Question

You leave the doctor's office after your annual checkup and recall that you weighed 688 N in her office. You then get into an elevator that, conveniently, has a scale. Find the magnitude and direction of the elevator's acceleration if the scale reads

Find the magnitude of the elevator's acceleration if the scale reads 726 N
Find the direction of the elevator's acceleration if the scale reads 726 N
Find the magnitude of the elevator's acceleration if the scale reads 598 N
Find the direction of the elevator's acceleration if the scale reads 598 N

Answer 1

Answer:

$a=0.5418\ m.s^{-2}$ upwards

$a=1.283\ m.s^{-2}$ downwards

Explanation:

Given:

weight of the person, $w=688\ N$

So, the mass of the person:

$m=\frac{w}{g}$

$m=\frac{688}{9.81}$

$m=70.132\ kg$

• Now if the apparent weight in the elevator, $w_a= 726\ N$

Then the difference between the two weights is :

$\Delta w=w_a-w$

$\Delta w=726-688$

$\Delta w=38\ N$ is the force that acts on the body which generates the acceleration.

Now the corresponding acceleration:

$a=\frac{\Delta w}{m}$

$a=\frac{38}{70.132}$

$a=0.5418\ m.s^{-2}$ upwards, because the normal reaction that due to the weight of the body is increased here.

• Now if the apparent weight in the elevator, $w_a= 598\ N$

Then the difference between the two weights is :

$\Delta w=w-w_a$

$\Delta w=688-598$

$\Delta w=90\ N$ is the force that acts on the body which generates the acceleration.

Now the corresponding acceleration:

$a=\frac{\Delta w}{m}$

$a=\frac{90}{70.132}$

$a=1.283\ m.s^{-2}$ downwards, because the normal reaction that due to the weight of the body is decreased here.

Answer 2

Answer with Explanation:

We are given that

Weight of person=w=688 N

a.Scale reading=n=726 N

$m=\frac{w}{g}=\frac{688}{9.8} m$

By using $g=9.8m/s^2$

Net force=ma=n-w

$a=\frac{n-w}{m}=\frac{726-688}{\frac{688}{9.8}}m/s^2$

$a=0.54 m/s^2$

The sign of acceleration(a) is positive.Therefore, the direction of elevator's accelerating is upwards.

b.Scale reading=n=598 N

$a=\frac{598-688}{\frac{688}{9.8}}=-1.28m/s^2$

$a=-1.28 m/s^2$

The sign of acceleration(a) is negative.Therefore, the direction of elevator's accelerating is downwards.