Newton's second law: A 60.0-kg person rides in elevator while standing on a scale. The elevator is traveling downward but slowing down at a rate of 2.00 m/s². The reading on the scale is closest to A) 589 N. B) 708 N. C) 469 N. D) 120 N. E) 349 N.

Question

Quizplus · Accepted Answer

The force acting on the person is the force of gravity (weight) which is equal to the product of the person's mass and the acceleration due to gravity, i.e.,
Fg = m*g, where m = 60.0 kg (mass of the person) and g = 9.81 m/s^2 (acceleration due to gravity)

On the other hand, the force reading on the scale is the normal force exerted by the scale on the person. When the elevator is accelerating downwards, the normal force is less than the weight of the person because some of the weight force is used to accelerate the person downwards. When the elevator is slowing down (i.e., accelerating upward), the normal force is greater than the weight of the person because some additional force is required to decelerate the person's downward motion.

Using Newton's second law, we can write the equation for the net force acting on the person in the downward direction as:
F_net = Fg - N = m*a
where N is the normal force (force reading on the scale), and a is the acceleration of the person (negative since it's downwards). We can rearrange this equation to solve for N:
N = Fg - m*a

When the elevator is slowing down at a rate of 2.00 m/s^2, i.e., a = -2.00 m/s^2, we have:
N = (60.0 kg)*(9.81 m/s^2) - (60.0 kg)*(-2.00 m/s^2) = 708 N

Therefore, the reading on the scale is closest to 708 N, which is answer choice B.

Newton's Second Law: a 60