March 4th, 2017, 01:30 PM  #1 
Member Joined: Sep 2016 From: zambia Posts: 31 Thanks: 0  work, energy and power
A 50 g pendulum bob hanging at rest on a 2 m long string is hit by a horizontal projectile of mass 80 mg moving at 200 km/h. Use the concept of energy conservation to estimate the angular displacement of the bob 
March 4th, 2017, 01:54 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,639 Thanks: 1317 
What kind of collision? Elastic, totally inelastic, ... ?

March 5th, 2017, 02:00 PM  #3 
Member Joined: Sep 2016 From: zambia Posts: 31 Thanks: 0 
The type of collision hasn't been specified, but I assume it's elastic.
Last edited by skipjack; March 5th, 2017 at 02:28 PM. 
March 5th, 2017, 02:07 PM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,639 Thanks: 1317  So, describe the physics properties of an elastic collision ...
Last edited by skipjack; March 5th, 2017 at 02:29 PM. 
March 5th, 2017, 02:16 PM  #5 
Member Joined: Sep 2016 From: zambia Posts: 31 Thanks: 0 
The kinetic energy in an elastic collision is conserved.
Last edited by skipjack; March 5th, 2017 at 02:29 PM. 
March 5th, 2017, 02:30 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,034 Thanks: 1393  
March 5th, 2017, 02:57 PM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 2,639 Thanks: 1317  ... and momentum is conserved. $mv_{1_0}+ Mv_{2_0} = mv_{1_f}+ Mv_{2_f}$ since $M$ is initially at rest ... $mv_{1_0} = mv_{1_f}+ Mv_{2_f}$ a shortcut for conservation of kinetic energy ... closing speed of the masses prior to the collision = opening speed of the masses after the collision $\implies v_{1_0}  v_{2_0} = v_{2_f}  v_{1_f}$. Of course, $v_{2_0} = 0$. Using this equation, solve for $v_{1_f}$ in terms of $v_{2_f}$ and $v_{1_0}$. Substitute the result into the momentum equation and solve for $v_{2_f}$. Once you have $v_{2_f}$, you can use energy conservation to determine how high the pendulum bob, $M$, swings ... some trig will get you the max angular displacement from equilibrium. 

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