A thin, uniform, rectangular sign hangs vertically above the door of a shop. The

Question

A thin, uniform, rectangular sign hangs vertically above the door of a shop. The sign is hinged to a stationary horizontal rod along its top edge. The mass of the sign is 2.40 kg and its vertical dimension is 45.0 cm. The sign is swinging without friction, becoming a tempting target for children armed with snowballs. The maximum angular displacement of the sign is 25.0 degree on both sides of the vertical. At a moment when the sign is vertical and moving to the left, a snowball of mass 500 g, traveling horizontally with a velocity of 160 cm/s to the right, strikes perpendicularly the lower edge of the sign and sticks there. Calculate the angular speed of the sign immediately before the impact. Calculate its angular speed immediately after the impact. The spattered sign will swing up through what maximum angle?

Explanation / Answer

b)

From Conservation of angular momentum

mvL+1/3 ML^2 Omega = (mL^2+1/2ML^2)* Omega new

Omega New =( mvL+1/3 ML^2 Omega)/ (ml^2+1/2ML^2)

Omega New = 0.5*1.6*0.45 + 0.33*2.4*0.45^2*2.5)/ (0.5*0.45^2+0.5*2.4*0.45^2)

Omega New = 0.76095 / 0.34425

Omega New = 2.21 rad/s

c)

From Law of conservation of energy,

and upon solving

cos theta = 1- (0.5*Omega new^2(mL^2+1/3ML^2) / (gL(M/2+m))

theta = 23.9 degrees

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