Respuesta :
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:
[tex]F_{net}=N_1-mg=N_1-690[/tex]
Now, from Newton's second law:
[tex]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)[/tex]
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:
[tex]F_{net}=mg-N_2=690-N_2[/tex]
Now, from Newton's second law:
[tex]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)[/tex]
Now, the difference in the scale reading is obtained by subtracting equation (2) from equation (1). This gives,
[tex]Difference=N_1-N_2=862.5-517.5=345\ N[/tex]
Therefore, the difference between the up and down scale readings is 345 N.
