Calculating Vertical Height in Ballistic Pendulum Experiment

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To calculate the vertical height in the ballistic pendulum experiment, the correct approach is to equate the kinetic energy of the bullet and pendulum system immediately after the collision to the potential energy at the maximum height. The initial kinetic energy of the bullet is 778 J, while the combined kinetic energy after the bullet embeds in the pendulum is 1.55 J. The potential energy formula mgh should be used to find the height, and the previous assumption of adding both energies was incorrect. The final height calculation will yield a result that is not 13.23 cm. The discussion concludes with the realization of the correct method for calculating the height.
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Verticle height. Please help!

A 12.0 g rifle bullet is fired with a speed of 360 m/s into a ballistic pendulum with mass 6.00 kg, suspended from a cord 70.0 cm long.

Compute the vertical height through which the pendulum rises in cm.



How would you find the verticle height? I have the equation KE=(sum of the masses)(gravity)(h) to find it but I get 13.23 and that's not right. I found the initial kenitic energy of the bullet to be 778J and the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum to be 1.55J.


Can someone please help me?
 
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KE of the bullet & block as 1.55 J is correct. Re calculate equating this KE with increase in potential energy (mgh) to get the vertical height h. It won't be 13.23 cm
 
Thank you soo much! I got it. I thought you had to have the KE as 1.55J +778J on the left hand side of the equation. Thats why i was getting it wrong. But thank you!
 

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