Question

Jonas has a 10.0 kg box, which he places on a scale inside an elevator. When the

elevator begins to move, the scale shows that the box weighs 83.4 N. What is the
magnitude and direction of the elevator's acceleration?

Answer 1

a = - 1.47 [m/s²], descending or going down

Step-by-step explanation:

To solve this problem we must use Newton's second law which tells us that the sum of forces on a body is equal to the product of mass by acceleration.

∑F = m*a

where:

∑F = Forces applied [N]

m = mass = 10 [kg]

a = acceleration [m/s²]

Let's assume the direction of the upward forces as positive, just as if the movement of the box is upward the acceleration will be positive.

By performing a summation of forces on the vertical axis we obtain all the required forces and other magnitudes to be determined.

`-m*g + N = m*a\\`

where:

g = gravity acceleration = 9.81 [m/s²]

N = normal force measured by the scale = 83.4 [N]

Now replacing:

`-(10*9.81)+83.4=10*a\\-14.7=10*a\\a=-1.47[m/s^(2) ]`

The acceleration has a negative sign, this means that the elevator is descending at that very moment.