Dynamics.September 2012

Objectives.

To describe how a force affects the motion of an object.

To interpret and construct free body diagrams.

To recognize Newton's laws of motion in real life situations.

Force

When you push a grocery cart, a motor lifts an elevator, or a hammer hits a nail, a force is being exerted.

If an object is at rest, to start it moving requires force, that is a force is needed to accelerate an object from zero velocity to moving.

A force exerted in different directions has a different effect. So force has a direction as well as magnitude, and is indeed a vector.

Intuitively, Force is any kind of push or pull on an object.

Newton’s First Law of Motion

Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

The tendency of an object to maintain its state of rest or uniform motion in a straight line is called inertia.

http://www.youtube.com/watch?v=Q0Wz5P0JdeU&feature=related

Example

http://www.stevespanglerscience.com/experiment/egg-drop-inertia-trick

Watch the following video and then discuss it in groups.

Share your comments with the rest of the group

You may try this at home, if and only if, you clean any mess you make.

Newton’s Second Law of Motion

The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.

∑ 𝐹→

=𝑚𝑎→

http://www.youtube.com/watch?v=WzvhuQ5RWJE&feature=related

From Newton’s second law we can make a more precise definition of force as an action capable of accelerating an object.

In SI units, the unit of force is called newton (N)

One Newton is the force required to impart an acceleration of 1 m/ to a mass of 1kg.

Thus 1N=1kg* m/

Definition of Force

Other units of force are the dyne (g*cm/) and pound (lb)

The tablecloth trick.

For next class please bring the following materials per team:

• Tablecloth• A full bottle of water (Closed)• Unbreakable dinner plates, saucers (The

heavier the better)• Spoons (metallic preferably)

Perform the magician’s tablecloth trick.

Explain your results according to Newton’s first law of movement.

Example: Force to stop a car

What average net force is required to bring a 1500 kg car to rest from a speed of 100 km/h within a distance of 55m.

Hint: first use the kinematic equation:

Solution: -1.1 x N

Newton’s Third Law of Motion

Whenever an object exerts a force on a second object, the second exerts an equal force in the opposite direction of the first.

This law is sometimes paraphrased as “to every action there is an equal and opposite reaction” This is perfectly valid. But to avoid confusion it is very important to remember that the “action” force and the “reaction” force are acting on different objects.

http://www.youtube.com/watch?v=cP0Bb3WXJ_k&feature=related

Activity

In groups discuss:

• What exerts the force on a car? • What makes the car go forward?

Share your results with the rest of the group.

http://www.youtube.com/watch?v=r8E5dUnLmh4&feature=related

Mass & Weight

The magnitude of the force of gravity on an object is commonly called the object’s weight.

An object’s weight will vary according to the force of gravity effects on different planets or in space.

For example de acceleration due to gravity on the moon is about one sixth the one on Earth.

The Normal Force

The net force on an object at rest is zero according to Newton’s Laws. Therefore the downward force of gravity on an object must be balances by an upward force. When a contact force acts perpendicular to the common surface of contact, it is referred to as the Normal Force.

Free-body Diagram

When solving problems involving Newton’s laws and force, it is important to draw a diagram showing all the forces on each object involved. Such diagram is called a free-body diagram.

Choose one object, and draw an arrow to represent each force acting on it. If the problem involves more than one object, a separate free-body diagram is needed for each object.

Practice

Pull a 10.0 kg box with a cord as shown on the figure. The magnitude of the force is 40.0 N and is exerted at a 30F angle. Calculate the acceleration of the box, and the magnitude of the upward force exerted by the table on the box.

Hint: Draw a free body diagram like this:

Solve for components of the force pulling the box.

Now apply Newton’s Second Law in x to find the acceleration.

The acceleration of the box is 3.46 m/to the right.

Next we solve for the vertical components to find .

Note that the normal force is lower than the weight because part of the pull of the cord is in the upward direction.

Two boxes connected by a cord.

Two boxes connected by a light cord (weightless) are resting on a frictionless table. The boxes have a mass of 12 kg and 10 kg. A horizontal force of 40.0 N is applied to the 10 kg box as shown. Find the acceleration of each box and the tension in the cord connecting the boxes.

Acceleration = 1.82 m/ Tension = 21.8 N

Friction

Friction exists between two solid surfaces because of its roughness. Even the smoothest looking surface is quite rough on a microscopic scale.

Sliding friction is usually called kinetic friction (kinetic is from the Greek for moving).

When an object slides along a rough surface, the force of kinetic friction acts opposite to the direction of the object’s velocity.

Experiments show that the friction force is approximately proportional to the normal force between the two surfaces. In many cases depends very little on the surface of contact so we can write the proportionality as an equation inserting a constant of proportionality.

So Kinetic Friction:

The term is called the coefficient of kinetic friction, and its value depends on the nature of the two surfaces.

There is also static friction, which refers to a force parallel to the two surfaces that can arise even when they are not sliding.

Suppose you are pushing a desk and it does not move. You are exerting a force on the desk, but it isn’t moving so there must be another force on the desk keeping it from moving. (The net force is zero on an object that doesn’t move). This is the force of static friction exerted by the floor on the desk.

If you push hard enough, the desk will eventually move, and kinetic friction takes over.

So Static Friction:

𝑭 𝒇𝒓 ≤𝝁𝒔 𝑭 𝑵

PracticePull a 10.0 kg box with a cord as shown on the figure. The magnitude of the force is 40.0 N and is exerted at a 30F angle. Calculate the acceleration of the box. This time assume a coefficient of kinetic friction of 0.30.

Solution: 1.1 m/

Inclines

www.youtube.com/watch?v=EgXOVGjIeyI

The inclined plane is one of the original six simple machines. It is a flat surface whose endpoints are at different heights. By moving the object up the plane rather than vertically the amount of force needed is reduced at the expense of increasing the distance the object is moved.

Problem Solving Using Inclines

Solving problems is usually easier if we chose the xy coordinate system so the x axis points along the incline and the y axis is perpendicular to the incline as shown in the figure.

Remember that the normal force is not vertical but perpendicular to the sloping surface of the plane, yet weight is indeed vertical and pointing down.

SkiingThe skier in the figure has just begun descending the 30F slope. Assuming the coefficient of kinetic friction is 0.10, calculate (a) her acceleration and (b) the speed she will reach after 4.0 s.

Solution: a= 4 m/ V=16 m/s

Activity

Watch the following video about static friction:

www.youtube.com/watch?v=jSu0Tvlm6LY&feature=related

www.youtube.com/watch?v=QMW_uYWwHWQ&feature=related

Then answer the questions.

Questions1. What are the wooden clamps for?

2. In the first tug-o-war Adam and Jaime find that the main problem is traction, explain why?

3. What is the scale measuring?

4. What was the problem with using cars to pull the interleaved books?

5. What was the equivalent force needed to separate the books equivalent to?

6. Can you think of another real life situation where friction plays an important role?

References

• Giancoli , Douglas C. Physics Sixth Edition. USA Pearson 2005

• Serway, Raymond A. Essentials of College Physics. USA Thomson 2007