Rachel has been reading her physics book. She takes her weighing scales into an elevator and stands on them. If her normal weight is 690 N (155 lbs) and the elevator moves upward at 0.25 g and then down at 0.25 g, what is the difference between the up and down scale readings?

345 N

Explanation:

Given:

Normal weight of Rachel (mg) = 690 N

Case 1: Upward motion of elevator

Given:

Acceleration of elevator (a) = 0.25 g

The scale reading is given by the normal force acting on Rachel. Let N₁ be the normal force.

So, the net force acting on Rachel is given as:

Now, from Newton's second law:

Case 2: Downward motion of elevator

Given:

Acceleration of elevator (a) = 0.25 g

The scale reading is given by the normal force acting on Rachel. Let N₂ be the normal force.

So, the net force acting on Rachel is given as:

Now, from Newton's second law:

Now, the difference in the scale reading is obtained by subtracting equation (2) from equation (1). This gives,

Therefore, the difference between the up and down scale readings is 345 N.

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