(12%) Problem 7: A rod of mass M = 130 g and length L = 47 cm can rotate about a
ID: 1787440 • Letter: #
Question
(12%) Problem 7: A rod of mass M = 130 g and length L = 47 cm can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m1 = 19 g, moving with speed V = 9 m/s, strikes the rod at angle = 34° a distance D = L/4 from the end and sticks to the rod after the collision ©theexpertta.com 33% Part (a) What is the total moment of inertia, 1, with respect to the hinge, of the rod-ball-system after the collision? Grade Summary Deductions Potential 0% 100% M L2 12 (MHTn)L2 3 ML2 3 Submissions Attempts remaining: 3 5% per attempt) detailed view ML2 3 Submit Hint I give up! Hints: 1 % deduction per hint. Hints remaining: 3 Feedback: 0% deduction per feedback 33% Part (b) what is the angular speed of the system immediately after the collision, in terms of system parameters and moment of inertia I 33% Part (c) Calculate the rotational kinetic energy of the system after the collision, in J.Explanation / Answer
(a) Itotal = (ML^2 / 3) + MD^2
Option 4
(b) V cos theta responsible for rotation
V" = V cos (34) = 9 x 0.829037573 = 7.46 m/s
Now
V" = Rw
w = V" / R
w = 7.46 / (L/4)
w = (7.46 x 4) / .47
w = 63.48 rad/s
(c) KEr = 1/2 I w^2
I = (ML^2 / 3) + mD^2 = (ML^2 / 3) + (m(L/4))^2 = (ML^2 / 3) + (mL^2/16)
I = ((.130 x .47^2 / 3)) + (.(019 x .47^2 / 16)) = 0.00983465208
KEr = .5 x 0.00983465208 x (63.48)^2
KEr = 19.81 J
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