Question

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?

Answer 1

Answer:

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:

$F_{net}=N_1-mg=N_1-690$

Now, from Newton's second law:

$F_{net}=ma\\\\N_1-690=m\times 0.25g\\\\N_1-690=0.25\times (mg)\\\\N_1-690=0.25\times 690\\\\N_1=690+172.5=862.5\ N------(1)$

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:

$F_{net}=mg-N_2=690-N_2$

Now, from Newton's second law:

$F_{net}=ma\\\\690-N_2=m\times 0.25g\\\\690-N_2=0.25\times (mg)\\\\690-N_2=0.25\times 690\\\\N_2=690-172.5=517.5\ N------(2)$

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

$Difference=N_1-N_2=862.5-517.5=345\ N$

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