Question

The top edge of a thin rectangular metal plate with a mass of 2.80 kg is attached to a horizontal rod parallel to the edge of the plate. The plate hangs from this rod and is free to rotate about it without friction. The vertical height of the plate is 45.0 cm. The plate is pulled to the right until it makes an angle of 28.0° from vertical and then released from rest. At the same time, a piece of clay is tossed at the plate, moving to the right. At the moment the plate reaches vertical, moving left, it collides with the clay. The piece of clay strikes the plate at its bottom edge, moving to the right perpendicular to the plate at the moment of impact. Its mass is 320 g and its speed just before impact is 160 cm/s. The clay sticks to the plate after impact. (a) What is the anqular speed (in rad/s of the plate the instant before it collides with the clay? (Round your answer to at least two decimal places.) rad/s (b) What is the angular speed (in rad/s) of the plate-clay system immediately after the collision? rad/s (c) What is the magnitude of the maximum angular displacement from the vertical (in degrees) that the plate-clay system will reach after the collision?

Answer 1

2) From Conservation of energy Io – migh (M4)=mg $(1-сoso) med w = /29 (1-60) 3 (9.80m/s) (1 - Cos28 77 rad/s) 0.45m b) From conservation & Angular momentum (met mL) wf = m2w; -mut wf = ŹMlWp-mv (*m*m) = $(2.8089 Yooysm) (26765 yards H0.32/g/1.6my ($ (280 kg) + 0.320kg) 0.45m) = 1.15 rades hom = (2-80kg) 0.225m)+(320kg)(45m) (2-80+01320) Kg 9 = 0.248om Fross Conservation of energy

(M+r)g hom l- cose) = ($m2+mL) w 8 = cos - (M + m) uh - L 2 (Menighem =cod (24130 401340) (-us) (15) 2 (208040320)(9380) or eu gom) 0 = 12. 076869359 o = 120