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College Physics for AP® Courses

Section Summary

College Physics for AP® CoursesSection 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 netF=0netF=0 size 12{F rSub { size 8{ ital "net"} } =0} {}.

9.2 The Second Condition for Equilibrium

  • 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
    τ = rF sin θ τ = rF sin θ size 12{τ= ital "rF""sin"θ} {}

    where ττ size 12{τ} {} is torque, rr size 12{r} {} is the distance from the pivot point to the point where the force is applied, FF size 12{F} {} is the magnitude of the force, and θθ size 12{θ} {} is the angle between FF size 12{F} {} and the vector directed from the point where the force acts to the pivot point. The perpendicular lever arm rr size 12{r rSub { size 8{ ortho } } } {} is defined to be

    r = r sin θ r = r sin θ size 12{r rSub { size 8{ ortho } } =r"sin"θ} {}

    so that

    τ=rF.τ=rF. size 12{τ=r rSub { size 8{ ortho } } F} {}
  • The perpendicular lever arm rr size 12{r rSub { size 8{ ortho } } } {} is the shortest distance from the pivot point to the line along which FF size 12{F} {} acts. The SI unit for torque is newton-meter (N·m)(N·m). The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero:
    net τ = 0 net τ = 0 size 12{"net "τ=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, both 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 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.
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