Practice Test 6

A 1.8 m uniform beam is hinged at the left end and supports a 180 N sign at the right end. The beam’s weight is 90 N acting at its center. A cable attaches to the beam 1.8 m from the hinge and pulls at an angle $\theta$ above the beam, providing an upward component that creates counterclockwise torque. The beam remains horizontal, so clockwise and counterclockwise torques must balance. With zero angular acceleration, Newton’s First Law in rotational form requires $\sum \tau_{\text{hinge}}=0$. Based on the system described, which change increases the counterclockwise torque from the cable without changing the cable tension magnitude?

A horizontal beam of length $4.0,\text{m}$ is held in static equilibrium by two vertical support cables at its ends. A $300,\text{N}$ load hangs $1.0,\text{m}$ from the left end, and the beam’s own weight is negligible. The upward tensions $T_L$ and $T_R$ act at the left and right ends, respectively, and the load’s weight acts downward at its attachment point. Taking torques about the left end, the lever arm for $T_R$ is $4.0,\text{m}$ and for the load is $1.0,\text{m}$. The beam does not rotate, so Newton’s First Law in rotational form implies $\sum \tau_{\text{left}}=0$. Considering the forces acting on the object, calculate the force needed at a specific point to maintain equilibrium.