2.1 Force

A force is a push or pull. A force of some kind is always required to change the state of motion of an object.

• Ex. A hockey puck at rest on ice remains at rest until a force is exerted on it. Once moving, it slides along the ice and will continue sliding until a force slows it down.

A force is needed to change an objects state of motion.

Most often, more than one force acts on an object, the combination of all forces acting on an object is called the net force. The net force on an object changes its motion.

Tension & Weight -

• Ex. If you tie a string around a 2-pound bag of sugar and suspend it from the scale, a spring in the scale stretches until the scale reads 2-pounds. The stretched spring is under “stretching force” called tension.

Force Vectors -

A vector is an arrow that represents the magnitude and direction of a quantity. A vector quantity is a quantity that needs both magnitude and direction for a complete description (force is an example of a vector quantity). In contrast, a scalar quantity is a quantity that can be described by magnitude only and has no direction (like time, area, and volume).

2.2 Mechanical Equilibrium

Mechanical Equilibrium is a state wherein no physical changes occur; it is a state of readiness. Whenever the net force on an object is zero, the object is said to be in mechanical equilibrium—this is known as the equilibrium rule (ΣF = 0)

2.3 Support Force

• Ex. Consider a book lying at rest on a table. The book is in equilibrium, one force of the book is due to gravity—the weight of the book. Since the book is in equilibrium, there must be another force acting on it to produce a net force of zero—an upward force opposite of the force of gravity.

We call this support force—the upward direction that balances the weight of an object on a surface. A support force is often called the normal force.

For an object at rest on a horizontal surface, the support force must equal the objects weight.

In this case, the support force must equal the weight of the book. The support force is positive and the downward weight is negative.

2.4 Equilibrium for Moving Objects

When an object isn’t moving, its in equilibrium. The forces on it add up to zero, but the state of rest is only one form of equilibrium. An object moving at a constant speed in a straight-line is also in a state of equilibrium. Once in motion, if there is no net force to change the state of motion, its in equilibrium.

An object with only one force acting on it cannot be in equilibrium. Net force in that case is not zero.

Only when there is no force, or two or more forces combine to zero can an object be in 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

If they are in the same direction, they add. If they are in opposite directions, they subtract. The sum of two or more vectors is called their resultant.

Practice Problems

2.1 -

1. What is the difference between force and net force on an object?

   1. A force is just a push or pull on an object, a net force is when all forces involved with the object are acting on it at the same time.

2. What is the net force of a box that is being pulled to the right with the force of 40N and pulled to the left with a force of 30N?

   1. 10N —> 40N-30N=10N

3. What name is given to the stretching force that occurs in a spring or rope being pulled?

   1. Tension

4. What two quantities are necessary to determine a vector quantity?

   1. Magnitude and Direction

5. How does a vector quantity differ from a scalar quantity?

   1. A vector quantity needs both magnitude and direction to be complete but a scalar quantity only needs magnitude

2.2 -

1. How much tension is in a rope that holds up a 20N bag of apples at rest?

   1. 20N

2. What is ΣF = 0?

   1. The equilibrium rule equation; the sum of force is equal to zero

3. What is the net force on an object at rest?

   1. Zero; if there are zero forces acting on the object then the net force is zero

4. When you do pull-ups and you hang at rest, how much of your weight is supported by each arm?

   1. an equal but divided amount on each arm, if you weigh 100lbs then each arm is supporting 50lbs

2.3 -

1. What is the angle between a support force and the surface force on object rests upon?

   1. Horizontal

2. What two forces compress a spring inside a weighing scale when you weigh yourself?

   1. Tension (upwards) and Weight (downwards)

2.4 -

1. Can an object be moving and still be in equilibrium?

   1. Yes, if the object is at a constant straight-lined direction then it can remain in equilibrium. The only way it wouldn’t be able to is if an external force acts on the object and if the direction changes while in motion.

2. Distinguish between static equilibrium and dynamic equilibrium?

   1. Static equilibrium is when an object is at rest and dynamic equilibrium is when an object is going in a straight-lined direction in a constant speed

2.5 -

1. According to the parallelogram rule for two vectors, what does the diagonal of a constructed parallelogram represent?

   1. The resultant

2. Consider the suspension of Nellie in Figure 2.11. Name all three forces acting on her. What is your evidence that they cancel to zero?

   1. the weight of both her right(1) and left arm(2) and the tension (3). They cancel to zero because the tension (upwards force) in the rope must be equal to her weight (downwards force)

Think & Explain Practice

• A cat lies on the floor. Can you say that no force acts on the cat? Or is it correct to say no net force acts on the cat? Explain.

  • There are forces on the cat, one being the support force (upwards force) from the floor and the cats weight (downward force). But there is no net force because the cat isn’t changing its motion, its at rest.

• Consider two forces, one having a magnitude of 20N and the other a magnitude of 12N. What is the maximum net force possible for these two forces? Minimum?

  • The maximum force is 32N, minimum is is 8N

• Faina says that an object cannot be in mechanical equilibrium when only a single force acts on it. Do you agree or disagree?

  • I disagree, for an object to be in mechanical equilibrium there must be a net force of zero because of the equilibrium rule—whenever the net force on an object is zero, the object is said to be in mechanical equilibrium.

• How many significant forces act on your physics book when it rests on a table? Identify the forces.

  • Support force (upwards/opposite force)

  • Weight (downward force/gravity)

• Why doesn’t the support force that acts on a book resting on a table cause the book to rise from the table?

  • Because the support force is only exerting as much force/the equal amount of force that is being pushed down on it. Equal but opposite. If it were to cause the book to rise off the table then the support force wouldn’t be equal to the weight of the book.

• Alyssa pulls horizontally on a crate with a force of 200N, and it slides across the floor at a constant speed in a straight line. How much friction is acting on the crate?

  • The friction would be 200 because as long as its at a constant speed then the force of friction is equal in magnitude but still opposite in direction of whichever direction the crate is being pushed.

• Lucy Lightweight stands with one foot on one bathroom scale and the other foot on the second bathroom scale. Each scale reads 300N. What is Lucy’s weight?

  • 600 Newtons

• Harry Heavyweight, who weighs 1200N, stands on a pair of bathroom scales so that one scale reads twice as much as the other. What are the scale readings?

  • 400N & 800N