U10: Statics and Torque

Statics is the study of forces in equilibrium, a large group of situations that makes up a special case of Newton’s second law

● There are forces acting, but they are balanced

The first condition of equilibrium is that the net external force on the system must be zero

● Net F = 0

● The net external force in any direction is zero (along x and y-axis)

● An object in static equilibrium is motionless

● An object in dynamic equilibrium is moving with constant velocity

The second condition of equilibrium involves avoiding accelerated motion (so you want to maintain a constant angular velocity)

● A rotating body or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it

● Torque is the rotational equivalent of a force

○ It is a measure of the effectiveness of a force in changing or accelerating a rotation

○ 𝜏 = 𝑟𝐹 𝑠𝑖𝑛𝜃

■ R is the distance from the pivot point to the point where the force is applied

■ 𝜃 is the angle between the force and the vector directed from the point of application to the pivot point

○ An alternate expression for torque is given in terms of the perpendicular lever arm

■ 𝜏 = 𝒓 ⊥ 𝑭

○ The SI unit of torque is newtons times meters (N x m)

○ Torque is always calculated with reference to some chosen pivot point

■ Torque is either clockwise or counterclockwise relative to the chosen pivot point

The third condition necessary to achieve equilibrium is that the net external torque on a system must be zero

● An external torque is one that is created by an external force

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 to the direction of the displacement

● Ex: an object experiencing a restoring force

A system is in unstable equilibrium if, when displaced, it experiences a net force or torque in the same direction as the displacement from equilibrium

● Ex: a ball resting on top of a hill that is displaced

A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position

● Ex: a marble on a flat horizontal surface

These are the steps to take for solving static equilibrium problems:

● Determine whether or not the system is in static equilibrium

○ The acceleration of the system is zero and accelerated rotation does not occur

● Draw a free body diagram for the system of interest

○ Label all forces and note their relative magnitudes, directions, and points of application

● Apply either or both of the conditions for equilibrium

○ net F = 0 and net 𝜏 = 0

● Check the solution to see if it is reasonable

○ Examine the magnitude, direction, and units of the answer

Mechanical advantage is the ratio of output to input force magnitudes for any simple machine

● 𝑀𝐴 = 𝐹o/𝐹i