Question

A 20.0 kg wood ball hangs from a 1.90 m -long wire. The maximum tension the wire can withstand without breaking is 600 N . A 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball.

whats the largest speed this projectile can have without causing the cable to break?

Answer 1

When the wood ball is hit by the projectile it will start rotating. This means that is will have a centripetal acceleration that sums up to the tension due to wieght, thus

$T=ma_c+mg=m\frac{v^2}{l}+mg$

And the problem translates into deribing the maximum speed od the system ball-projectile after the anelastic collision, so that the wire does not break.

Thus

$v=\sqrt{\frac{l}{m_b+m_p}(T-(m_p+m_b)g)}=6m/s$

w

According to linear momentum conservation

$m_pv_p=(m_p+m_b)v$

Thus projectile velocity is before collision is

$v_p=\frac{m_p+m_b}{m_p}v_p=139m/s$