A 5kg object...

Question

A 5kg object is hanging by a 1.5m wire when it is suddenly hit by a 3kg missile traveling horizontally at 12m/s. The missile embeds itself in the object during the collision. What is the tension in the rod immediately after the collision?

Answer 1

In the first sentence the question uses the word "wire", and in the last sentence

it uses the word "rod".

I assume that they are meant to be the same thing, and I will use the word "wire".

I will also assume that the wire does not break as a result of the collision.

I will also assume that the object was not moving before the impact.

Let

r = 1.5 m be the length of the wire,

M = 5 kg be the mass of the object,

m = 3 kg be the mass of the missile,

v = 12 m/s be the speed of the missile before impact,

V (unknown) be the speed of the object together with the missile after the impact,

g = 9.81 m/s² be gravitational acceleration.

After the impact the tension on the wire has to provide two forces:

1) the force keeping the object and the missile suspended against gravity; this force is

(m+M)g

2) the force providing circular motion of the new combined object; this centripetal force is

(m+M)V²/r

It remains to calculate the speed V.

That can be done from conservation of momentum:

The momentum of the missile before impact becomes the momentum of the combined object.

mv = (m+M)V

So

V = mv/(m+M)

So the total tension in the wire is

(m+M)g + m²v²/r(m+M)

Substituting actual numbers

8×9.81 + 3²×12²/(1.5×8) = 186.48 N