Question

Darth vader pushes luke skywalker with 17n, who then accelerates at 11m/s squared. Luke is thrown into c-3po and send him flying at a velocity of 8m/s. From this information find the mass of c-3po

Answer 1

Answer on Question #39567 – Physics – Other

Let $M$ and $m$ be the masses of Luke and c-3po respectively, $v$ and $w$ – velocities of Luke and c-3po after collision.

Darth Vader pushes Luke with 17N. According to the Newton’s Second law:

$$F = M a$$ $$M = \frac {F}{a} = \frac {17N}{\frac {11m}{s^{2}}} = \frac {17}{11} kg$$

According to the law of conservation of momentum:

$$M v _ {0} = M v + m w$$

where $v_{0}$ is the initial velocity of Luke.

Using the law of conservation of momentum:

$$\frac {M v _ {0} ^ {2}}{2} = \frac {M v ^ {2}}{2} + \frac {m w ^ {2}}{2}$$

From the first equation we have

$$v = v _ {0} - \frac {m}{M} w$$

Supstitute it into the second equation:

$$\frac {M v _ {0} ^ {2}}{2} = \frac {M (v _ {0} - \frac {m}{M} w) ^ {2}}{2} + \frac {m w ^ {2}}{2}$$ $$\frac {M v _ {0} ^ {2}}{2} = \frac {M v _ {0} ^ {2}}{2} - \frac {2 M v _ {0} \frac {m}{M} w}{2} + \frac {M \frac {m ^ {2}}{M ^ {2}} w ^ {2}}{2} + \frac {m w ^ {2}}{2}$$ $$0 = - v _ {0} m w + \frac {m ^ {2} w ^ {2}}{2 M} + \frac {m w ^ {2}}{2}$$

Divide the equation by $m$:

$$0 = - v _ {0} w + \frac {m w ^ {2}}{2 M} + \frac {w ^ {2}}{2}$$ $$m = \frac {2 M}{w ^ {2}} \left(v _ {0} w - \frac {w ^ {2}}{2}\right)$$

Substitute $M = \frac{17}{11} kg$, $w = 8m/s$ and $v_0 = v_0(t) = at = 11t$:

$$m = \frac {2 \cdot \frac {17}{11}}{64} \left(11t \cdot 8 - \frac {64}{2}\right) = \frac {17}{11 \cdot 32} (88t - 32) = 4.25t - \frac {17}{32}$$

So the mass of c-3po is $4.25t - \frac{17}{32}$. It depends how long (in seconds) Dart Vader applied his force.