Aim: How can we explain the motion of elevators using Newton’s 2 nd law? Do Now: What is the acceleration of this object? m = 20 kg F = 150 N F = 100 N.

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Presentation transcript:

Aim: How can we explain the motion of elevators using Newton’s 2 nd law? Do Now: What is the acceleration of this object? m = 20 kg F = 150 N F = 100 N F Net = ma 150 N – 100 N = (20 kg)a 50 = 20a 2.5 m/s 2 up = a

Elevator Problems F g = Weight = mg F N = 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: F Net = 0 Forces are balanced F g = F N While the elevator is moving with a constant velocity Objects moving with a constant velocity: F Net = 0 Forces are balanced F g = F N

A 50 kg man is standing on a scale in an elevator while it is at rest. How much does he weigh? F g = mg F g = (50 kg)(9.8 m/s 2 ) F g = 490 N What does the scale read? F Net = 0 F N = F g F N = 490 N

The elevator now accelerates up at 2 m/s 2 What does the scale read? F g = 490 N F N = ? F Net = ma The object will always accelerate in the direction of the larger force F N is larger F N – F g = ma F N – 490 N = (50 kg)(2 m/s 2 ) F N – 490 = 100 F N = 590 N I feel heavier!!! This is your apparent weight

The elevator now accelerates down at 1 m/s 2 What does the scale read? F g = 490 N F N = ? F Net = ma The object will always accelerate in the direction of the larger force F g is larger F N - F g = ma F N N = -(50 kg)(1 m/s 2 ) F N N = -50 N F N = 440 N I feel lighter!!!

The elevator now moves with a constant velocity of 3 m/s up. What does the scale read? F g = 490 N F N = ? F Net = 0 F N = F g F N = 490 N I feel normal!!!

The elevator now is in free fall. What does the scale read? F g = 490 N F N = ? F Net = ma The object will always accelerate in the direction of the larger force F g is larger F g – F N = ma 490 N – F N = (50 kg)(9.8 m/s 2 ) 490 – F N = 490 F N = 0 N The person seems weightless

Spinning in Zero Gravity

F g = 630 N F N = 980 N What is the acceleration of the elevator? F Net = ma The object will always accelerate in the direction of the larger force F N is larger F N – F g = ma 980 N – 630 N = ma 350 = 64.3a a = 5.4 m/s 2 up F g = mg 630 N = m(9.8 m/s 2 ) m = 64.3 kg