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.
