Question

An upward force of 1.2 x104N acts on an elevator of mass 2.0x103kg. Calculate the acceleration of the elevator. Take g=9.8m/s2

Answer 1

Answer on Question#55216 – Physics – Mechanics | Kinematics | Dynamics

$$3.8 \left(\frac {m}{s ^ {2}}\right)$$

Question

An upward force of $1.2 * 10^{4} \, N$ acts on an elevator of mass $2.0 * 10^{3} \, kg$. Calculate the acceleration of the elevator. Take $g = 9.8 \frac{m}{s^2}$.

Solution

Denote the upward force $(F_{u})$, the gravity force $(F)$. Consider coordinate system as displayed on the picture.

Write down relevant formulae:

$$m a = \sum_ {i} F _ {i}$$ $$\sum_ {i} F _ {i} = F - F _ {u}$$ $$F = m g,$$

where $m$ – mass of the elevator, $a$ – acceleration, $\sum_{i} F_{i}$ – result force.

Rearrange formulae and factor out $a$:

$$m a = F - F _ {u}$$ $$m a = m g - F _ {u}$$ $$a = g - \frac {F _ {u}}{m}$$

Plug in numbers:

$$a = 9.8 - \frac {1.2 * 10^{4}}{2 * 10^{3}} = 9.8 - 0.6 * 10^{1} = 9.8 - 6.0 = 3.8 \left(\frac {m}{s ^ {2}}\right)$$

Note: acceleration directed downwards.