Gravity Suspension

Classical Mechanics Level 3

A wooden block of mass 0.9 kilograms is suspended from the ceiling of a room by thin wires.

A bullet of mass 0.1 kilograms moving with a horizontal velocity of 100 m s − 1 100 ms^{-1} strikes the block and sticks to it.

What is the height to which the block rises?

Details and assumptions:
To make the calculations easier take the acceleration due to gravity as 10 m s − 2 10ms^{-2}

Fine I can't find it! I give up! How can it rise! The bullet is travelling horizontally! 3 1 10 5 None of these! because my answer is different! 6

View wiki
Sravanth C. by Sravanth C. , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Chew-Seong Cheong
Mar 11, 2015

It is given that:

  • m 1 = m_1 = mass of wooden block = 0.9 k g = 0.9 kg
  • m 2 = m_2 = mass of bullet = 0.1 k g = 0.1 kg
  • v 0 = v_0 = velocity the bullet striking wooden block = 10 m s − 1 = 10ms^{-1}
  • g = g = acceleration due to gravity = 10 m s − 2 =10ms^{-2}

By conservation of momentum, the velocity of the wooden block and bullet together v 1 v_1 after the bullet strikes the wooden block is given by:

m 2 v 0 = ( m 1 + m 2 ) v 1 ⇒ 0.1 ( 100 ) = ( 0.9 + 0.1 ) v 1 ⇒ v 1 = 10 m s − 1 m_2v_0 = (m_1+m_2)v_1 \quad \Rightarrow 0.1(100) = (0.9+0.1)v_1\quad \Rightarrow v_1 = 10 ms^{-1}

By conservation of energy, we have the height h h the block rises is given by:

1 2 ( m 1 + m 2 ) v 1 2 = ( m 1 + m 2 ) g h \frac {1}{2}(m_1+m_2)v_1^2 = (m_1+m_2)gh

⇒ 1 2 ( 1 ) ( 100 ) = ( 1 ) ( 10 ) h ⇒ h = 5 m \Rightarrow \frac {1}{2}(1)(100) = (1)(10)h \quad \Rightarrow h = \boxed{5}m

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Perfect! That's what I've expected!

Sravanth C. - 6 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...