Question

An upward force of
1:2×104
N acts on an elevator of mass
2:0×103
kg. Calculate the acceleration of the elevator. Take
g=9:8ms−2

Answer 1

Answer on Question #40804, Physics, Mechanics

Question:

An upward force of $1.2 \times 10^{4} \, \text{N}$ acts on an elevator of mass $2.0 \times 10^{3} \, \text{kg}$.

Calculate the acceleration of the elevator. Take $g = 9.8 \frac{m}{s^2}$.

Answer:

Newton’s second law of motion:

The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus,

$$F = m a$$

where $F$ is the net force acting on the object, $m$ is the mass of the object and $a$ is the acceleration of the object.

$$F = F_{up} - m g$$

Therefore:

$$a = \frac{F_{up} - m g}{m} = \frac{F_{up}}{m} - g = \left(\frac{1.2}{2} 10 - 9.8\right) \frac{m}{s^2} = -3.8 \frac{m}{s^2}$$

Therefore acceleration directed downward.

Answer: $3.8 \frac{m}{s^2}$