Question

A Federation starship (8.5 ✕ 106 kg) uses its tractor beam to pull a shuttlecraft (1.0 ✕ 104 kg) aboard from a distance of 14 km away. The tractor beam exerts a constant force of 4.0 ✕104 N on the shuttlecraft. Both spacecraft are initially at rest. How far does the starship move as it pulls the shuttlecraft aboard?

Answer 1

Force applied by the beam is given as

$F = 4 * 10^4 N$

now the acceleration of starship is given as

$a_1 = \frac{F}{m_1}$

$a_1 = \frac{4 * 10^4}{8.5 * 10^6} = 4.7 * 10^{-3} m/s^2$

acceleration of space craft will be given as

$a_2 = \frac{F}{m_2}$

$a_2 = \frac{4 * 10^4}{1 * 10^4} = 4 m/s^2$

now the relative acceleration is given as

$a = a_1 + a_2 = 4.0047 m/s^2$

now the distance between them is d = 14000 m

now we can use kinematics to find the time to cover this distance

$d = \frac{1}{2} at^2$

$14000 = \frac{1}{2}*4.0047* t^2$

$t = 83.62 s$

now we have to find the distance moved by starship

$d_1 = \frac{1}{2} a_1t^2$

$d_1 = \frac{1}{2}*0.0047* 83.62^2$

$d_1 = 16.4m$

so it will move by 16.4 m distance