Introduction to Mechanics Examples

A floor slab has an area of $180\ \text{m}^2$, while a façade tie carries a $24.0\ \text{kN}$ force directed $20^\circ$ above the horizontal. Classify the quantities.

A precast panel has mass $m=2500\ \text{kg}$. Determine its weight using $g=9.81\ \text{m/s}^2$.

A brace exerts $F=100\ \text{kN}$ at $30^\circ$ above the positive horizontal axis. Determine $F_x$ and $F_y$.

Two cables pull a ring with $40.0\ \text{kN}$ to the right and $30.0\ \text{kN}$ upward. Determine the resultant magnitude and direction.

Several cables meet at a compact roof-ring connection. The goal is only to determine the cable tensions from concurrent forces. Select the appropriate idealization.

Wind acts on a canopy and the design question is whether the canopy tends to rotate about its supports. Should the canopy be modeled as a particle or rigid body?

A chandelier pulls downward on its suspension cable with $8.00\ \text{kN}$. State the third-law partner force.

A draft calculation proposes $F=ma+v$, where $m$ is mass, $a$ is acceleration, and $v$ is velocity. Determine whether the equation can be physically valid.

A rigid frame is pulled by an $18.0\ \text{kN}$ force. First, the force is moved to another point on the same line of action. Then consider moving it to a parallel line $0.750\ \text{m}$ away. Determine when the two representations are statically equivalent.

An elevator car is accelerating upward at $1.20\ \text{m/s}^2$. A preliminary calculation proposes treating the resultant force as zero to determine the cable force. Is that static idealization valid?