Question

A uniform stick has a mass of 4.42 kg and a length of 1.23 m. It is initially lying flat at rest on a frictionless horizontal surface and is struck perpendicularly by a puck imparting a horizontal impulsive force of impulse 12.8 N s at a distance of 46.4 cm from the center. Determine the subsequent motion of the stick.

Answer 1

10.7 rad/s is the final angular velocity of the stick.

Given:

Mass of the stick = 4.42 kg

Length of the stick = 1.23m

Force of impulse (I) = 12.8 N s

The linear velocity of the stick, $v=\frac{I}{m}$

                                                  $v=\frac{12.8 N.s (\frac{1 kg m/s^2}{1 N}) }{4.42 kg}$

                                                  $v$  $= 2.89 m/s$

Therefore, the final linear velocity of the stick is 2.89 m/s

∴$w=\frac{12 Ir}{ml^{2} }$

$w=\frac{12 ( 12.8 N.s ) ( 46.4 cm)}{(4.42 kg) (1.23 m)^2}$

$w= \frac{12 (12.8 N.s) (46.4 cm) (\frac{10^-^2 m}{1 cm} )}{(4.42 kg) (1.23m)2}$

$w=10.7 rad/s$

Therefore, 10.7 rad/s is the final angular velocity of the stick.

Learn more about linear velocity here:

brainly.com/question/15154527

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