200Kg, call it A ,went right and one with mass 1800Kg went left. Let's establish right as positive and left as negative for our speed convention.

Both have initial acceleration of 300N, assuming for one second, by newton's second law F=ma, 'A' will have acceleration of 1/4m/s^ which will induce velocity of 0.25m/s as well.

So A has velocity of $\frac{1}{4} m/s$ towards right direction.

and B has velocity of - $\frac{1}{6} m/s$ towards left direction.

Relative Velocities.

and 'B' will have acceleration of $\frac{1}{6} m/s^2$ which will also produce velocity of $\frac{1}{6} m/s$.

$V_{AB} = V_{A} -V_{B}$ = $\frac{1}{4} --\frac{1}{6}= \frac{5}{12}m/s$ (Read as Velocity A with respect to B) (1)

$V_{BA} =V_{B} -V_{A} = -\frac{1}{6}-\frac{1}{4} =-\frac{5}{12} m/s$ (Read as Velocity B with respect to B). (2).