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	   "source": [
       "# Chapter 10: Collisions"
	   ]
	},
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		   "metadata": {},
		   "source": [
			"## Example 10.1: Sample_Problem_1.sce"
		   ]
		  },
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"exec('degree_rad.sci',-1)\n",
"\n",
"//Given that\n",
"m = 140 * 10^-3  //in kg\n",
"Vi = -39  //in m/s\n",
"Vf = 39  //in m/s\n",
"\n",
"//Sample Problem 10-1a\n",
"printf('**Sample Problem 10-1a**\n')\n",
"//J = Pf - Pi\n",
"J = m *(Vf - Vi)\n",
"printf('The magnitude of impulse acted on the ball from bat is equal to %fN-s\n', J)\n",
"\n",
"//Sample Problem 10-1b\n",
"printf('\n**Sample Problem 10-1b**\n')\n",
"t = 1.20* 10^-3  //in sec\n",
"Favg = J/t\n",
"printf('The average force during the collision is %fN\n', Favg)\n",
"\n",
"//Sample Problem 10-1c\n",
"printf('\n**Sample Problem 10-1c**\n')\n",
"Vf = 45* [cos(dtor(30)), sin(dtor(30))]\n",
"Vi = [-39, 0]\n",
"J = m* (Vf - Vi)\n",
"printf('The magnitude of new inpulse is %fN-s\n', norm(J))\n",
"printf('The new impulse makes an angle of %f degress with the horizontal', rtod(atan(J(2)/ J(1))))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.2: Sample_Problem_2.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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"source": [
"//Given that\n",
"M = 5.4  //in kg\n",
"m = 9.5* 10^-3  //in kg\n",
"g = 9.8  //in m/s^2\n",
"h = 6.3* 10^-2  //in meter\n",
"\n",
"//Sample Problem 10-2\n",
"printf('**Sample Problem 10-2**\n')\n",
"//Mechanical energy conservation-\n",
"//0.5*(M+m)*Va^2 = (M+m)*g*h\n",
"Va = sqrt(g*h/0.5)\n",
"//Momentum conservation for the collision\n",
"Vb = (M+m)*Va/m\n",
"printf('The velocity of the bullet before collision is %fm/s', Vb)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.3: Sample_Problem_3.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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	   "outputs": [],
"source": [
"//Given that\n",
"m1 = 0.70  //in kg\n",
"m = [0.14, 3.2]  //in kg\n",
"k = [4.1* 10^4, 2.6* 10^6]  //in N/m\n",
"d = [16* 10^-3, 1.1* 10^-3]  //in meter\n",
"\n",
"//Sample Problem 10-3a\n",
"printf('**Sample Problem 10-3a**\n')\n",
"name = ['board', 'block']\n",
"U = zeros(2,1)\n",
"for count = 1:2\n",
"    U(count) = 0.5* k(count)* d(count)^2\n",
"    printf('The energy stored in %s is %fJ\n', name(count), U(count))\n",
"end\n",
"\n",
"//Sample Problem 10-3b\n",
"printf('\n**Sample Problem 10-3b**\n')\n",
"for count = 1:2\n",
"    //Energy conservation\n",
"    Vf = sqrt(U(count)/(0.5*(m1+m(count))))\n",
"    //Momentum conservation\n",
"    Vi = (m1 + m(count))*Vf/m1\n",
"    printf('The minimum velocity required to break the %s is %fm/s\n', name(count), Vi)\n",
"end"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.4: Sample_Problem_4.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"exec('collision.sci', -1)\n",
"\n",
"//Given that\n",
"m1 = 30*10^-3  //in kg\n",
"h1 = 8*10^-2  //in m\n",
"m2 = 75*10^-3  //in kg\n",
"g = 9.8  //in m/s^2\n",
"e = 1\n",
"\n",
"//Sample Problem 10-4\n",
"printf('**Sample Problem 10-4**\n')\n",
"//velocity just before collision\n",
"Vi = zeros(1,2)\n",
"Vi(1) = sqrt(2*g*h1)\n",
"Vi(2) = 0\n",
"Vf= fsolve([0,0], collision)\n",
"printf('The velocity of m1 after collision is %fm/s', abs(Vf(1)))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.5: Sample_Problem_5.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Given that\n",
"Ma = 83  //in kg\n",
"Va = [6.2, 0]  //in km/h\n",
"Mb = 55  //in kg\n",
"Vb = [0, 7.8]  //in km/h\n",
"\n",
"//Sample Problem 10-5a\n",
"printf('**Sample Problem 10-5a**\n')\n",
"Vf = (Ma*Va + Mb*Vb)/(Ma+Mb)\n",
"printf('The common velocity after the collision is %fm/s\n', norm(Vf))\n",
"\n",
"//Sample Problem 10-5b\n",
"printf('\n**Sample Problem 10-5**\n')\n",
"printf('The velocity of center of mass is not altered due to collision')"
   ]
   }
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