PHY183-Lecture30pre

# PHY183-Lecture30pre - Equilibrium Conditions In chapter 4...

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1 March 20, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 30 Static Equilibrium Equilibrium Conditions In chapter 4 we explored the conditions for mechanical equilibrium We found that the necessary condition for mechanical equilibrium is the absence of a net external force In that case Newton’s First Law stipulates that an object in mechanical equilibrium stays at rest or moves with constant velocity But most often we want to explore the conditions that are needed for an object to stay at rest, in static equilibrium March 20, 2012 Physics for Scientists&Engineers 1 2 Equilibrium Conditions A famous example for such a collection of objects in static equilibrium is shown below Part of what makes this sculpture by Alexander Calder so amazing is that the eye does not want to accept that the configuration it is in is a stable static equilibrium March 20, 2012 Physics for Scientists&Engineers 1 3 Equilibrium Conditions The requirement of no translational or rotational motion means that the linear and angular velocities of this object are zero at all times Since the values of the linear and angular velocities do not change in time The linear and angular accelerations are zero at all times Static Equilibrium Condition 1: An object can stay in static equilibrium only if the net force acting on it is zero. Static Equilibrium Condition 2: An object can stay in static equilibrium only if the net torque acting on it is zero. Even if Newton’s First Law is satisfied and an object has no translational motion, it will still rotate if it experiences a net torque. March 20, 2012 Physics for Scientists&Engineers 1 4 net net 0 and 0 Fm a I τα == Equilibrium Conditions Torque is always defined with respect to a pivot point The pivot point is the intersection of the plane determined by the force and moment arm vectors and the axis of rotation When we compute the net torque, the pivot point must be the same for all forces For static equilibrium with zero net torque, the net torque has to be zero for any pivot point chosen A clever choice of pivot point can be the key to a quick solution For example, we can select the point where an unknown force acts as the pivot point Then the unknown force would not contribute to the net torque because it would have a zero moment arm March 20, 2012 Physics for Scientists&Engineers 1 5 Equilibrium Conditions March 20, 2012 Physics for Scientists&Engineers 1 6

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PHY183-Lecture30pre - Equilibrium Conditions In chapter 4...

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