Which set of weights will the strong man be able to lift faster?

Force, mass and acceleration

Which set of weights will the strong man be able to lift faster?

Force, mass and acceleration

Not exactly a challenging question, eh?

Isaac Newton figured out that this relationship between force F, mass m and acceleration a could be expressed mathematically:

F = maWhich is the same as

a = F/m And

m = F/a

Force, mass and acceleration

Newton’s Second Law

If there is a net force on an object, the object accelerates.◦Its acceleration is directly proportional to the net force

◦Its acceleration is inversely proportional to the object’s mass

◦Its acceleration is in the same direction as the net force.

“directly proportional” means:

If the net force doubles, the acceleration doubles.

If the net force triples, the acceleration triples.

If the net force is half as much, the acceleration is half as much.

Etc.

“inversely proportional” means:

If the object’s mass doubles, its acceleration will be half as much.

If the object’s mass triples, its acceleration will be one-third as much.

If the object’s mass is half as much, its acceleration doubles.

Etc.

What is “mass”? Mass measures the inertia of an object. All objects made of matter have inertia -

that is, they resist accelerations (Newton’s First Law), but some objects resist more than others.

Mass is a scalar quantity. SI unit of mass is the kilogram (kg).

Newton’s Second Law In symbols:

a = Fnet

m

Fnet = ma

Fnet

m a

A = F/m

A = (80 N)/(0.045 kg)

A = 1777.777… ~ 1800 m/s2

A golf ball with mass of 0.045 kilogram is hit with a force of 80 Newtons. What is its acceleration?

F = ma

F = (0.08 kg)(200 m/s2)

F = 16 N

A volleyball with a mass of 0.08 kilogram is given an acceleration of 200 m/s2. How much force was used?

m = F/a

m = (80 N)/(120 m/s2)

m = 0.67 kg

A basketball is struck with a force of 80 Newtons. It attains an acceleration of 120 m/s2. What is the mass of the basketball?

30 kgForceApplied = 300 NForceFriction = 25 N

What is the net (overall) force acting on this object?

What happens to the object as a result – what is its acceleration?

30 kgForceApplied = 300 NForceFriction = 25 N

Net force = ForceApplied – Force Friction

= -25 N + 300 N

Net Force = 275 N

25 N 300 N

275 N

30 kgForceApplied = 300 NForceFriction = 25 N

Net Force = 275 NAcceleration = Net Force

mass

Acceleration = 275 N 30 kg

Acceleration = 9.1 m/s2

Net Force = (500 N – 80 N) = 420 N to the right

Acceleration = Net Force/mass

Acceleration = (420 N)/(30 kg)

Acceleration = 14 m/s2

30 kgForceApplied = 500 NForceFriction = 80 N

Net force = 255 N + 195 N – 18 N

Net force = 432 N

Acceleration = Net force/mass

Acceleration = (432 N)/(25 kg)

Acceleration = 17.28 m/s2

25 kg

ForceApplied = 195 NForceFriction = 18 N

ForceApplied = 255 N

Preconceptions

There are 2 major preconceptions to address:◦Mass is not the same as weight.

◦Force is not the same as pressure.

Mass is not Weight Mass is a property of an object that

measures how much it resists accelerating. An object is difficult to accelerate because

it has mass.

Weight Weight is a force - an interaction between 2

objects involving a push or a pull. One of these objects is typically VERY big - the Earth or the Moon, for instance.

Weight is NOT a property of an object.

What does weight depend on?

The weight of an object depends on the object’s mass.◦ In fact, an object’s weight is directly

proportional to the object’s mass. The weight of an object also depends on

the object’s location.◦ In fact, an object’s weight is directly

proportional to its free fall acceleration, g at its current location.

Weight

In symbols:

W = mg

Wm g

Weight of a 1 kg object

Since W = mg, the weight of a 1 kg object is:◦ W = (9.8 m/s2)(1 kg) = 9.8 N on Earth◦ W = (1.6 m/s2)(1 kg) = 1.6 N on the Moon

Mass vs. Weight We typically think that an object is difficult

to accelerate because it is heavy (has

weight) - but it is heavy because it has mass.

So, objects are difficult to accelerate

because they have mass.

Force is not Pressure

Force determines how much an object will accelerate.

Pressure determines how that acceleration will feel.

What does pressure depend on?

The pressure exerted on an object depends on:

The force exerted on the object. In fact, pressure is directly proportional to force.

The area over which the force is applied.◦ In fact, pressure is inversely proportional to

area.

Pressure Units

A force of 1 N applied over an area of 1 m2 exerts a pressure of 1 Pascal.

Another common unit of pressure is pounds per square inch (lb/in2).

Pressure

In symbols:

P =FA

F

AP

Video clips:◦ Newton’s Law 2 on FMA◦ Newton’s 2nd Law of Motion (1)◦ Newton’s 2nd Law of Motion (Hewitt)◦ How acceleration is produced (Hewitt)

Interactive: ◦ pushing an elephant◦ Online text with occasional self-quizzes

Still Confused?