parts b and c (7%) Problem 7: A rod of mass M= 107 g and length L 48 cm can rota

Question

parts b and c

(7%) Problem 7: A rod of mass M= 107 g and length L 48 cm can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m = 13 g, moving with speed V = 7 m/s, strikes the rod at angle = 35° a distance D = 2 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? 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 Grade Summary Deductions Potential 100% 0% rot - Submissions cos() | tan() | | ( | ) | 7 | 8 | 9 sinO Attempts remaining: S (4% per attempt) detailed view 4 5 6 cotan0asinacoso atan0 acotan sinhO coshO tanhO cotanh0 END Degrees Radians vO Hint I give up! Submit

Explanation / Answer

moment of inertia of rod, I1 = M L^2 / 3

= (0.107)(0.48^2) / 3

= 8.218 x 10^-3 kg m^2

moment of inertia of ball = m D^2 = (0.013) (0.48/2)^2

= 0.749 x 10^-3 kg m^2

(A) moment of inertia of rod-ball system,

I = I1 + I2

= 8.97 x 10^-3 kg m^2

(b) Applying angular momentum conservation,

m v D cos(theta) = I w

0.013 x 7 x (0.48/2) x cos35 = (8.97 x 10^-3) w

w = 2 rad/s

(c) after the collision,

KE = I w^2 /2

= (8.97 x 10^-3) (2^2) / 2

= 17.9 x 10^-3 J

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