A 544-N physics student stands on a bathroom scale in an 871-kg (including the s

Question

A 544-N physics student stands on a bathroom scale in an 871-kg (including the student) elevator that is supported by a cable. As the elevator starts moving, the scale reads 499 N .

(a) Find the magnitude of the acceleration of the elevator.

(b) Find the direction of the acceleration of the elevator.

(c) What is the acceleration if the scale reads 653 N?

(d) If the scale reads zero, should the student worry? Explain

(e) What is the tension in the cable in part A?

(f) What is the tension in the cable in part D?

Explanation / Answer

Here

weight of student , W1 = 544 N

mass of elevator , m = 871 Kg

reading on the scale ,W2 = 499 N

a) let the acceleration of the elevator is a

Using second law of motion

considering upwards as the positive direction

(544/9.8) * a = -544 + 499

a = -0.81 m/s^2

the magnitude of acceleration of the elevator is 0.81 m/s^2

b)

as the acceleration is negative

the direction of acceleration of the elevator is downwards.

c)

for W3 = 653 N

Using second law of motion

(544/9.8) * a = 653 - 544

a = 1.96 m/s^2

the acceleration is 1.96 m/s^2 upwards

d)

if the scale reads zero

then the acceleration of elevtor = 9.8 m/s^2

and the elevator is in freefall.

Yes , Student should worry.

e)

for the tension in the cable

Tension = 499 + m * (g - a)

Tension = 499 + 871 * (9.8 - 0.81)

Tension = 8329 N

the tension in cable in part A is 8329 N

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