Aim: How can we explain the Aim: How can we explain the motion of elevators using motion of elevators using

Newton’s 2Newton’s 2ndnd law? law?

Do Now:

What is the acceleration of this object?

m = 20 kg

F = 150 N

F = 100 N

FNet = ma

150 N – 100 N = (20 kg)a

50 = 20a

2.5 m/s2 up = a

Elevator ProblemsElevator Problems

Fg = Weight = mg

FN = Normal Force (scale reading)

A man is standing on a scale while in an elevator

What forces exist?

While the elevator is at rest

Objects at rest: FNet = 0

Forces are balanced

Fg = FN

While the elevator is moving with a constant velocity

Objects moving with a constant velocity:FNet = 0Forces are balancedFg = FN

A 50 kg man is standing on a scale in an elevator while it is at rest.

How much does he weigh?

Fg = mg

Fg = (50 kg)(9.8 m/s2)

Fg = 490 N

What does the scale read?

FNet = 0

FN = Fg

FN = 490 N

The elevator now accelerates up at 2 m/s2

What does the scale read?

Fg = 490 N

FN = ? FNet = ma

The object will always accelerate in the direction of the larger force

FN is larger

FN – Fg = ma

FN – 490 N = (50 kg)(2 m/s2)

FN – 490 = 100

FN = 590 N

I feel heavier!!!

This is your apparent weight

The elevator now accelerates down at 1 m/s2

What does the scale read?

Fg = 490 N

FN = ? FNet = ma

The object will always accelerate in the direction of the larger force

Fg is larger

FN - Fg = ma

FN - 490 N = -(50 kg)(1 m/s2)

FN - 490 N = -50 N

FN = 440 N

I feel lighter!!!

The elevator now moves with a constant velocity of 3 m/s up.

What does the scale read?

Fg = 490 N

FN = ?FNet = 0

FN = Fg

FN = 490 N

I feel normal!!!

The elevator now is in free fall.

What does the scale read?

Fg = 490 N

FN = ? FNet = ma

The object will always accelerate in the direction of the larger force

Fg is larger

Fg – FN = ma

490 N – FN = (50 kg)(9.8 m/s2)

490 – FN = 490

FN = 0 N

The person seems weightless

Spinning in Zero Gravity

Fg = 630 N

FN = 980 N

What is the acceleration of the elevator?

FNet = ma

The object will always accelerate in the direction of the larger force

FN is larger

FN – Fg = ma

980 N – 630 N = ma

350 = 64.3a

a = 5.4 m/s2 up

Fg = mg

630 N = m(9.8 m/s2)

m = 64.3 kg