Question

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

          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

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 θ = 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 (ωOQ) and the angle (θ). 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 (ωOQ) and PQ (ωPQ) as well as the angle (θ). Express
your result in unit vector notation (i, j).
3. Show that
ωPQ = -ωOQ = ω
(1)
vP = 2 ω (1.2 m) sin(θ)
4. Using relative motion analysis, derive an expression for the velocity (v⃗G) of the center of bar QP in
terms of (ω) and the angular position (θ).
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 θ = 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
θ
00
P

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