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Force Causes Acceleration

• Acceleration deals with changes in motion• There is zero acceleration at constant velocity• The cause of acceleration is force• A constant force produces motion at a constant acceleration• Acceleration ~ net force

– The ~ symbol means, “directly proportional to”

valtime_inter

velocitychange_in_onaccelerati

The great acceleration of the racing car is due to its ability to produce large forces.

Mass Resists Acceleration

• For a given force the acceleration is inversely proportional to the mass

massonaccelerati

1~

Mass Resists Acceleration

massonaccelerati

1~

6 times the mass1/6 the acceleration

Newton’s Second Law

• By using consistent units: N for force, kg for mass and m/s2 for acceleration the equation becomes exact:

mass

forcenetonaccelerati

_~

m

Fa

kg

Nsm

1

1/1 2

What acceleration is produced by a force of 2000 N applied to a 1000 kg car?

m

Fa

2000 N/1000 kg = 2 m/s2

If the force is 4000 N, what is the acceleration?

Doubling the force on the same mass simply doubles the acceleration.

Newton’s Second Law

• If mass and acceleration are known then the equation would look like this:

maF

maF Head = 4 kg

Newton’s Second Law

Newton’s Second Law

maF Head = 4 kg

Acceleration of head = 25 m/s2

2/254 smkgF

NF 100

Friction

Friction acts on materialsthat are in contact with each other, and it always acts in a direction to oppose motion.

The force of friction between the surfaces depends on the kinds of material in contact and how much the surfaces are pressed together.

• Rubber against concrete produces more friction than steel against steel.

Why are concrete road dividers more effective than steel rails?

Friction also occurs in liquids and gases (fluids).

Air resistance – frictionacting on something moving through the air

Applying Force--Pressure

• Pressure—The amount of force per unit of area• One Newton per square meter is equal to one

pascal (Pa)

A

FP Pressure

Force

Area of application

Applying Force--Pressure

• Pressure—The amount of force per unit of area

A

FP Pressure

Force

Area of application

The smaller the area supporting a given force, the greater the pressure on that surface.

• You exert more pressure on the ground when you stand on one foot than when you stand on both feet. (Decreased area of contact)

• Stand on one toe like a ballerina and the pressure is huge.

Why don’t the nails puncture the skin?

The driving forceper nail is not enoughto puncture the skin.

m

F =m

F

A 10 kg cannonball will hit the ground at the same time as a 1

kg stone!

Free Fall Explained

gsmkg

N

m

weight

m

Fa 2/8.9

1

8.9

A 10 kg cannonball will hit the ground at the same time as a 1

kg stone!

gsmkg

N

m

weight

m

Fa 2/8.9

10

98

1 kg stone

10 kg cannonball

g = acceleration of free fall

The weight at the Earth’s surface is 9.8 N per 1 kg.

Free Fall • The net force on each object is only its weight.• The ratio of weight to mass is the same for

both.• All freely falling objects undergo the same

acceleration at the same place on Earth.

If you were on the moon and dropped a hammer and a feather from the same elevation at the same time, would they strike the surface of the moon at the same instant?

Answer

• Yes• On the moon, the hammer and

feather weigh only 1/6 of their Earth weights, and there is no air to provide friction.

• The ratio of moon-weight to mass for each object is the same, and they both accelerate at (1/6)g.

Air Drag

150-200 km/hA heavier person willattain a greater terminalspeed than a lighterperson.

Falling and Air Resistance (drag)

Terminal speed (acceleration terminates)

15-25 km/h

A parachute increases air resistance.

• Air drag builds up as speed increases. The result is reduced acceleration.

• More reduction can occur by increasing the surface area encountered by the air. (Diver spreads out)

• If there were no air drag, like on the moon, there would be no terminal speed. (free fall and each object hits the ground at the same time).

Falling and Air Resistance

• When air resistance equals the weight, the net force is zero and no further acceleration occurs. Acceleration terminates; the object has reached its terminal speed.

• If we are concerned with direction (such as down for falling objects), the object has reached its terminal velocity.

His weight is 100 kg, so his weight at the Earth’ssurface is a constant 1000 N (9.8 N rounded). Air resistance (R) varies. Find his acceleration at each position.

m

RW

m

Fa net

R=0W=1000N

R=400NW=1000N

R=1000NW=1000N

R=1200NW=1000N

R=2000NW=1000N

R=1000NW=1000N

a.

b.

c.

d.

e.

f.

A = 10 m/s2

A = 6 m/s2

A = 0 m/s2

A = -2 m/s2

A = -10 m/s2

A = 0 m/s2