Question

Elizabeth, with a mass of 56.1kg stands on a scale in an elevator. Total mass of elevator plus Elizabeth=850kg. As the elevator starts moving, the scale reads 450N. Find the acceleration and tension in the cable.

Answer 1

Answer:

acceleration = 1.79 m/s^2

Tension = 6817 N

Explanation:

First let's find Elizabeth's weight:

$P = m*g = 56.1 * 9.81 = 550.34\ N$

Her weight is greater than the normal force (N = 450 N), so the elevator is going downwards.

The acceleration of Elizabeth is given by:

$P - N = m*a$

Where P is the weight of Elisabeth, N is her normal force, m is her mass and a is the acceleration. Then, we have that:

$56.1*9.81 - 450 = 56.1*a$

$a = 100.34 / 56.1 = 1.79\ m/s^2$

The tension in the cable is given by:

$P - T = m*a$

In this case, we use the total mass, so we have:

$850*9.81 - T = 850*1.79$

$T = 850 * 8.02 = 6817\ N$