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### Chapter 4

Forces and the Laws of Motion

Force

- A push or pull exerted on an object that causes the object’s velocity to change
- The object will accelerate
- Three ways to accelerate: speed up, slow down, or to change the direction of velocity
- No force applied if the object maintains the same velocity
- A vector
- direction and magnitude
- indicated by boldfaced F in your textbook

System

- An object of interest on which force is applied
- Everything else is called external world

(Ex) System?

External world?

Contact Forces

- Forces applied when the system and the external world are in contact

(Ex)

(Ex) Air resistance (=drag), friction, normal force, external push or pull, tension

Agent

- applies a force on a system

(Ex) I push a book with my hand.

System? Agent?

(Ex) A falling book. System? Agent?

- Without an agent, a force can’t be applied

Free-body Diagram

- a drawing that shows the system and the forces acting on it
- A dot to represent the system
- Arrows for the forces and identify each force with “Fagent”

(Ex)

Practices

- Identify all the forces.
- an object free falling (Ignore air resistance)
- a sky diver falling at a constant velocity (Air exerts upward force on the person)

3) A cable pulls a crate at a constant speed across a horizontal surface. The surface provides a force that resists the crate’s motion

- A rope lifts a bucket at a constant speed. (Ignore air resistance)
- A rope lowers a bucket at a constant speed. (Ignore air resistance)

Types of Forces

- Friction, Ff
- Normal Force, FN : Any force coming from the surface and acting at a right angle to the surface

4) Tension force, FT

Tension, FT

- The total force on the massless rope = 0

6) Weight = gravitation force, Fg(Always vertically downward)

*Scales measure weight while balances measure mass

Net Force

- the vector sum of all forces exerted on an object
- Fnet= F1 + F2 + F3 + ……

(Ex) Determine the net force.

*When Fnet = 0, the system is said to be at equilibrium and the forces are balanced

*Object may be at rest or moving at a constant velocity

Fnet ≠ 0

- Fnet= F1 + F2 + F3 + …… ≠ 0
- The forces are unbalanced
- Object accelerates in the direction of the net force
- “Acceleration” = the change in velocity

Sample Problem, 4A, Pg 132

Derek left a physics book on a table inclined at 35 ˚ angle. The weight of the book = 22 N, the friction = 11 N; the normal force = 18 N

- Find the net external force acting on the book.
- Determine if the book will remain on the table.

Newton’s Three Laws of Motion

- 1st Law = law of inertia
- inertia: the tendency of an object to resist any change
- 2nd Law = force-acceleration relationship
- 3rd Law = action-reaction

First Law of Motion

- If no net force is acting on an object, the object will continue to stay at rest or to move with constant speed.
- Demos (2 min)

2nd Law of Motion

- Fnet = a∙m
- Units of force: kg∙m/s2, N (1 N = 1 kg∙m/s2)

(Ex) 1 N is the force needed to increase the speed of 1 kg of mass 1 m/s for every second

- 1 kg ≈ 2 lbs
- 1 m/s ≈ 1 yd/s
- The object accelerates in the same direction as the net force
- Fg = g∙m
- g = -9.8m/s2

Examples

- A watermelon has the mass of 4.0 g. What is the weight of the melon?
- Taru and Reiko simultaneously grab a 0.75-kg piece of rope and begin tugging on it in opposite directions. If Taru pulls with a force of 16.0 N and the rope accelerates away from her at 1.25 m/s2, with what force is Reiko pulling?

4) One of the floats in a Thanksgiving Day parade requires four people pulling on ropes to maintain a constant speed of 3.0 km/h for the float. Two people pull with a force of 210 N each, and the other two pull with a force of 140 N each. What is the force of friction between the float and the ground?

5) A large model rocket engine can produce a thrust of 12.0 N upon ignition. This engine is part of a rocket with a total mass of 0.288 kg when launched.

a) What is the net force that is acting on the model rocket just after it leaves the ground?

b) What is the initial acceleration of the rocket?

Apparent Weight

- The weight read on a scale
- at still
- accelerating upward
- accelerating downward
- free falling

Apparent Weight

- The weight read on a scale
- at still (apparent weight = weight)
- accelerating upward (apparent weight > weight)
- apparent wt = wt + ma
- accelerating downward (apparent weight < weight)
- apparent wt = wt - ma
- free falling
- apparent wt = 0 (wt = ma)

Example

Your mass is 75.0 kg, and you are standing on a bathroom scale in an elevator. Starting from rest, the elevator accelerates upward at 2.00 m/s2 for 2.00 s and then continues at a constant speed.

- What is your weight at rest?
- What is your weight reading while the elevator was accelerating?

Types of Forces

- Friction, Ff
- Normal Force, FN
- Spring force, Fsp
- Tension force, FT
- Thrust force, Fthrust
- Weight
- Apparent weight

Effect of Apparent Weight

- http://video.google.com/videoplay?docid=-3381069933559988396#

Spring Force, Fsp

What is the mathematical relationship between Fsp and x?

What is the “stretchability” of the spring (spring constant)?

Examples

1) How much force is required to accelerate a 22 kg mass at 6 m/s2?

2) A 50 kg rocket generates 990 N of thrust. What will be its acceleration if it is launched straight up?

Drag Force

1) Force exerted by a fluid (gas or liquid) on a moving object in the opposite direction to motion

- Magnitude depends on:
- speed of object (faster speed = greater drag force)
- shape and size of object (pointy vs. blunt)
- properties of fluid (thick fluid vs. thin fluid)

*viscosity = resistance to flow (higher viscosity = thicker fluid)

- the max velocity reached by a falling object
- the velocity when weight = drag force

A Sky diver falling in his belly

*Terminal velocity for a sky diver with arms and legs tucked in = 90 m/s

Interaction Forces(Newton’s 3rd Law)

- Forces always come in pairs
- For every action, there’s an equal an opposite reaction.
- Object A exerts force on Object B; B does the same on A

Examples

A gunpowder explosion creates hot gases that expand outward allowing the rifle to push forward on the bullet. What is the other force?

Kent Budgett is pulling upon a rope that is attached to a wall. In the bottom picture, the Kent is pulling upon a rope that is attached to an elephant. In each case, the force scale reads 500 Newton. What is the other force in each case?

6)

Interaction Pair(Action-Reaction Pair)

- Two forces that are opposite in directions and have equal magnitude
- FAon B = -FB on A

(Ex) Earth pulls me (= weight) and I pull Earth with equal force

- Newton’s 3rd Law (Action – Reaction Law)

Example

When a softball with a mass of 0.18 kg is dropped, its acceleration toward Earth is equal to g, the acceleration due to gravity. What is the force on Earth due to the ball, and what is Earth’s resulting acceleration? Earth’s mass is 6.0×1024 kg.

Normal Force, FN

- The upward force perpendicular exerted by the contact surface

Example

Paloma hands a 13-kg box to 61-kg Stephanie, who stands on a platform. What is the normal force exerted by the platform on Stephanie?

- Resolving gravitational force (= weight)
- Normal force
- Frictional force

Resolving Fg

A gunpowder explosion creates hot gases that expand outward allowing the rifle to push forward on the bullet. Consistent with Newton\'s third law of motion, the bullet pushes backwards upon the rifle. The acceleration of the recoiling rifle is ________, and the force of the recoiling rifle is _________.

Friction, Ff

- due to the interaction between two surfaces in contact
- ‖Ff‖ proportional to ‖FN‖

Friction, Ff

- static friction, Fs
- keeps an object from moving
- All non-moving objects experience
- Fs = -Fapplied
- Fs,max = the maximum static friction
- When Fs,max < Fapplied, the object starts to move
- Fapplied‒ Fs,max = ma
- coefficient of friction,

- the retarding frictional force
- Fk< Fs,max
- Fapplied‒ Fk = ma

Air resistance, Fair , is a form of friction

- Proportional to the object’s speed
- When Fair = Fg , Fnet = 0 and a = 0 (the terminal speed)
- video http://www.youtube.com/watch?v=4qeCcvq2_io

Example 4C, Pg 145

A 24 kg crate initially at rest on a horizontal surface requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor.

All Forces Acting on an Object

A gunpowder explosion creates hot gases that expand outward allowing the rifle to push forward on the bullet. Consistent with Newton\'s third law of motion, the bullet pushes backwards upon the rifle. The acceleration of the recoiling rifle is ________, and the force of the recoiling rifle is _________.

Tension (force), T or FT

- The force of a rope or string that is pulling on an object

Always points away from the object

- Assume the rope or string that does not stretch (like a spring) – constant length – and has no mass
- Tension is equal everywhere along the rope

(1)T + mg = Fnet = 0 if the rope is at still or moving at constant speed

(2) T + mg = Fnet = ma if

the rope is accelerating

upwards or downwards at a

Example

A 50.0-kg bucket is being lifted by a rope. The rope will not break if the tension is 525 N or less. The bucket started at rest, and after being lifted 3.0 m, it is moving at 3.0 m/s. If the acceleration is constant, is the rope in danger of breaking?

You are helping to repair a roof by loading equipment into a bucket that workers hoist to the rooftop. If the rope is guaranteed not to break as long as the tension does not exceed 450 N and you fill the bucket until it has a mass of 42 kg, what is the greatest acceleration that the workers can give the bucket as they pull it to the roof?

Summary of 1-dim Forces

- F1 + F2 + F3 + ….. = Fnet = ma
- Fnet= 0
- The object is moving at a constant velocity or standing still
- The object is at equilibrium
- Fnet = ma
- The object is accelerating at “a” in the same direction as Fnet

Problem-Solving Strategy

- Read the question carefully, noticing the measurements
- Draw a picture or free-body diagram
- Identify all the forces.
- Special attention to the direction, indicating with “+” or “–”
- Do not mix the x and y forces.
- There are two net forces: one for x and one for y
- Fnet = 0 if the object is still or moving at a constant speed
- If Fnet ≠ 0, then Fnet= ma
- Determine what is solved for (≈unknown)
- Select the formula(s) and solve for the unknown
- Check if your answer, especially the sign, is reasonable

Solving Fnet on inclined surface

Identify all forces.

Example, Pg 146

A student moves a box of books by attaching a rope to the box and pulling with a force of 90.0N at an angle of 30.0˚. The box of books has a mass of 20.0kg, and the coefficient of kinetic friction between the box and the side walk is 0.50. Find the acceleration of the box.

Example (#28, Pg 153)

A block with a mass of 5.0 kg is held in equilibrium on a incline of angle θ = 30.0˚ by the horizontal force, F, as shown in the figure.

- Find the magnitude of F.
- Find the normal force exerted by the incline on the block. (Disregard friction.)

F

θ

Example (#53, Pg 154).

- A box slides down a 30.0˚ ramp with an acceleration of 1.20 m/s2. Determine the coefficient of kinetic friction between the box and the ramp. (Why is the mass of the box not given?)

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