9 Connected Bodies and Basic Mechanical Systems Free Online FlashCards

What properties are assumed for an ideal cable?

A massless, inextensible cable has constant length, carries tension along its length, and pulls but does not push.

How does tension vary along one continuous ideal cable?

For one continuous ideal cable passing over a frictionless, massless pulley, the tension has the same magnitude throughout.

What forces can a smooth contact exert?

A smooth contact exerts a normal force but no friction force.

What belongs on a body's free-body diagram?

Show only forces and moments acting on that body. A tension arrow points along the cable, away from the body.

Which forces are omitted from a system-level free-body diagram?

When bodies are combined into one system, internal forces cancel and are omitted; forces from the surroundings remain.

Is cable tension always equal to a suspended load's weight?

Tension is an unknown force, not automatically equal to a load's weight. It equals the weight only when the force balance supports that result.

What does a negative solved direction or acceleration indicate?

A negative result means the actual direction is opposite to the assumed positive direction.

What motion constraint links two bodies joined by one cable over a fixed pulley?

For coordinates chosen to increase their cable segments, the constant-length condition is $x_1+x_2=\text{constant}$, so $v_1+v_2=0$ and $a_1+a_2=0$.

What tension supports a stationary load on an ideal movable pulley with two supporting segments?

The two cable segments each pull upward with tension $T$, so equilibrium gives $2T-W=0$, or $T=\frac{W}{2}$.

How are free-end and load displacements related for a movable pulley?

The changing cable length is $x+2y=\text{constant}$, so the free end moves twice as far as the movable pulley, in the opposite direction.

What equations express static equilibrium for a rigid body in a plane?

A rigid body in static equilibrium satisfies $\sum \mathbf F=\mathbf 0$ and $\sum M_O=0$.

What force equation applies to a translating body that accelerates?

For a translating body, the resultant force equals mass times acceleration: $\sum \mathbf F=m\mathbf a$.