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3) System of two masses: kinetics and kinematics ( 40 pts ) Assume there is no gravity in this problem. Consider a system of two identical masses ( \( m_{1}=m_{2} \) ), connected by a massless rigid bar of length \( 2 l \). The center of mass (CM) is located along a frictionless track, along which it may move. The bar is also free to rotate around the CM. As shown in the figure, an external force \( \mathbf{F}_{\text {ext }} \) acts on one mass, and a constraint force \( \mathbf{N} \) from the track acts on the bar at the CM. The resulting velocity of mass 1 is \( \mathbf{v}_{\mathrm{CM}}+\boldsymbol{\omega} \times \boldsymbol{l} \hat{\mathbf{b}} \), where \( \hat{\mathbf{b}} \) is a unit vector attached to the bar. Below, write the requested quantities in terms of the quantities appearing above. You need not evaluate the cross products. In the linear momentum balance \( \mathbf{F}=m a_{\mathrm{Cm}} \), a) Identify \( \mathbf{F} \) ( 10 pts\( ) \) b) Identify \( m \) (5 pts) In the angular momentum balance \( \mathbf{M}_{\mathrm{CM}}=\dot{\mathbf{H}}_{\mathrm{CM}} \), c) Identify \( \mathbf{M}_{\mathrm{CM}}(5 \mathrm{pts}) \) d) Identify \( \mathbf{H}_{\mathrm{Cm}}(10 \mathrm{pts}) \) e) What is \( \dot{\hat{\mathbf{b}}} \) ? ( 10 pts\( ) \)

          3) System of two masses: kinetics and kinematics ( 40 pts )

Assume there is no gravity in this problem. Consider a system of two identical masses ( \( m_{1}=m_{2} \) ), connected by a massless rigid bar of length \( 2 l \). The center of mass (CM) is located along a frictionless track, along which it may move. The bar is also free to rotate around the CM. As shown in the figure, an external force \( \mathbf{F}_{\text {ext }} \) acts on one mass, and a constraint force \( \mathbf{N} \) from the track acts on the bar at the CM. The resulting velocity of mass 1 is \( \mathbf{v}_{\mathrm{CM}}+\boldsymbol{\omega} \times \boldsymbol{l} \hat{\mathbf{b}} \), where \( \hat{\mathbf{b}} \) is a unit vector attached to the bar.

Below, write the requested quantities in terms of the quantities appearing above. You need not evaluate the cross products.
In the linear momentum balance \( \mathbf{F}=m a_{\mathrm{Cm}} \),
a) Identify \( \mathbf{F} \) ( 10 pts\( ) \)
b) Identify \( m \) (5 pts)

In the angular momentum balance \( \mathbf{M}_{\mathrm{CM}}=\dot{\mathbf{H}}_{\mathrm{CM}} \),
c) Identify \( \mathbf{M}_{\mathrm{CM}}(5 \mathrm{pts}) \)
d) Identify \( \mathbf{H}_{\mathrm{Cm}}(10 \mathrm{pts}) \)
e) What is \( \dot{\hat{\mathbf{b}}} \) ? ( 10 pts\( ) \)

3) System of two masses: kinetics and kinematics ( 40 pts )

Assume there is no gravity in this problem. Consider a system of two identical masses ( m1=m2 ), connected by a massless rigid bar of length 2 l. The center of mass (CM) is located along a frictionless track, along which it may move. The bar is also free to rotate around the CM. As shown in the figure, an external force 𝐅ext acts on one mass, and a constraint force 𝐍 from the track acts on the bar at the CM. The resulting velocity of mass 1 is 𝐯CM+ω×l𝐛̂, where 𝐛̂ is a unit vector attached to the bar.

Below, write the requested quantities in terms of the quantities appearing above. You need not evaluate the cross products.
In the linear momentum balance 𝐅=m aCm,
a) Identify 𝐅 ( 10 pts)
b) Identify m (5 pts)

In the angular momentum balance 𝐌CM=𝐇̇CM,
c) Identify 𝐌CM(5 pts)
d) Identify 𝐇Cm(10 pts)
e) What is 𝐛̇̂̇ ? ( 10 pts)

Added by Lorenzo P.

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