Chapter Two Physics

Mechanical equilibrium

*The state where no physical changes occur*; it is a state of steadiness. Whenever the net force on an object is zero, the object is said to be in mechanical equilibrium. For a suspended object at rest, the forces acting upward on the object must be balanced by other forces acting downward to make the vector sum equal zero.

What can you multiply one of the vectors by to get the resultant when the magnitude of two vectors are equal?

1.414

Force

A push or a pull, which is always required to change an objects state of motion.

Scalar quantity

A quantity that can be described by magnitude only and has no direction. Ex. Time, area, volume

Vector quantity

A quantity that need both magnitude and direction for a complete description. Ex. Force

Put these images in order from least to greatest tension.

A, B, D, C

If you push a spring down on a table does the force going into your hand increase or decrease?

Actually, it stays the same. The spring pushes up into your hand with as much force as you push down on the spring.

Scalers are always _________ whereas vectors are not necessarily.

Additive, because scalar cannot have opposing directions. Vectors can oppose and therefore subtract and not be additive.

Vector

An arrow that represents the magnitude and direction of a quantity.

Applying the parallelogram rule

As the angle between the supporting ropes increases, the tension increases.

On a straight road a car at a constant speed of 80 mph drives past you in a different lane. Your cruise control is set to 70 mph. Who is in mechanical equilibrium?

Both are because you are both driving at a constant speed in a straight line.

The parallelogram rule

Find the resultant of two nonparallel vectors. Construct a parallelogram wherein the two vectors are adjacent sides of the parallelogram shows a resultant.

Suppose you stand on two bathroom scales with your weight evenly distributed between the two scales. What is the reading on each of the scales? What happens when you stand with more of your weight on 1 foot than the other?

In the first case, the reading on each scale is half your weight. (The sum of the scale readings balances your weight, and the net force on you is zero.) In the second case, if you lean more on one scale than the other, more than half your weight will be read on that scale but less than half on the other. In this way they add up to your weight.

Consider a gymnast hanging from two rings. If she hangs with her weight evenly divided between the two rings, how would scale readings in both supporting ropes compare with her weight? Suppose she hangs with slightly more of her weight supported by the left ring. How would the scale on the right read?

In the first case, the reading on each scale will be half her weight. In the second case, when more of her weight is supported by the left ring, the reading on the right reduces to less than half her weight. But in both cases, the sum of the scale readings equals her weight

Static equilibrium

Mechanical equilibrium when an object is at rest.

Dynamic equilibrium

Mechanical equilibrium when an object is moving in a constant speed in a straight line path.

An airplane flies horizontally at constant speed in a straight line direction. Its state of motion is unchanging. In other words, it is in equilibrium. Two forces act on the plane one is the thrust of the propeller that pulls it forward. The other is the force of air resistance (air friction) that acts in the opposite direction. Which force is greater?

Neither, for both forces have the same strength. Call the thrust positive. Then the air resistance is negative. Since the plane is in equilibrium the two forces combine to equal zero.

Scientific unit of force

Newton (N)

Consider what would happen if you suspended a 10 N object midway along a very tight, horizontally stretched guitar string. Is it possible for the string to remain horizontal without a slight sag at the point of suspension?

No way! If the 10 N load is to hang in equilibrium, there must be a supporting 10 N upward resultant. The tension in each half of the guitar string must form a parallelogram with a vertically upward 10 N resultant. For a slight sag, the sides of the parallelogram are very, very long and the tension force is very large. To approach no sag is to approach an infinite tension.

Can an object under the influence of only one force be in equilibrium?

No, equilibrium is a state of no change. Only when there is no force at all, or when two or more forces combine to zero, can an object be in equilibrium.

Net force

The combination of all forces acting upon an object.

Applied forces

The forces are going in the same direction.

How is a support force produced on a book resting on a table?

The molecules in the table act like a spring. When you compress the molecules in the table by resting a book on top, they contract. While doing this they press up on the book with as much force as it is being pressed down by, much like a spring.

What would happen if friction accedes an applied force?

The object would slow down because it is no longer in equilibrium. The friction is greater than the force.

Resultant

The sum of two or more vectors.

Two sets of swings are shown on the back. If the children on the swings are of equal weights, the ropes of which swing are more likely to break?

The tension is greater in the ropes hanging at an angle. The angled ropes are more likely to break than the vertical ropes.

Support force

The upward force that balances the weight of an object on a surface. Also called 'normal force'. For an object to rest on the horizontal surface, the support force must equal the objects weight.

The Pythagorean theorem

This is how you find the resultant of two nonparallel vectors. *only* right triangle

How many forces act upon an objects supported by two vertical ropes?

Three.

When do you use the parallelogram rule?

Two *non-parallel* vectors.

In which scenario would the parallelogram rule be useful? One dimension, two dimension or three dimension?

Two dimension.

A falling object reaches terminal velocity. Is in in mechanical equilibrium?

Yes. The gravity and the air resistance are equal therefore it is in mechanical equilibrium.

What is the net force on a bathroom scale when a 110 pound person stands on it?

Zero, as the scale is at rest. The scale reads the support force (which has the same magnitude as weight), not the net force.

What is the net force of a rock you are holding in your hand?

Zero, because you are pushing upward on it with as much force as Earth's gravity pulls it down.