Phys Notes Feb21

# Phys Notes Feb21 - Y12 ch 8.5 1 Section 8.5 Center of...

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Y12 ch 8.5 1 Section 8.5 Center of Mass (motion of the center of mass) Thecenterofmass(CM)ofasystemistheaveragepo- sition of the mass of the system. Its motion under given forces is the same as though all the mass were concentrated at the center of mass. f31 d P dt = F ext , P = M V , V = m 1 v 1 + m 2 v 2 m 1 + m 2 = d dt R YF’s notation: P = M v cm , v cm = m 1 v 1 + m 2 v 2 m 1 + m 2 = d dt r cm

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Y12 ch 8.5 2 In coordinates R = X ˆ ı + Y ˆ j + Z ˆ k ( r cm = x cm ˆ ı + y cm ˆ j + z cm ˆ k ) where X = m 1 x 1 + m 2 x 2 + ... m 1 + m 2 + Y = m 1 y 1 + m 2 y 2 + m 1 + m 2 + Z = m 1 z 1 + m 2 z 2 + m 1 + m 2 +
Y12 ch 8.5 3 ¨ r 1 =(2 ˆ ı +5 ˆ j ) m, m 1 =2 kg, r 2 =(3 ˆ ı 4 ˆ j ) m, m 2 = 3 kg. How far is CM from m 1 ? ¥ Solving collision problem by transforming to CM sys- tem: ¨ Consider a head-on collision of two block of masses, m A =4 kg, m B kg. If u A =6 m/s, u B =3 m/s, what are the velocities after the collision?

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Y12 ch 8.5 4 ¨ Consider a simplified model of a water molecule, in which the angle between the O-H bonds is 90 and distance between the oxygen and hydrogen atoms is
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Phys Notes Feb21 - Y12 ch 8.5 1 Section 8.5 Center of...

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