(10%) Problem 10: A rod is laid out along the x-axis with one end at the origin and the other end at x = L. The linear density is given by the following: p ( x ) = Pot ( p 1 - P 0 ) ( x / [ )-. where po and py are constant values. @theexpertta.com - tracking 1 cordance with Expert TA's Terms of Service. copying this information to any solutions sharing website is strictly forbidden. Doing so may result nation of your count. DA For L = 0.95 m, po = 1.6 kg/m, and py = 7.7 kg/m, determine the center of mass of the rod, in meters. Grade Summary XCOM = Deductions 0% Potential 100% sin( cos( tan( 7 8 9 HOME Submissions cotan() asin() acos() 4 6 Attempts remaining: 5 (4% per attempt) atan() acotan() sinh( 2 detailed view cosh() tanh() cotanh() 0 END O Degrees O Radians BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Hints: 1% deduction per hint. Hints remaining: 3 Feedback: 2% deduction per feedback.(10%) Problem 7: The eight ball, which has a mass of m = 0.5 kg, is initially moving with a velocity v = 4.2i m/s. It strikes the six ball inelastically, which has an identical mass and is initially isicat rest. After the collision the eight ball is deflected by an angle of @ = 210 and the six ball is 8 soideflected by an angle of = 20.5, as shown in the figure. V 18 6 6 theexpertta.com - tracking In accordance with Expert TA's Terms of Service. Otheexpertta.com opying this information to any solutions sharing tly forbidden. Doing so may result in termination of your Expert TA Account. A 33% Part (a) Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the problem and the magnitude of the eight ball's initial velocity, v. Grade Summary Deductions 1% Potential 100% cos(a) cos(D) cos(9) cotan(0) 7 9 HOME Submissions sin(a) sin($) sin(0) 4 5 6 Attempts remaining: 5 (4% per attempt) tan(0) W B 2 3 detailed view d g h END t tan(() V VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Hints: 1% deduction per hint. Hints remaining: 2 Feedback: 2% deduction per feedback. 4 33% Part (b) What is the magnitude of the velocity, in meters per second, of the six ball? A 33% Part (c) What is the magnitude of the velocity of the eight ball, in meters per second, after the collision?(10%) Problem S: Three beads are placed along a thin rod. The first bead, of mass m1 = 26 g, is placed a distance d1 = 1.1 cm from the left end of the rod. The second bead, of mass my = 15 g, is placed a distance d2 = 2.1 cm to the right of the first bead. The third bead, of mass my = 51 g, is placed a distance d; = 3.4 cm to the right of the second bead. Assume an x-axis that points to the ight m my -d2 d Otheexpertta.com @theexpertta.com - tracking In accordance with Expert TA's Terms of Service. copying this information to any solutions sharing e is strictly forbidden. Doing so may result in termination of your Expert TA Account. A 25% Part (a) Write a symbolic equation for the location of the center of mass of the three beads relative to the left end of the rod, in terms of the variables given in the problem statement. Grade Summary Xem = Deductions 0% Potential 100% B 7 8 9 HOME Submissions d d1 dz 4 5 6 Attempts remaining: 5 (4% per attempt g h 1 2 3 detailed view m m1 + 0 END m3 P t VO BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 1% deduction per hint. Hints remaining: 1 Feedback: 2% deduction per feedback. A 25% Part (b) Find the center of mass, in centimeters, relative to the left end of the rod A 25% Part (c) Write a symbolic equation for the location of the center of mass of the three beads relative to the center bead, in terms of the variables given in the problem statement. A 25% Part (d) Find the center of mass, in centimeters, relative to the middle bead.(10%) Problem 9: A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 31 cm, height H = 13 cm, and area mass density o. dy I H B Otheexpertta.com theexpertta.com ance with Expert TA's Terms of Service. copying his information to any solutions sharing website ctly forbidden. ay result in termination of your Expert TA Account. A 14% Part (a) The horizontal center of mass of the sheet will be located: OOn the center line. O Not enough information to determine. Grade Summary Deductions 0% O To the left of the center line. O To the right of the center line. Potential 100% Submissions Attempts remaining: 3 (33% per attempt) detailed view Submit Hint Feedback I give up! Hints: 1% deduction per hint. Hints remaining: 1 Feedback: 2% deduction per feedback A 14% Part (b) The vertical center of mass of the sheet will be located: A 14% Part (c) Write a symbolic equation for the total mass of the triangle. % Part (d) Consider a horizontal slice of the triangle that is a distance y from the top of the triangle and has a thickness dy. Write an equation for the area of this slice in terms of the distance y, and the base B and height H of the triangle. 14% Part (e) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C J f(v) where C has all the constants in it and f() is a function of y. What is f(v)? A 14% Part (f) Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward A 14% Part (g) Find the numeric value for the distance between the top of the triangle and the center of mass in cm