Dynamics

• Kinematics (Chs.2&3) is the study of how things move.
• Dynamics is the study of why things move.
• Consider this “thought experiment”:
• James Bond is standing still in the middle of an ice-covered lake.
• If the surface and the bottoms of his shoes were both perfectly slippery, no stickiness at all, would he be able to move?
• What if someone threw him a rope?

System, Environment, External Interactions.

• A system is the object or group of objects that we choose to analyze. We often draw a little dashed line around the system.
• Everything outside that system is called its environment and consists of objects that might interact with the system (touch, push, or pull it) and affect its motion through external interactions.

What is a force?

• A force is a physical quantity that characterizes how hard and in what direction an external object pushes or pulls on the system.
• We say that an external object exerts a force on the system.
• From the system’s perspective, it has a force exerted on it
• A force is either a contact force (like normal) or a long-range force (like gravity).
• The S.I. unit of force is the Newton (N)

Drawing force vectors

• The sum of the force vectors is not a new force being exerted.
• Rather, it is the combined effect of all the forces being exerted on the system.
• Because of this, the resultant vector should never be included in the free body diagram for that system.

Newton’s First Law of motion

1

A body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force.

What is Mass?

• Mass is a scalar quantity that describes an object’s inertia.
• It describes the amount of matter in an object.
• Mass is an intrinsic property of an object.

• It tells us something about the object, regardless of where the object is, what it’s doing, or whatever forces may be acting on it.

Newton’s Second Law of motion

2

The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.

From this morning’s preclass survey

• Question: When you walk on the floor, is the force of the floor acting on your feet that pushes you forward friction? If it is friction, is there another friction that pushes backward and hampers your motion but smaller than the first friction? Should the two forces be considered as just one force (the friction of the floor acting on your feet) ?
• Harlow answer: This is jumping ahead to Chapter 5 material!
• But, since you ask, yes, friction is the force that pushes you forward when you walk (this is called static friction).
• Static friction is the main force in physics we will put on the free-body diagram for propulsion in walking. We don’t often add a backward force in our model.
• But there certainly are small “dissipative forces” which generate heat and act against your forward motion. Drag force from air resistance is one. Also the squishing of the soles of your shoes create heat, compression of the surface you are walking on, even the friction in your joints and rustling of your clothes all takes away your forward kinetic energy and converts it to lost heat.

​

​

Observing a bowling ball: 1

Situation 1: Large initial velocity to the right.

No pushing force. Small friction force from the floor acting opposite to the velocity.

​

Result: Velocity is almost constant. Slow deceleration.

Free-body diagram:

Net force:

Acceleration:

Observing a bowling ball: 2

Situation 2: No initial velocity.

Pushing force to the right from a meter stick. Small friction force from the floor acting opposite to the velocity once it is rolling.

​

Result: Velocity is increasing – the bowling ball keeps speeding up.

Free-body diagram:

Net force:

Acceleration:

Observing a bowling ball: 3

Situation 3: Large initial velocity to the right.

Pushing force to the left from a meter stick. Small friction force from the floor acting opposite to the velocity.

​

Result: Bowling ball slows down fairly quickly, then eventually reverses velocity.

Free-body diagram:

Net force:

Acceleration:

List of Forces you might encounter

The forces we deal with most often in PHY131/132 are:

• Gravitational Force
• Normal Force
• Tension
• Kinetic Friction
• Static Friction
• Spring Force
• Drag force (fluid resistance)

• Electric
• Magnetic
• Thrust (like from a rocket)
• Muscle

Normal Force

“The table exerts an upward normal force on Harlow.”

Tension Force

“The rope exerts a tension force on Harlow.”

Gravity Force (a.k.a “weight”)

“The Earth exerts a gravity force on the Angry Bird.”

Note:

• The direction “down” varies with position.
• “Down” means toward the centre of the Earth.

Example. A wagon has a mass of 50 kg, and you pull it to the right with a rope with a tension force of 100 N, at an angle of 30° above the horizontal. The wagon accelerates to the right.

(a) What is the normal force of the floor on the wagon?

(b) Assume there are no friction forces acting backward on the wagon. What is its acceleration?

y

x

Newton’s Third Law of motion

3

Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts.

Forces always come in pairs.

• Every force interaction involves two objects, and two forces.
• These forces
• are equal in strength and opposite in direction.
• are always the same kind of force (ie gravity, normal, friction, tension, etc.)
• always act on different objects.

From this morning’s preclass survey

NO!

From the Preclass Survey

• Q: When we're drawing free-body diagrams on the test, do we need to always put on the force of gravity and normal force that acts on the object
• Harlow Answer: Yes! Please put all non-negligible external forces, even if they cancel.
• Q: Is there a maximum amount of tension an object can have and how do we determine it?
• Harlow Answer: Yes! When the fish is too big, the line breaks and that fish gets away! But there is no formula to determine the maximum tension. You have to look it up for a particular rope with specific age and wear.
• Q: In high school I was taught that the normal force originates from electrostatic repulsion on the atomic level, as opposed to the deformation approach taken in this text. Are any of these "more" or "less" correct?
• Harlow Answer: Both are correct. The fundamental force behind Normal is electrostatic. Also the surface deforms.

​

​

Forces always come in pairs.

• Every force interaction involves two objects, and two forces.
• These forces
• are equal in strength and opposite in direction.
• are always the same kind of force (ie gravity, normal, friction, tension, etc.)
• always act on different objects.

Newton’s Third Law of motion

• A truck is pushing a car up an incline with a constant forward acceleration.
• The incline has an angle θ with respect to the horizontal.
• Note: the car and the truck remain in contact during this acceleration.
• In this situation, as in ALL situations, Newton’s Third Law is true.
• The force of the truck on the car is equal to the force of the car on the truck.

Tell the truth: Do you believe it?

• Imagine a compressed spring between the truck and car.
• The spring has negligible mass compared to the truck or car.
• The spring is symmetric; it doesn’t know the difference between its left and right end.
• So it pushes with an equal force on the truck and car.

Draw Free Body Diagrams for the Truck and Car.

Identify the Interaction Pair that links the two objects.

Last time I asked:

• There is an old fable:
• A farmer has a donkey.
• Every morning the donkey pulls a wagon from the shed to the field.
• The donkey begins to take PHY131 (the asynchronous section, so he can do it in the evenings).
• One morning, the donkey refuses to pull the wagon.
• The farmer asks him what is wrong, and the donkey replies, “Professor Harlow says that according to Newton’s Third Law, if I exert a forward force on the wagon, the wagon will exert an equal magnitude force backwards on me. So I can never accelerate the wagon!”
• What is the flaw in the donkey’s reasoning?

First sentence is correct: the wagon really does pull back on the donkey with an equal opposite force that the donkey pulls on the wagon!

Second sentence is not correct: forces cannot cancel each other if they are on different objects.

The forward static friction on the donkey’s feet is larger than the backward rolling friction on the wheels of the wagon, so the system of Donkey and the wagon has a forward net force, provided by the Earth (static friction). That is why they both can accelerate.

​

​

Donkey’s reasoning: “Professor Harlow says that according to Newton’s Third Law, if I exert a forward force on the wagon, the wagon will exert an equal magnitude force backwards on me. So I can never accelerate the wagon!”

​

​

Car/Earth Friction Interaction

• Consider an accelerating car.
• The tires of the car are pushing backward on the Earth (static friction).
• The Earth is pushing forward on the tires of the car (static friction).

Rocket/Gas Pressure Interaction

• Consider a rocket accelerating upward.
• The rocket is pushing down on the expelled gas (pressure).
• The expelled gas is pushing up on the rocket (pressure).

This morning’s Preclass Survey

A cart of mass M is on a track which is at an angle of θ above the horizontal.

The cart is attached to a string which goes over a pulley; the other end of the string is attached to a hanging mass, m.

What is the acceleration of the cart?

REPRESENT MATHEMATICALLY

Two 100 N weights are attached to a spring scale as shown. What does the scale read?

1. 0
2. 100 N
3. 200 N
4. Some other reading

• Christina: Can you explain again top hat question #4 in our last class? I’m still confused about how the spring works.

Thought Experiment (1 of 3)

• Let’s go through three steps.
• Step 1: If that spring-scale was attached to the ceiling, what do you think it would read?
• Let’s hope it reads 100 N, or it’s not a very good spring-scale!

Ceiling

Thought Experiment (2 of 3)

• Step 2: Tilt the same spring-scale on its side, and attach it to a fixed wall instead of a ceiling.
• NOTE: A pulley takes that tension force and curves it around a corner without changing the magnitude of the force.
• What do you think the spring scale would read?

​

WALL

Thought Experiment (3 of 3)

• Step 3: Now replace the fixed wall with another hanging mass which balances the first one.
• Now what do you think the spring scale would read?
• How is the spring scale supposed to know if it’s attached to a wall or a hanging mass at its top?

• A string is attached to the rear-view mirror of a car. A ball is hanging on the other end of the string. The car is accelerating to the left in this diagram.
• You measure the angle that the ball hangs is θ to the right of vertically down.
• What is the acceleration of the car?

Let’s take it a little farther…

Assume: The windows are rolled up, so inside the car there is very little wind.

Ropes and Pulleys

• The tension in a taught string or rope is a positive scalar number, T, in Newtons.
• If we can neglect the mass of the string compared to the other objects in the problem, each end of the string pulls inward with the same force, of magnitude T.

• If the string is wrapped over a frictionless pulley, and we can neglect the mass of the pulley, then the string has the same tension T on both sides of the pulley.

Mass B has mass m_B = 3.5 kg.

Mass A has mass m_A = 13.2 kg.

What is the acceleration of Mass B?

In Practicals This Week!

You have to find the angle, θ, for which the cart and hanging mass are in equilibrium (no acceleration). Assume no friction.

Fundamental Interactions

• Forces are interactions.
• The forces we experience all can be explained by four fundamental interactions in nature:
• Gravity
• Electromagnetism
• Weak Interaction
• Strong Interaction

Gravity

• Gravity is an extremely long range force that attracts any two massive objects.
• When you are living near a very massive object, such as the 6 x 10²⁴ kg Earth, there is a dominant gravity force that pulls all objects toward the centre of that mass.

What are we made of?

• Atoms are the building blocks of all matter
• They are too small to be seen with visible light
• One gram of water has a volume of 1 cm³ and contains more than 10²³ atoms!

• These are scanning tunneling microscope images of graphite taken by Loji Thomas and Michael Reichling at Osnabrück University in Germany.
• The dots are individual carbon atoms

• Atomic structure is composed of:
• An atomic nucleus, which contains nearly all the mass
• Orbiting electrons
• The nucleus is composed of protons and neutrons, which are in turn made of smaller quarks

[Image retrieved Jan.10, 2013 from http://www.safetyoffice.uwaterloo.ca/hse/radiation/rad_sealed/matter/atom_structure.htm ]

• Protons have electric charge +1
• Electrons have electric charge -1
• All neutral atoms have the same number of protons as electrons

Electromagnetism

• In PHY132 you will study the Electric Force and the Magnetic Force as being two different forces.
• However, it is possible, with Special Relativity, to unite these two forces, meaning they are actually two different aspects of the same, more fundamental force:

The Electromagnetic force.

• The Electromagnetic force is responsible for Normal Force, Tension, Friction, Spring force, drag force, thrust and muscle force.

From today’s Preclass Survey

Strong and Weak Interactions

• These are forces that don’t extend beyond the nuclei inside atoms.
• The weak interaction is responsible for beta-decay, which is when a neutron transforms into a proton plus an electron and an anti-neutrino.
• The strong interaction is what binds protons and neutrons together in the nucleus. This is important because protons repel each other electrically, and so without the strong force, all nuclei would explode.

Example

Example