AP Physics C: Static Equilibrium Questions and Answer Key

📚 Quick Study Guide

• ⚖️ Definition: Static equilibrium means an object is not moving (translational equilibrium) and not rotating (rotational equilibrium).
• 🍎 Conditions: For an object to be in static equilibrium:
  • The net force acting on the object must be zero: $\sum \vec{F} = 0$
  • The net torque acting on the object must be zero: $\sum \vec{\tau} = 0$
• 📐 Torque: Torque is the rotational equivalent of force. It depends on the force applied, the distance from the axis of rotation, and the angle between the force and the lever arm.
  • $\tau = rF\sin(\theta)$ where:
    • $\tau$ is the torque
    • $r$ is the distance from the axis of rotation to the point where the force is applied
    • $F$ is the magnitude of the force
    • $\theta$ is the angle between the force vector and the lever arm.
• 💡 Problem-Solving Strategy:
  • Draw a free-body diagram showing all forces acting on the object.
  • Choose a convenient coordinate system.
  • Resolve forces into components along the axes.
  • Apply the equilibrium conditions: $\sum F_x = 0$, $\sum F_y = 0$, and $\sum \tau = 0$.
  • Solve the resulting equations to find the unknowns.
• 🧱 Center of Gravity: The point where the weight of an object can be considered to act. For uniform objects, it's at the geometric center.

Practice Quiz

1. A uniform beam of length $L$ and weight $W$ is supported by two vertical ropes at its ends. What is the tension in each rope?
   1. $W/4$
   2. $W/2$
   3. $W$
   4. $2W$
2. A sign of weight $W$ is hung from a uniform beam of length $L$ as shown. The beam is supported by a hinge and a cable. Which of the following is necessary for the system to be in static equilibrium?
   1. The sum of the forces in the x-direction must be zero.
   2. The sum of the forces in the y-direction must be zero.
   3. The sum of the torques about any point must be zero.
   4. All of the above.
3. A ladder leans against a smooth wall. The floor is rough. What force prevents the ladder from sliding?
   1. Normal force from the wall
   2. Normal force from the floor
   3. Frictional force from the floor
   4. Gravitational force
4. A mass $m$ hangs from the end of a uniform bar of length $L$ and mass $M$, which is pivoted at one end. What is the torque due to gravity about the pivot point?
   1. $mgL$
   2. $MgL$
   3. $(m + M)gL$
   4. $mgL + \frac{1}{2}MgL$
5. An object is in static equilibrium. If the sum of the external forces is zero, what else must be true?
   1. The object is not moving.
   2. The sum of the external torques is zero.
   3. The object has constant angular velocity.
   4. The object has a non-zero net force.
6. A seesaw is balanced with two children of different weights. Which of the following is true about the torques exerted by the children?
   1. The torques are equal in magnitude and direction.
   2. The torques are equal in magnitude but opposite in direction.
   3. The heavier child exerts a greater torque.
   4. The lighter child exerts a greater torque.
7. A tightrope walker is standing on a rope. The tension in the rope is $T$. What is the net force on the tightrope walker?
   1. $T$
   2. $2T$
   3. $0$
   4. $mg$