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 its top edge. The mass of the sign is 2.40 kg and its vertical dimension is 50.0 cm. The sign is swinging without friction, becoming a tempting target for children armed with snowbals. The maximum angular displacement of the sign is 25.0° on both sides of the vertical. At a moment when the sign is vertical and moving to the left, a snowball of mass 420 9. traveling horizontally with a velocity of 160 cm/s to the right, strikes perpendicularly the lower edge of the sign and sticks there. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) Calculate the angular speed of the sign immediately before the impact. rad/s (b) Calculate its angular speed immediately after the impact rad/s (c) The spattered sign will swing up through what maximum angle? Noed Help? LRostn

Explanation / Answer

(a) Applying energy conservation,

Pei + KEi = PEf + KEf

m g L (1 - cos25) + 0 = 0 + I w^2 / 2

m g L (1 - cos25) = m L^2 w^2/ 6

6 x 9.8 x (1 - cos25) / 0.50 = w^2

w = 3.32 rad/s

(B) Applying angular momentum conservation,

m v0 r + I w = I wf + m wf r^2

(0.420 x 1.60 x 0.50) + (2.40 x 0.50^2 / 3)(-3.32) = ((2.40 x 0.50^2/3) + (0.420 x 0.50^2)) wf

wf = - 1.10 rad/s

angular speed = 1.10 rad/s

(c) (2.40 x 0.50^2 / 3) (1.10^2 / 2) = 2.40 x 9.8 x 0.50 (1 - cos(theta))

1 - cos(theta) = 0.01

theta = 8.2 deg

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.