What force does a 180-lb man exert on the floor of an elevator that is moving downward and decelerating at 15 ft/s^2?
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The force exerted by the man on the floor of the elevator is the sum of the gravitational force acting on him and the force due to the deceleration of the elevator.
The gravitational force (weight) acting on the man is given by his mass times the acceleration due to gravity. In the English system of units, the acceleration due to gravity is approximately 32.2 ft/s^2. However, the man's weight is already given in pounds, which is a unit of force, so we don't need to calculate this.
The force due to the deceleration of the elevator is given by the man's mass times the deceleration. However, we need to convert the man's weight to mass before we can do this. In the English system of units, 1 lb is the force exerted by a mass of 1 slug under the acceleration due to gravity. Therefore, the man's mass is 180 lb / 32.2 ft/s^2 = 5.59 slugs.
The force due to the deceleration of the elevator is then 5.59 slugs * 15 ft/s^2 = 83.85 lb.
The total force exerted by the man on the floor of the elevator is then 180 lb - 83.85 lb = 96.15 lb. The force is less than the man's weight because the deceleration of the elevator is acting in the opposite direction to the gravitational force.
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