Section Summary

8.1 Static Equilibrium Revisited

• 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 [latex]\text{net}\phantom{\rule{0.25em}{0ex}}\mathbf{F}=0[/latex].

8.2 Torque

• The second condition assures those torques are also balanced. Torque is the rotational equivalent of a force in producing a rotation and is defined to be
  [latex]\tau =\text{rF}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta[/latex]

  where [latex]\tau[/latex] is torque, [latex]r[/latex] is the distance from the pivot point to the point where the force is applied, [latex]F[/latex] is the magnitude of the force, and [latex]\theta[/latex] is the angle between [latex]\mathbf{\text{F}}[/latex] and the vector directed from the point where the force acts to the pivot point. The perpendicular lever arm [latex]{r}_{\perp }[/latex] is defined to be

  [latex]{r}_{\perp }=r\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta[/latex]

  so that

  [latex]\tau ={r}_{\perp }F.[/latex]
• The perpendicular lever arm [latex]{r}_{\perp }[/latex] is the shortest distance from the pivot point to the line along which [latex]F[/latex] acts. The SI unit for torque is newton-meter [latex]\text{(N·m)}[/latex]. The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero:
  [latex]\text{net}\phantom{\rule{0.25em}{0ex}}\mathbf{\tau }=0[/latex]

  By convention, counterclockwise torques are positive, and clockwise torques are negative.

8.3 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.

8.4 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, both the general problem-solving strategies and the special strategies for Newton’s laws, discussed in Chapter 4.5: Problem-Solving Strategies, still apply.

8.5 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.

8.6 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 a way that the person’s center of gravity lies directly above the pivot point in the hips, thereby avoiding back strain and damage to disks