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.

at right angles to each other