6. Intro to Forces (Dynamics)

Consider a simple truss consisting of three members forming a right triangle: member $AB$ is horizontal, member $AC$ is vertical, and member $BC$ is the hypotenuse. A load of $1000N$ is applied downward at joint $C$. If the truss is supported at $A$ (pinned) and $B$ (roller), which statement correctly describes the forces in members $AB$, $AC$, and $BC$, and whether they are in tension or compression?

Two objects of masses $m_1$ and $m_2$ are connected by a massless string and placed on a frictionless horizontal surface. If a horizontal force $F$ is applied to $m_1$, what is the tension in the string between the objects?

Which two external forces most commonly act on darts as they travel toward a dartboard?

An L-shaped object consists of three point masses, each of mass $m$, connected by light rods to form a right angle. If the lengths of the rods are $a$ and $b$, what is the moment of inertia of the system about an axis perpendicular to the plane and passing through the vertex of the L-shape?

In the truss shown, member $BD$ is connected to joints $B$ and $D$, and the truss is supported by a pin at $C$ and a roller at $A$. If a downward load of $10 \mathrm{kN}$ is applied at joint $B$, what is the force in member $BD$ and the horizontal and vertical components of the reaction at support $C$?

For the cantilever beam of length $L$ fixed at one end and subjected to a downward point load $F$ at its free end, what is the magnitude of the reaction force at the fixed support?

A rigid beam is supported by a pin at point C and an $A-36$ steel guy wire AB. If a downward force of $10 \mathrm{kN}$ is applied at the end of the beam, which of the following best describes the role of the guy wire AB in the system?

Three $250g$ masses are connected by massless, rigid rods to form a straight line and are suspended horizontally. If the system is in equilibrium and the tension in the leftmost rod is $T$, what is the value of $T$ in newtons? (Assume $g=9.8m/s^2$.)