When I tutor my physics students, I want them to understand the fundamentals of the concept, not just how to plug in numbers into an equation. I wished when I was learning physics, my teachers drew upon real life applications more, things we already understand about the world to help us really get it.
I’m hoping that this example will appeal to all my fellow avid skiers out there.
When I was young and learning to ski I was terrified of chairlifts (I still am a bit). Dangling high up in the open air was scary. When the chairlift was full, when I was sitting on it with my entire family- everything seemed balanced, I was safely squished in there. But, if I was on the chairlift by myself, if I sat on one edge, the chairlift would tip heavily to that side.
Or if it was me (a light child) sitting with my Dad (much heavier than a child), the chairlift would tip to his side.
I came to understand through years of riding the chairlift how I could keep the chairlift balanced. If I was alone, I should sit in the middle. If I was with my Dad, he could sit just slightly off center on one side, and I could sit all the way to one edge on the other side. This would allow the chairlift to stay horizontal.
Have any of you noticed this when sitting on a chairlift with someone much lighter or heavier than you?
Here are some rules about sitting on a chairlift - think about if they make sense to you.
- Alone sitting in the middle will make the chairlift horizontal.
- A heavier person will tip the chairlift more than a light person when sitting equally far apart from the center.
- There is a way to achieve equilibrium by two people of unequal weights sitting calculated distances away from the center.
This fundamental physics concept is called moment.
What is Moment?
The MOMENT of a force is a measure of its tendency to cause a body to rotate about a specific point or axis.
When I sit on a chairlift, I am creating a moment that causes the chairlift to rotate around the pivot.
How do you calculate moment?
The moment is equal to the force applied multiplied by the distance away from the pivot:
Moment = Force x Distance
Let's try an example
A child weighing 60lbs is sitting 2 feet away from the center of the chairlift. How far away from the center on the opposite side of the chairlift does her father (who weighs 180lbs) have to sit, so that the chairlift is horizontal (“balanced”)?
First calculate the moment caused by the child:
NOTE: We can model the chairlift as a weightless beam
Moment = Force x Distance
(60 lbs)(2 feet) = 120 ft-lbs
With the child sitting to the left of the pivot point which way does the chairlift tip?
She causes the chairlift to pivot counterclockwise.
Counterclockwise moments are considered negative values.
In order for the chairlift to be in equilibrium the moment acting on the pivot from the Father must be equal and opposite to the child.
The child caused a -120 ft-lbs moment, therefore her father needs to create a +120ft-lbs moment.
120 ft-lbs = (180 lb)(x feet)
x = ⅔ feet = 8 inches.
Which side of the pivot point does the Father need to sit in order to balance the child
The right side!
WIth the Father sitting on the right side, he causes the chairlift to tip clockwise.
Clockwise moments are considered positive values.
With the Father sitting 8” to the left of the pivot he creates a -120 ft-lbs moment around the pivot. An equal and opposite moment to the child’s. Therefore the chairlift is in equilibrium.
What other real life applications can you think of involving moments?
- If a nut is difficult to undo with a short wrench, a longer wrench will help. This is because there will be a bigger moment on the nut, when the same force is applied further from the pivot.
- Try pushing a door open really close to its hinge point. The closer to the hinge point, the harder you have to push. If the door is extremely heavy, push the door open right at the edge farthest from the hinge. That’s another real life application of moment.
Physics can seem abstract and confusing when you’re drawing beams and free-body diagrams. But physics is everywhere. When you learn a new concept in physics, challenge your tutors to come up with real life examples and explain how the theory applies in practice!
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