Equilibrium & Newton’s 2nd Law of Motion

Review: Law Of Inertia

Newton's 1st Law - If there is no net force acting on a body, then it will continue in it's state of constant velocity (which may be zero).

Mathematically.

Add all the forces acting on a body. R = 0 - constant velocity or zero.

It is at equilibrium – acceleration = 0

The netThe net force acting on an object is theforce acting on an object is thevector sum of all the forces acting on it.vector sum of all the forces acting on it.

Find the net force on each – it is helpful to Find the net force on each – it is helpful to treat treat horizontal (x)horizontal (x) & & vertical (Y)vertical (Y) separately.separately.

10 N

4 N

3 N

7 N

3 N

3 N

4 N, right

6 N, up

What is the motion of each box?

10 N

4 N

3 N

7 N

3 N

3 N6 N, up

4 N, right

Accl rightAccl up

Objects Objects notnot in Equilibrium will in Equilibrium will accelerateaccelerate in the direction of the net in the direction of the net force.force.

But how much?

““Law of Acceleration”Law of Acceleration”

m - mass in kga - m/s2.

F - Newtons (N):1 N = 1kg m

s2

Fnet means sum the forces in one direction.

A constant net force causes constant/uniform acceleration!

aa =FFnetnet

mmFFnetnet

= mm aa

One Newton = the amount of One Newton = the amount of force needed to accelerate a 1 force needed to accelerate a 1 kg mass to at a rate of 1 m/skg mass to at a rate of 1 m/s22..

More massive objects require more force to accelerate!!

Finding acceleration

• Sketch a free body diagram show all forces on one object.

• Calculate magnitude & direction of Fnet.

• Use a = Fnet/m to find a in any direction where Fnet ≠ 0.

1. A 2000-kg car’s engine exerts a westward force of 12500-N. Friction between the tires and the road is 500-N.

• Sketch the free body diagram.

• Calculate Fnet

• Calculate the acceleration.

2. An 80-kg man who weighs 800-N fell out of an airplane. As he falls air resistance pushes him up with a force of 150-N.

• Sketch the free body diagram.

• Calculate his acceleration as he falls to Earth.

• Why is his actual acceleration different than g?

3. Find the acceleration of the box below. Assume the box has mass 2.5 kg.

4 N8 N

7 N

3 N

3 N

X & Y forces separately.

Horizontally, +8N +4N (right), -7N (left), so Fnet is +12 – 7 = +5 N.

a = F/m+5N / 2.5 kg = 2 m/s2. Acceleration to the right.

Vertically, we have +3N(up) and –3N (down), so they add to zero.

Vertically, a = 0.

example prb’s

• 1. Moving down.

• 2. At rest

• 3. Moving up

• 4. In freefall.

The forces on the man in the elevator are balanced. Which of the following are possible? He could be:

Graphs of Newton’s 2nd Law

• Equation: a = Fnet/m.

• Slope = • 1/mass

Graphs of Newton’s 2nd Law

• Equation: a = Fnet/m.

• Slope = • mass.

Increasing Mass vs. AccelerationHold Fnet constant

• a = Fnet/ m

• How to find Fnet?

Because a requires a Fnet, you feel acceleration!!

If there is a net force on you, you feel pushed or pulled.

If you are moving at a constant velocity, you feel normal.

Weight & Mass

What is mass?

The amount of matter / stuff.

Review.

• Newton 1

• Newton 2

• Weight

• Friction.

• Normal force.

Prac Set

What is weight?

The force of gravity acting on mass.

Mass in kg, weight in Newtons (N).

Weight (W or Fg)

• Since F = ma, • then near Earth’s surface:

• Fg = mg.• g = Fg/m m = Fg/g

• m in kg• g = 9.81 m/s2

• Fg = W in N.

Fg = mg

4. What is the weight of a 100-kg person on Earth?

=(100 kg)(9.81 m/s2)

= 981 N.

Ex 5: What is the weight of a 500-g ball on earth?

• 500g x 1 kg/103 g = 0.5 kg.

• 0.5 kg x 9.81 m/s2 = 4.9 N.

Ex 6. A 600-N student weighs 100-N on Planet Jordan. What is the acceleration of gravity on Planet Jordan?

• Find the mass on Earth.

• m = Fg/g

• 600N/9.81 m/s2

• 61 kg.

• Find g on Jordan,

• g = Fg/m

• = 100 N/ 61 kg

• g = 1.6 m/s2.

If you are not accelerating toward the Earth, then some

force is balancing your weight!

You feel acceleration!!

If there is a net force on you, you feel pushed or pulled.

If you are moving at a constant velocity, you feel normal.

Newton 2 6 minutes.

• http://www.youtube.com/watch?v=WzvhuQ5RWJE&feature=relmfu

Or Weight with spring scale.

http://www.youtube.com/watch?v=iH48Lc7wq0U

Newton’s 3 Laws 4.5 minutes.

152 #20,21, 25-27

Weight Packet.

Weight with spring scale.

Constant Fnet = uniform a

Equilibrium

• When all forces are balanced they are in equilibrium.

• How can we determine 3 force could be in equilibrium?

• See Starreview pg 83.

Ted Elevator Forces

• http://ed.ted.com/lessons/would-you-weigh-less-in-an-elevator-carol-hedden