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 (

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?

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Verity 5 years 2021-08-22T03:04:01+00:00 1 Answers 65 views 0

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  1. Nho
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    2021-08-22T03:05:47+00:00
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    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.

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