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 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: 2,611 Thanks: 1295 What kind of collision? Elastic, totally inelastic, ... ? Thanks from Joppy
 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
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Quote:
 Originally Posted by jeho The type of collision hasn't been specified, but I assume it's elastic.
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
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Quote:
 Originally Posted by jeho . . . the angular displacement of the bob
When?

March 5th, 2017, 02:57 PM   #7
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Quote:
 Originally Posted by jeho The kinetic energy in an elastic collision is conserved.
... 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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# a 50g pendulum hanging at rest on a 2m long string is hit by a horizontal projectile of mass 80mg moving at 200kn/h.use the concept of energy conservation to estimate the angular displacement of the bob

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