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Answer :
Final answer:
The force a 180-lb man would exert on the floor of a downward moving and decelerating elevator at 15 ft/s² is 90 lb, considering his weight and the deceleration impact on his apparent weight.Therefore,correct option is option d) 90 lb
Explanation:
To determine the force a 180-lb man exerts on the floor of a moving and decelerating elevator, we need to understand the concepts of weight, gravity, and acceleration within the context of Newton's laws of motion.
In a static situation where an elevator is not moving, the force exerted by a man on the floor of the elevator would simply be his weight due to gravity. However, in a situation where the elevator is decelerating (meaning it is moving downward but slowing down), the net force exerted by the man on the floor is the result of the difference between his weight and the force caused by the deceleration.
The man's weight (W) can be calculated using the equation W = mg, where m is his mass and g is the acceleration due to gravity (which is approximately 32 ft/s2).
The force (F) exerted by the man on the floor while the elevator is decelerating is given by:
F = W - ma
Here, W is the weight of the man, m is his mass, and a is the deceleration of the elevator.
To find the mass of the man (m), you would normally convert his weight from pounds to kilograms and then to the slug unit to use the acceleration due to gravity in ft/s2. But since we are looking for the force in pounds and given g in ft/s2, we can skip the conversion to mass.
Let's calculate:
- W = 180 lb (since the weight in pounds effectively represents the force exerted by gravity)
- a = 15 ft/s2
- F = 180 lb - (180 lb / 32 ft/s2) * 15 ft/s2 = 180 lb - 84.375 lb
- F = 95.625 lb
However, since we need to match to the nearest answer choice, we round off to 90 lb, which is answer choice (d).
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