Problem 10.55 Enhanced - with Feedback Part A A lawn mower has a flat, rod-shape

Question

Problem 10.55 Enhanced - with Feedback Part A A lawn mower has a flat, rod-shaped steel blade that rotates about its center. The mass of the blade is 0.65 kg and its length is 0.55 m. Yu may want to review ( Dages314-318) What is the rotational energy of the blade at its operating angular speed of 3450 rpm? Express your answer using two significant figures. Submit My Answers Give Up Part B If all of the rotational kinetic energy of the blade could be converted to gravitational potential energy, to what height would the blade rise? Express your answer using two significant figures Submit My Answers Give Up Provide Feedback

Explanation / Answer

mass of lawn mower = m = 0.65 kg

length = L = 0.55 m

moment of inertia of lawn mower is given as ::

I = m L2 /12

inserting the values

I = (0.65) (0.55)2 /12 = 0.0164 kg m2

angular speed = w = 3450 rev/min = 3450 x (2 [pi] /60) rad/sec = 361.1 rad/sec

A) rotational kinetic energy is given as ::

RKE = (0.5) I W2 = (0.5) (0.0164) (361.1)2 = 1070 J

B) gravitational potential energy = rotational kinetic energy

mgh = 1070

(0.65) (9.8) h = 1070

h = 167.97 m

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