Forces and the Laws of Motion

Review

What is Force?

A force is a push or pull on an object.Forces cause an object to accelerate… To speed up To slow down To change direction

Newton’s First Law

A body in motion stays in motion at constant velocity and a body at rest stays at rest unless acted upon by a net external force.This law is commonly referred to as the Law of Inertia.The first law describes equilibrium.

The First Law is Counterintuitive

Aristotle firmly believed this.But Physics B students know better!

Implications of Newton’s 1st Law

If there is zero net force on a body, it cannot accelerate, and therefore must move at constant velocity, which means it cannot turn, it cannot speed up, it cannot slow down.

What is Zero Net Force?

Even though there are forces on the book, they are balanced.

Therefore, there is no net force on the book.

F = 0

PhysicsA book rests on a table.

Gravity pulls down on the book.

FG

The table pushes up on the book.

FT

Motion with constant velocity also means no net force

Even though there are forces on the book, they are balanced.

Therefore, there is no net force on the book.

F = 0

Physics

A book is pushed at a constant speed across a table.

Gravity pulls down on the book.

FG

The table pushes up on the book.

FT

Friction resists the motion

An applied force pushes the book

FA

Ff

DiagramsDraw a force diagram and a free body diagram for a book sitting on a table.

N

W

Free Body Diagram

Physics

N

W

Force Diagram

Sample Problem

a) A monkey hangs by its tail from a tree branch. Draw a force diagram representing all forces on the monkey

FT

FG

Sample Problem

b) Now the monkey hangs by both hands from two vines. Each of the monkey’s arms are at a 45o from the vertical. Draw a force diagram representing all forces on the monkey.

FG

Fa1 Fa2

Mass and Inertia

Chemists like to define mass as the amount of “stuff” or “matter” a substance has.Physicists define mass as inertia, which is the ability of a body to resist acceleration by a net force.

Newton’s Second Law

A body accelerates when acted upon by a net external force.The acceleration is proportional to the net force and is in the direction which the net force acts.

Newton’s Second Law

∑F = ma where ∑F is the net force

measured in Newtons (N) m is mass (kg) a is acceleration (m/s2)

Units of force

Newton (SI system) 1 N = 1 kg m /s2

1 N is the force required to accelerate a 1 kg mass at a rate of 1 m/s2

Pound (British system) 1 lb = 1 slug ft /s2

Working 2nd Law Problems

1. Draw a force or free body diagram.2. Set up 2nd Law equations in each

dimension.Fx = max and/or Fy = may

3. Identify numerical data. x-problem and/or y-problem

4. Substitute numbers into equations. “plug-n-chug”

5. Solve the equations.

Sample ProblemIn a grocery store, you push a 14.5-kg cart with a force of 12.0 N. If the cart starts at rest, how far does it move in 3.00 seconds?

a = F/m = 12.0 N/14.5 kg =0.828 m/s2

d = ½ at2 = 0.5(.828 m/s2)(3.00 s)2 = 3.73 m

Sample ProblemA catcher stops a 42 m/s (92 mi/h) pitch in his glove, bringing it to rest in 0.15 m. If the force exerted by the catcher is 803 N, what is the mass of the ball?

Use kinematics equations to find the acceleration, then the second law of motion to find the mass.

Sample ProblemA 747 jetliner lands and begins to slow to a stop as it moves along the runway. If its mass is 3.50 x 105 kg, its speed is 27.0 m/s, and the net braking force is 4.30 x 105 N

a) what is its speed 7.50 s later?b) How far has it traveled in this time?

First, find the acceleration:

a = F/m = (4.30 x 105 N)/(3.50 x 105 kg) = 1.23 m/s2

Then use kinematics to solve for the other quantities

Newton’s Third LawAll forces are a result of interactions between two objectsFor every action there exists an equal and opposite reaction.If A exerts a force F on B, then B exerts a force of -F on A.There are always two forces and they are always equal in magnitude

Examples of Newton’s 3rd Law

Copyright James Walker, “Physics”, 1st edition

Sample ProblemYou rest an empty glass on a table.

a) How many forces act upon the glass?

b) Identify these forces with a free body diagram.

c) Are these forces equal and opposite?

d) Are these forces an action-reaction pair?

Newton’s 2nd Law in 2-D

The situation is more complicated when forces act in more than one dimension.You must still identify all forces and draw your force diagram.You then resolve your problem into an x-problem and a y-problem (remember projectile motion????).

Mass and Weight

Many people think mass and weight are the same thing. They are not.Mass is inertia, or resistance to acceleration.Weight can be defined as the force due to gravitation attraction.W = mg

Apparent weight

If an object subject to gravity is not in free fall, then there must be a reaction force to act in opposition to gravity.We sometimes refer to this reaction force as apparent weight.

Elevator rides

When you are in an elevator, your actual weight (mg) never changes.You feel lighter or heavier during the ride because your apparent weight increases when you are accelerating up, decreases when you are accelerating down, and is equal to your weight when you are not accelerating at all.

Going Up?

W

Wapp

Groundfloor

Normal feeling

v = 0a = 0

W

Wapp

Juststarting up

Heavy feeling

v > 0a > 0

W

Wapp

Betweenfloors

Normal feeling

v > 0a = 0

W

Wapp

Arriving attop floor

Light feeling

v > 0a < 0

W

Wapp

Topfloor

Normal feeling

v = 0a = 0

W

Wapp

Arriving atGround floor

Heavy feeling

v < 0a > 0

W

Wapp

Betweenfloors

Normal feeling

v < 0a = 0

W

Wapp

Beginningdescent

Light feeling

v < 0a < 0

Going Down?

Sample ProblemAn 85-kg person is standing on a bathroom scale in an elevator. What is the person’s apparent weighta) when the elevator accelerates upward at 2.0 m/s2?b) when the elevator is moving at constant velocity between floors?c) when the elevator begins to slow at the top floor at 2.0 m/s2?

Wapp = 85 kg(9.8 m/s2 + 2.0 m/s2) = 1000N

Sample ProblemA 5-kg salmon is hanging from a fish scale in an elevator. What is the salmon’s apparent weight when the elevator is

a) at rest?

b) moving upward and slowing at 3.2 m/s2?

c) moving downward and speeding up at 3.2 m/s2?

d) moving upward and speeding up at 3.2 m/s2?

Normal force

The normal force is a force that keeps one object from penetrating into another object.The normal force is always perpendicular a surface.The normal exactly cancels out the components of all applied forces that are perpendicular to a surface.

Normal force on flat surface

The normal force is equal to the weight of an object for objects resting on horizontal surfaces.N = W = mg

mg

N

Normal force on rampThe normal force is perpendicular to angled ramps as well. It’s always equal to the component of weight perpendicular to the surface.

mg

N

mgcos

mgsin

N = mgcos

Normal force not associated with weight.

A normal force can exist that is totally unrelated to the weight of an object.

applied forcefriction

weightnormal

N = applied force

The normal force most often equals the weight of an object…

…but this is by no means always the case!

Draw a free body diagram for the skier.

Sample problemA 5.0-kg bag of potatoes sits on the bottom of a stationary shopping cart. Sketch a free-body diagram for the bag of potatoes. Now suppose the cart moves with a constant velocity. How does this affect the free-body diagram?

Sample problema) Find the normal force exerted on a 2.5-kg book resting on a

surface inclined at 28o above the horizontal.

b) If the angle of the incline is reduced, do you expect the normal force to increase, decrease, or stay the same?

Sample problemA gardener mows a lawn with an old-fashioned push mower. The handle of the mower makes an angle of 320 with the surface of the lawn. If a 249 N force is applied along the handle of the 21-kg mower, what is the normal force exerted by the lawn on the mower?

Sample problemLarry pushes a 200 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N.

a) Draw a free body diagram. b) What is the acceleration of the block?

c) What is the normal force exerted on the block?