Sections

Section Summary
# Section Summary

### 9.1 The First Condition for Equilibrium

- Statics is the study of forces in equilibrium.
- Two conditions must be met to achieve equilibrium, which is defined to be motion without linear or rotational acceleration.
- The first condition necessary to achieve equilibrium is that the net external force on the system must be zero, so that $\text{net}\phantom{\rule{0.25em}{0ex}}\mathit{F}=0$.

### 9.2 The Second Condition for Equilibrium

- The second condition ensures those torques are also balanced. Torque is the rotational equivalent of a force in producing a rotation and is defined to be
$$\tau =\text{rF}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\mathrm{\theta ,}$$
where $\tau $ is torque, $r$ is the distance from the pivot point to the point where the force is applied, $F$ is the magnitude of the force, and $\theta $ is the angle between $F$ and the vector directed from the point where the force acts to the pivot point. The perpendicular lever arm ${r}_{\perp}$ is defined to be

$${r}_{\perp}=r\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\mathrm{\theta ,}$$so that

$$\tau ={r}_{\perp}F.$$ - The perpendicular lever arm ${r}_{\perp}$ is the shortest distance from the pivot point to the line along which $F$ acts. The SI unit for torque is "newton times meter"? $\text{(N\xb7m)}$. The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero
$$\text{net}\phantom{\rule{0.25em}{0ex}}\tau =0.$$
By convention, counterclockwise torques are positive, and clockwise torques are negative.

### 9.3 Stability

- A system is said to be in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite the direction of the displacement.
- A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium.
- A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.

### 9.4 Applications of Statics, Including Problem-Solving Strategies

- Statics can be applied to a variety of situations, ranging from raising a drawbridge to bad posture and back strain. We have discussed the problem-solving strategies specifically useful for statics. Statics is a special case of Newton's laws; the general problem-solving strategies and the special strategies for Newton's laws, discussed in Problem-solving Strategies, still apply.

### 9.5 Simple Machines

- Simple machines are devices that can be used to multiply or augment a force that we apply, often at the expense of a distance through which we have to apply the force.
- The ratio of output to input forces for any simple machine is called its mechanical advantage.
- A few simple machines are the lever, nail puller, wheelbarrow, crank, etc.

### 9.6 Forces and Torques in Muscles and Joints

- Statics plays an important part in understanding everyday strains in our muscles and bones.
- Many lever systems in the body have a mechanical advantage of significantly less than one, as many of our muscles are attached close to joints.
- Someone with good posture stands or sits in such as way that his or her center of gravity lies directly above the pivot point in the hips, thereby avoiding back strain and damage to discs.