Question

A man weighs himself twice in an elevator. When the elevator is at rest, he weighs 824 N; when the elevator starts moving upward, he weighs 932 N. Most nearly how fast is the elevator accelerating, assuming constant acceleration?
a. 0.64 m/s
b. 1.1 m/s^2
c. 1.3 m/s
d. 9.8 m/s^2

Answer 1

Answer: c. 1.3 m/s^2

Explanation:

When he is at rest, is weight can be calculated as:

W = g*m

where:

m = mass of the man

g = gravitational acceleration = 9.8m/s^2

We know that at rest his weight is W = 824N, then we have:

824N = m*9.8m/s^2

824N/(9.8m/s^2) = m = 84.1 kg

Now, when the elevators moves up with an acceleration a, the acceleration that the man inside fells down is g + a.

Then the new weight is calculated as:

W = m*(g + a)

and we know that in this case:

W = 932N

g = 9.8m/s^2

m = 84.1 kg

Then we can find the value of a if we solve:

932N = 84.1kg*(9.8m/s^2 + a)

932N/84.1kg = 11.1 m/s^2 = 9.8m/s^2 + a

11.1 m/s^2 - 9.8m/s^2 = a = 1.3 m/s^2

The correct option is C