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Solutions to various problems related to mechanics and motion, including topics such as forces, diagrams, equations of motion, and friction. The problems involve concepts such as contact force, tension, angular frequency, and acceleration.
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SOLUTIONS Problem p oints v 0 sin pts a vy v sin g t t (^0) g pts b y v v sin t (^0 0) g^ t
v 0 sin (^) v 0 sin y v 0 sin (^) g (^) g g 2 y v^ sin (^2) 0 g pts c v 0 v 0 sin pts d x v 0 v 0 cos t t (^) g v 20 sin cos x g
Problem p oints a mg l mv A^ vA l
pts g 2 pts b Net force up must b e macen m mg T mg mg T mg pts c gravity mg l tension vA l
Problem p oints
R pts b Ip Ic M b M M b
pts c p Ip bM g sin ^ M R^ M b^ bg (^1) R (^2) b 2 sin 2 pts d Under the small angle approximation sin and the equation bg of motion is given by ^ (^1) R 2 b^2 which is simple harmonic with
bg an angular frequency given by (^1) R 2 b 2 The p erio d is given by
(^1) R (^2) b 2 2 bg pts e There must b e a force at P or the CM would accelerate straight downwards
Problem p oints pts a The diagram
pts b R v R v z 2 pts c a v R a 2 R x 2 pts d F^ ma F^ m 2 R 2 x pts e T sin m 2 R 2 T cos mg tan 2 R g 2
Problem p oints
mv ^ mM^ G^ v M G pts a R R v 0 pts b mv R sin � mV R (^) V (^0) sin � ^
0 R 2 mM G m 0 mM^ G pts d same as in c or
v
R R 2 pts e ^ mv ^ mM^ G^ ^ m v^0 mM^ G 0 R 2 R (^) M G 0 M G
v
Problem p oints pts a M V 0 pts b W W M g Fbuoy Fbuoy M g W 0 W M g M g W 0 W
W 0
Problem p oints
2
fr
F ma I no slipping Ffr ma R Ffr mR a a R Ffr mR ma ma a a
^ a a
^ a
