A lift is accelerating vertically upwards at 2.6 metres per second squared. A man of mass one 124 kilograms is standing inside. Determine the reaction force of the floor on the man.
The acceleration of 2.6 metres per second squared we’ll name 𝑎. And we’ll call the man’s mass 124 kilograms 𝑚. We want to determine the reaction force of the floor on the man. We’ll call that reaction force 𝐹 sub 𝑟. To begin on our solution, let’s draw a diagram of the man in the lift.
In this scenario, we have a man standing in a lift, which is accelerating upward at a rate 𝑎. If we drew in the forces that are acting on the man as arrows in our diagram, there is a downward force we can call the weight force 𝐹 sub 𝑤 caused by the man’s mass and the fact that he’s in a gravitational field. There’s also a reaction force 𝐹 sub 𝑟 of the floor of the lift on the man pushing him upward. These are the two forces acting on the man in the vertical direction.
If we recall Newton’s second law, we know this law tells us that the net force acting on an object is equal to the object’s mass times its acceleration. If we choose the upward direction as the direction of positive motion, then we can apply Newton’s second law by writing 𝐹 sub 𝑟 minus 𝐹 sub 𝑤 is equal to mass times acceleration of the man, where 𝐹 sub 𝑤 — the weight force — is equal to the man’s mass times the acceleration due to gravity 𝑔.
If we add 𝑚𝑔 to both sides of our equation, we find that 𝐹 sub 𝑟 is equal to the man’s mass times the quantity 𝑔 plus 𝑎. The man’s mass and acceleration are given in the problem statement. And 𝑔 the acceleration due to gravity is 9.8 metres per second squared.
When we plug in for 𝑚, 𝑔, and 𝑎 and enter these values on our calculator, we find that 𝐹 sub 𝑟 is 1537.6 newtons. That’s the reaction force of the floor on the man.