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### Course: Physics archive>Unit 3

Lesson 2: Normal force and contact force

# Normal force in an elevator

Explore the concept of normal force in different scenarios, particularly in elevators. Understand how acceleration and velocity impact the normal force, and how our bodies perceive these changes. This knowledge is crucial for understanding physical processes, making it a key topic for premed studies. Created by Sal Khan.

## Want to join the conversation?

• At , Sal mentions the j unit vector. What is that?
• The j unit vector is a unit vector (a vector of magnitude/length 1) that points in the positive "y" direction on an x-y graph. Two dimensional vectors are often written in terms of their x-y components, expressed as a number multiplied by the i unit vector (the x component) and a number multiplied by the j unit vector (the y component).
• In the second case, isn't it the external force that pulls the elevator in the upper direction? As I see it, the toddler is at rest relative to the elevator, which means that it was accelerated by the external upper force along with the elevator rather than by a normal force?
• Yes, you are correct. The external force is the wire that pulls the elevator. The "actual" normal force comes from the floor of the elevator exerting the same force as the baby's weight (force) which follows Newton's third law. Therefore the baby does not plummet down the earth. And it goes same for the fourth case.

Hope this helped and +1 vote for you for your good observation :D
• I don't understand it. In example 2 (second elevator) if we have gravity force which is - 98N and force which is F= m *a F = 10*2 = 20 therefore positive force will suggest that it's direction is up, therefore this 20N will balance out partially this 98N down and natural force will have to balance out only 78 N left. Similarly in elevator 4 we get F = -20 therefore it will add up to -98N and natural force will have to balance out 118N! Is there mistake in my logic or is there a mistake in video?
• Everybody's explanation in here is wrong because their answer disobeys Newton's third law. The normal force does not lift the elevator instead, it would accelerate the baby to space. The force that accelerates the elevator comes from the cable of the elevator. And yes, Normal force is present but comes from the floor of the elevator which always exerts the same force of 98 N to balance the baby and prevent it from plummeting to the center of the earth; and this follows the Newton's third law. The video only gave you simple explanation but your question is required to be answered in depth.
• I'm very confused with this topic in particular. Since the elevator is also accelerating with the toddler, isn't it an outside force that is causing them to accelerate and not the normal force? From what I've learned, normal force on a horizontal surface must be equal and opposite to the applied force, so I don't think it is the normal force which is accelerating the toddler.
• It's important that you understand the concept of a diagram of forces. In order to understand the physics of a situation, you must understand how the forces act on the object(s).

In the 1st and 3rd scenarios, the forces on the toddler are identical, i.e. a 98N downward-acting force due to gravity, and a 98N upward-acting force due to the normal force of the elevator floor pushing up on the toddler's feet.

Here's where it gets tricky: in the 2nd and 4th scenarios, the gravity force and the normal force are identical to the 1st and 3rd scenarios, except that in the 2nd and 4th scenarios, there is an additional force in the normal direction which must be accounted for. In the 2nd scenario, there is a 10kg*2m/s^2=20N upward force added to the normal force of 98N for a total upward force of 118N. In the 4th scenario, the direction of the 20N force is in the opposite direction, yielding a total of 78N upward.

To summarize, from a diagram of forces perspective, in scenario 1, there are two force arrows at 98N, equally opposed and balanced. In scenario 2, there are the same two arrows, but a third unbalanced 20N arrow points up. In scenario 3, there are the same two opposing arrows as scenario 1. In scenario 4, the same two opposing arrows, with a third, unbalanced 20N force pointing downward.
• Can someone please explain to me the concept of INERTIAL and NON-INERTIAL frames?
• Inertial frames are frames that have a uniform speed relative to the outside world. This means that speed must be constant, and therefore acceleration must be 0 m/s². However, non-inertial frame do not have a uniform speed: this is where it differs from inertial frames. Non-inertial frames have an acceleration that is usually constant, but not equal to 0 m/s².
I hope that clarifies a little bit about the concept of (non-)inertial frames.
• I would have thought that the negative acceleration (in the last example) creating the 20 N of force would be added to the force pointing downwards, and not reduce the normal force exerted by the floor. Is that assumption wrong or is it another way of thinking about the problem?
• The better way to think about it is that the normal force normally acts as a buffer. In this case, 98 Newtons down, 20 Newtons, up, and the elevator 's force needs to balance out, so let's add 78 N of normal force in the upward direction to the elevator. In this case 20N is canceling out with the normal force, but rather that since there are 20 N of force upward already, only 78 N of normal force is needed.
• When Sal mentions 'in the J direction' such as in "acceleration is 2 meters per second square in the j direction', what does he mean by j direction
• j is a unit vector along the Y axis, or in the upward direction.
• Taken from physics.bu.edu which was much more helpful
N = mg if the elevator is at rest or moving at constant velocity
N = mg + ma if the elevator has an upward acceleration
N = mg - ma if the elevator has a downward acceleration
• I have a bit of a random question. If you were in an object that was accelerating at a constant rate, but not at a rate of zero, would you be able to tell that you were moving, assuming you cannot tell from any other external factors (turbulence, windows, etc.)?

I'm trying to figure out whether you can feel acceleration or if what you're feeling when the elevator accelerates is really just the jerk.