The last stage of a rocket is traveling at a speed of 8250 m/s. This last stage

Question

The last stage of a rocket is traveling at a speed of 8250 m/s. This last stage is made up of two parts that are clamped together, namely, a rocket case with a mass of 330.00 kg and a payload capsule with a mass of 150.00 kg. When the clamp is released, a compressed spring causes the two parts to separate with a relative speed of 910 m/s. What are the speeds of the two parts after they have separated? Assume that all velocities are along the same line.

a) What is the speed of the payload?

b)What is the speed of the rocket case?

Find the total kinetic energy of the two parts before and after they separate; account for any difference.

c)The kinetic energy before they separate?

d) The kinetic energy after they separate?

Explanation / Answer

Initially, we have two objects stuck together moving at a constant speed at a particular instant. Then those two objects separate, but during separation, a spring exerts a force on both objects causing them to separate with a speed of 910m/s relative to one another.

Momentum is conserved

P = P'

(m1+m2)v = m1v1' + m2v2'

We know that the objects separate with a speed of 910m/s RELATIVE TO EACH OTHER. This means that

(m1+m2)v = m1(910m/s + v2') + m2v2'

(m1+m2)v = m1*910m/s + m1*v2' + m2v2'

(m1+m2)v = m1*910m/s + (m1+m2)v2'

(m1+m2)v - m1*910m/s = (m1+m2)v2'

Let (m1+m2) = M = 480kg

M*v - m1*910m/s = M*v2'

(M*v - m1*910m/s)/M = v2'

v2' = v - (m1*910m/s)/M

We still have not defined which part is m1 (with corresponding v1')and which part is m2 (with corresponding v2'). Since the first question asks for the speed of the ROCKET lets say that
m2 is the mass of the rocket and
v2' is the speed of the rocket (after separation)

v2' = 8250m/s - (150kg*910m/s)/480kg

v2' = 7965.625 m/s ( speed of rocket after separation)

__________________________________________________

We used the equation

v1' =  910m/s + v2'

So plugging in the value we got into this equation we have:

v1' =  910m/s + 7965.625m/s

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