October 19th, 2015, 01:49 AM  #1 
Senior Member Joined: Dec 2014 From: The Asymptote Posts: 142 Thanks: 6 Math Focus: Certainty  Another Linear momentum Question
A 22g bullet strikes and becomes embedded in a 1.35kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction is 0.28, and the impact drives the block a distance of 8.5m before it comes to rest, what was the muzzle speed of the bullet? $\displaystyle F_{fr} = F_N \mu_k$ $\displaystyle m\cdot a = m\cdot g \cdot\mu_k$ $\displaystyle a = g\cdot \mu_k$ $\displaystyle a = 9.8(0.29) = 2.744ms^{2}$ $\displaystyle v^2 = v_0^2 + 2ad$, final speed after collision is 0m/s $\displaystyle v_0 = \sqrt{2ad}$ $\displaystyle v_0 = \sqrt{[2]\cdot [2.744]\cdot[8.5]}$ $\displaystyle v_0 = 6.83ms^{1} = v'$ $\displaystyle p = p'$ $\displaystyle m_1v_1 = (m_1 + m_2)v'$ $\displaystyle v_1 = \frac{(0.022 + 1.35)\cdot 6.83}{0.022}$ muzzle speed = $\displaystyle v_1 = 397.88 = 398ms^{1}$, Is this correct?? Thank you in advance. 
October 19th, 2015, 03:34 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319 
check your arithmetic for the final calculation of $v_1$ ... I get approx 426 m/s

October 20th, 2015, 08:55 PM  #3 
Senior Member Joined: Dec 2014 From: The Asymptote Posts: 142 Thanks: 6 Math Focus: Certainty 
Thanks skeeter... recalculated and $\displaystyle v_1 = 487ms^{1}$ 
October 21st, 2015, 07:04 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319  huh?

October 21st, 2015, 07:12 AM  #5 
Senior Member Joined: Dec 2014 From: The Asymptote Posts: 142 Thanks: 6 Math Focus: Certainty 
apologies... My calculator gives 487. I've tried another calculator (CASIO) and it now gives 425.9. Just to make sure, I used an online calculator and yes it is 425.9. Don't know why my calculator is giving 487. Last edited by hyperbola; October 21st, 2015 at 07:14 AM. 
October 22nd, 2015, 06:11 AM  #6 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,068 Thanks: 692 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
You get 487 m/s if you accidentally type 0.22 instead of 0.022 in the bracket on the numerator.


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