Question Video: Finding the Reaction of the Floor of an Elevator Moving Upward on a Man | Nagwa Question Video: Finding the Reaction of the Floor of an Elevator Moving Upward on a Man | Nagwa

Question Video: Finding the Reaction of the Floor of an Elevator Moving Upward on a Man Mathematics • Third Year of Secondary School

An elevator is accelerating vertically upward at 2.6 m/s². A man of mass 124 kg is standing inside. Determine the reaction force of the floor on the man.

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Video Transcript

An elevator is accelerating vertically upward at 2.6 meters per second squared. A man of mass 124 kilograms is standing inside. Determine the reaction force of the floor on the man.

We will begin by sketching a diagram to model the situation and then add on the given forces. We are told that the elevator is accelerating vertically upwards at 2.6 meters per second squared. There is a man of mass 124 kilograms standing inside the lift. He will cause a downward force due to his weight, which we will call 𝐹 sub 𝑤. And since weight is equal to mass multiplied by gravity, then we can calculate this weight force by multiplying 124 kilograms by 9.8 meters per second squared. This is equal to 1215.2 newtons, and this is the force acting vertically downwards.

We want to calculate the reaction force which acts vertically upwards and we will call 𝐹 sub 𝑟. Recalling Newton’s second law, we know that the net force acting on an object is equal to the object’s mass multiplied by its acceleration. If we let the positive direction be vertically upwards, then the net force in this case will be equal to 𝐹 sub 𝑟 minus 1215.2.

This will be equal to the mass of 124 grams multiplied by the acceleration of the man, 2.6 meters per second squared, as his acceleration will be the same as the acceleration of the elevator. 124 multiplied by 2.6 is equal to 322.4. We can then solve our equation by adding 1215.2 to both sides. This gives us 𝐹 sub 𝑟 is equal to 1537.6. And we can therefore conclude that the reaction force of the floor on the man is 1537.6 newtons.

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