Chapter 2 Mechanical Equilibrium

Equilibrium refers to a condition of balance. Things in mechanical equilibrium are stable, without changes in motion. The rocks are in mechanical equilibrium. They will stay that way indefinitely unless an unbalanced external force would be needed to change their resting state.

2.1 Force Force - is a push or pull A force is needed to change an object’s state of motion State of Motion may be one of two things: At Rest Moving uniformly along a straight-line path

Net Force Net Force- is the combination of all forces acting on an object. Applied forces result in net forces The net force on an object changes its motion Can add or subtract forces to get resultant net force If forces acting on object equals zero then we say the net force acting on the object = 0 Scientific unit for force are Newtons (N)

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Force and Net Force When the girl holds the rock with as much force upward as gravity pulls downward, the net force on the rock is zero.

Tension and Weight Downward force caused by Earth’s gravity is known as weight. Upward “stretching force” is called tension. Ropes, chains, strings, etc…all can experience tension. When you hang an object from a spring scale there are two forces acting on the object: - force of gravity pulling down - tension force pulling upward When the two forces are equal and opposite in direction, their net force = 0N.

Force Vectors – visual representation of a quantity Forces can be represented by arrows length of arrow represents amount (magnitude) of the force direction of arrow represents direction of the force refer to these arrows as vectors, which represent both the magnitude and direction of a force.

Vector Quantity Scalar Quantity needs both magnitude and direction for a complete description. ex: force, velocity, momentum can be described by magnitude only and has no direction ex: temperature, speed, distance

Scalar or Vector Quantity? Time Interval Mass Speed Velocity Temperature Displacement Acceleration Click For The Answers scalar scalar vector scalar vector vector

2.2 Mechanical Equilibrium Mechanical Equilibrium is a state wherein no physical changes occur; it is a state of steadiness. When net force equals zero, an object is said to be in mechanical equilibrium. Expressed mathematically as the equilibrium rule: ΣF=0 Σ – Greek Letter, Stands for “ the sum of” F - Stands for “forces” 0 - all the forces acting on something add vertically to zero

Mechanical Equilibrium- a closer look The equilibrium rule explains how and why these men are able to remain balanced on their painting scaffold.

Mechanical Equilibrium- a closer look Each man’s weight is represented with downward vectors. Additionally the scaffold they’re standing on has weight.

Mechanical Equilibrium- a closer look The tension of the ropes holding both men and the scaffold is represented with the two upward arrows.

Mechanical Equilibrium- a closer look The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in Equilibrium.

2.3 Support Force Support Force- the upward force that balances the weight of an object on a surface. The upward force balances the weight of an object Support force often called normal force For an object at rest on a horizontal surface, the support force must equal the object’s weight. Support Force Weight (due to gravity)

2.3 Support Force The upward support force is considered positive and the downward weight is considered negative. The two forces add mathematically to zero. Another way to say the net force on the book is zero is F = 0. Support Force +2N Weight -2N +2N – 2N = 0 0N = Rest

2.4 Equilibrium of Moving Objects Equilibrium can exist in both objects at rest and objects moving at a constant speed, in a straight-line path. Equilibrium means state of no change. Sum of forces equal zero When the push on the desk is the same as the force of friction between the desk and the floor, the net force is zero and the desk slides at an unchanging speed.

Equilibrium of Moving Objects Static Equilibrium Dynamic Equilibrium Objects at rest are said to be in static equilibrium. Objects moving at a constant speed in a straight- line path are said to be in dynamic equilibrium.

2.5 Vectors Parallel Vectors Add vectors if in same direction Subtract vectors if in opposite direction The sum of two or more vectors is called the resultant same direction- add opposite direction- subtract

2.5 Vectors Non- Parallel Vectors The Parallelogram Rule - To find the resultant of nonparallel vectors, we use the parallelogram rule. - Consider two vectors at right angles to each other, as shown below. The constructed parallelogram in this special case is a rectangle. The diagonal is the resultant R.

Applying the Parallelogram Rule When Nellie is suspended at rest from the two non-vertical ropes, is the rope tension greater or less than the tension in two vertical ropes? You need to use the parallelogram rule to determine the tension. Notice how the tension vectors form a parallelogram in which the resultant R is vertical.

Applying the Parallelogram Rule Think! Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break?

Applying the Parallelogram Rule Think! Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break? Answer: The tension is greater in the ropes hanging at an angle. The angled ropes are more likely to break than the vertical ropes. - As Angles Increase, Tension Increases CLICK FOR ANSWER

Chapter 2 Mechanical Equilibrium

Equilibrium refers to a __________________________ Things in mechanical equilibrium are stable, without changes in motion. The rocks are in mechanical equilibrium. They will stay that way indefinitely unless an unbalanced external force would be needed to change their resting state.

2.1 Force Force - ___________________________ A force is needed to change an object’s ______________________ State of Motion may be one of two things: .

Net Force Net Force- ___________________ ________________________________ Applied forces result in net forces The net force on an object changes its motion Can add or subtract forces to get ______________ net force If forces acting on object equals zero then we say the net force acting on the object = 0 Scientific unit for force are ___________________( )

Net Force – a closer look Net Force depends on the ________________and _________________of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Net Force – a closer look Net Force depends on the magnitudes and directions of the applied forces.

Force and Net Force When the girl holds the rock with as much force upward as gravity pulls downward, the net force on the rock is zero.

Tension and Weight Downward force caused by Earth’s gravity is known as ______________. Upward “stretching force” is called ___________ Ropes, chains, strings, etc…all can experience tension. When you hang an object from a spring scale there are two forces acting on the object: - force of gravity pulling ____________ - tension force pulling ______________ When the two forces are equal and opposite in direction, their net force = 0N.

Force Vectors – visual representation of a quantity Forces can be represented ____________________________ length of arrow represents ___________________________________ direction of arrow represents _________________________________ refer to these arrows as vectors, which represent both the magnitude and direction of a force.

_________________ __________________ needs both magnitude and direction for a complete description. ex: force, velocity, momentum can be described by magnitude only and has no direction ex: temperature, speed, distance

Scalar or Vector Quantity? _________ Time Interval Mass Speed Velocity Temperature Displacement Acceleration _________ _________ _________ _________ _________ _________

2.2 Mechanical Equilibrium __________________________ is a state wherein no physical changes occur; it is a state of steadiness. When net force equals zero, an object is said to be in mechanical equilibrium. Expressed mathematically as the equilibrium rule: ΣF=0 Σ – ________________________________ F - _____________________ 0 - ________________________________

Mechanical Equilibrium- a closer look The equilibrium rule explains how and why these men are able to remain balanced on their painting scaffold.

Mechanical Equilibrium- a closer look Each man’s weight is represented with downward vectors. Additionally the scaffold they’re standing on has weight.

Mechanical Equilibrium- a closer look The tension of the ropes holding both men and the scaffold is represented with the two upward arrows.

Mechanical Equilibrium- a closer look The sum of the upward vectors equals the sum of the downward vectors. F = 0, and the scaffold is in Equilibrium.

2.3 Support Force Support Force- the upward force that balances the _______________________________________________________. The upward force balances the weight of an object Support force often called ________________________ For an object at rest on a horizontal surface, the support force must equal the object’s weight. Support Force Weight (due to gravity)

2.3 Support Force The upward support force is considered _________ and the downward weight is considered ____________. The two forces add mathematically to zero. Another way to say the net force on the book is zero is F = 0. Support Force +2N Weight -2N +2N – 2N = 0 0N = Rest

2.4 Equilibrium of Moving Objects Equilibrium can exist in objects both at rest and objects moving at a constant speed, in a straight-line path. Equilibrium means state of no change. Sum of forces equal zero When the push on the desk is the same as the force of friction between the desk and the floor, the net force is zero and the desk slides at an unchanging speed.

Equilibrium of Moving Objects _______________________ _______________________ Objects at rest are said to be in static equilibrium. Objects moving at a constant speed in a straight- line path are said to be in dynamic equilibrium.

2.5 Vectors Parallel Vectors Add vectors if in same direction Subtract vectors if in opposite direction The sum of two or more vectors is called the resultant same direction- add opposite direction- subtract

2.5 Vectors Non- Parallel Vectors The Parallelogram Rule - To find the resultant of nonparallel vectors, we use the parallelogram rule. - Consider two vectors at right angles to each other, as shown below. The constructed parallelogram in this special case is a rectangle. The diagonal is the resultant R.

Applying the Parallelogram Rule When Nellie is suspended at rest from the two non-vertical ropes, is the rope tension greater or less than the tension in two vertical ropes? You need to use the parallelogram rule to determine the tension. Notice how the tension vectors form a parallelogram in which the resultant R is vertical.

Applying the Parallelogram Rule Think! Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break?

Applying the Parallelogram Rule Think! Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break? Answer: