Forces

• Contact Forces - those resulting from physical contact between objects

– Normal Force

– Friction

– Tension (spring/rope)

– Compression

• Action at a Distance Force - Field Forces

– Gravity

– Electromagnetic

– Strong Nuclear Force• Holds Nucleus Together

– Weak Nuclear Force• Decay Process

•Force - The capacity to cause physical change in the motion of an object.

Newton’s First Law – Law of Inertia

• An object at rest will remain at rest – and an object in motion will continue in motion at a

constant velocity (Magnitude and Direction)– unless acted upon by a nonzero net external force.

• Inertia – The tendency of a body to maintain its state of rest or constant velocity.

• Equilibrium - A condition during which the velocity of an object is constant or the object is at rest. The net force acting on the object is zero.

• Inertial Reference Frame – Place where Newton's Laws are valid. (at rest or constant velocity)– Non-inertial reference frames are accelerating.

Weight and Mass

• Mass - A term used to quantify/measure inertia.

– Has SI units of kilogram.

– The amount of a substance.

– The quantity of matter.

– Scalar

• Weight - Force exerted on an object while it is under the influence of a gravitational field.

– Vector

• Density - The amount of a substance per unit volume.

Newton’s Second Law

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

direction of the net force acting on the object.

Fa

m

F vector sum of all forces

F ma

Units

PhysicalQuantity

DimensionSymbol

SI MKS SI CGS USCustomary

Length [L] m cm ft

Mass [M] kg g slug

Time [T] sec sec sec

Acceleration [L/T2] m/s2 cm/s2 ft/s2

Force [M-L/T2] newton (N)kg-m/s2

dyneg-cm/s2

pound (lb)slug- ft/s2

1 lb 4.45 N

Alternate Statement of the Second Law

• Momentum - The quantity of an object’s motion. The product of an object’s mass and velocity.

• The time rate of change of the momentum of an object is equal to the resulting net external force acting on the object.

p mv

dpF

dt

Weight and Mass

• Mass - A term used to quantify/measure inertia.

– Has SI units of kilogram.

– The amount of a substance.

– The quantity of matter.

– Scalar

• Weight - Force exerted on an object while it is under the influence of a gravitational field.

– Vector

• Density - The amount of a substance per unit volume.

GˆF mg mgj

Example 1

• What constant net force must be used to bring a 1500 kg car to rest from a speed of 100 km/hr within a distance of 55 m?

Newton’s Third Law

• If two objects interact (contact or at a distance),

• the force exerted on body 1 by body 2 (F12)

• is equal and opposite the force exerted on body 2 by body 1 (- F21 ).

On By

Cautions on the Third Law

• The forces of an action-reaction pair always act on different bodies. They do not combine to give a net force and cannot cancel each other.

Model Assumptions

• Surfaces are frictionless (*)• The mass of a rope or string is zero.• The tension in a rope is the same everywhere in

the rope. (The force(s) it exerts is(are) on the object(s) it is attached to).

• Ropes are non-extensive (do not get longer)• A pulley has no friction or mass (*). It simply

redirects the tension in another direction.

Problem Solving Approach• Read the problem. Several times if necessary.

• Write down the information that is given or looked up in a table.

• Write down what is to be found.

• Draw a picture or sketch. Draw and label with forces, velocities, accelerations, etc. Isolate the object(s) of interest.– Free body diagram.

– Specify your coordinate system.

– Resolve forces along these coodinate axes.

• Write down the fundamental relationships/definitions/formula you need to solve the problem.– Apply Newton’s laws in component form along coordinate axes.

• Manipulate the equations. # Equations = # Unknowns.

• Check that your answer makes sense.

• Actually plug in numbers at the very end. Include unit analysis.

• Box your final answer. Include units and check for significant digits.

Big Picture

• If the object is at rest or moving at a constant velocity it is in equilibrium and the 1st Law applies.

• If the the forces don’t seem balanced the object will accelerate and the second law applies

F 0

F ma

Example 2

• A 10 kg box is sitting on the table.

• You pull up with a string attached to the box and apply 40 N.

• What is the normal force applied by the table on the box?

Example 3

• Two boxes are connected by a cord and pulled by a second cord attached to the first box with a force of 40.0 N

• The two boxes have masses of 12.0 kg and 10.0 kg as shown.

• Find the acceleration of each box and the tension in the cord

Example 4 – Hanging Objects

1 2

m

1 21T

2T

mg

F 0

Resolve into components

mg

1 21T

2T

mg

2 2T sin

2 2T cos

1 1T sin

1 1T cos

1 1y 2 2T sin T nF mi0 gs 1x 2 21T cos TF 0 cos

Block on a smooth incline plane

mgsin

mg cos

NF

mg

y NF mg co0 sF x mgsinF ma

Atwood’s Machine (a pulley)

Object 1: Elevator Car

y T 1 1F F m g m a

Object 2: Counterweight

y T 2 2F F m g m a

Incline plane (no friction)

• m2 = 7 kg• Which way do

blocks move?• What is

acceleration?• What is tension

in cord?

Inside the elevator (non-inertial frame)

While moving up at constant velocity:

y NF F mg 0 Scale reads correctly

While slowing down:

y NF F mg ma Scale reads light!