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 = (F)/(m_1)`

`a_1 = (4 * 10^4)/(8.5 * 10^6) = 4.7 * 10^(-3) m/s^2`

acceleration of space craft will be given as

`a_2 = (F)/(m_2)`

`a_2 = (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 = (1)/(2) at^2`

`14000 = (1)/(2)*4.0047* t^2`

`t = 83.62 s`

now we have to find the distance moved by starship

`d_1 = (1)/(2) a_1t^2`

`d_1 = (1)/(2)*0.0047* 83.62^2`

`d_1 = 16.4m`

so it will move by 16.4 m distance