Solving Kinetic Problems: Energy Method
The sleeve P in fig.2 slides on the smooth horizontal bar. The mass of each bar is 4.0 kg and the mass of
the sleeve P is 2.0 kg. If the system is released from rest with $\theta$ = 60°
1. using relative motion analysis between O and Q, derive an expression for the velocity of joint Q in
terms of the angular velocities of member OQ ($\omega_{OQ}$) and the angle ($\theta$). Express your result in unit
vector notation (i, j).
2. Using relative motion analysis between Q and P, derive an expression for the velocity of joint P in
terms of the angular velocities of members OQ ($\omega_{OQ}$) and PQ ($\omega_{PQ}$) as well as the angle ($\theta$). Express
your result in unit vector notation (i, j).
3. Show that
$\omega_{PQ} = -\omega_{OQ} = \omega$
(1)
$v_P = 2 \omega (1.2 \text{ m}) \sin(\theta)$
4. Using relative motion analysis, derive an expression for the velocity ($\vec{v}_G$) of the center of bar QP in
terms of ($\omega$) and the angular position ($\theta$).
5. Using the work energy principle (or equivalently the conservation of energy principle if it applies),
find the magnitude of the velocity of the sleeve P when $\theta$ = 40°.
Leave this space blank
Show all work and reasoning to receive full credit. You will also be graded on the quality of
the documentation including drawings, units, etc.
2
1.2 m
1.2 m
$\theta$
00
P
