Question

What is the tension in the string attached to the pictured mass, which is hanging from the ceiling of an elevator that is accelerating upward at 3.00${m/{s^2}}$?

A. 68.6N
B. 89.6N
C. 21.0N
D. 47.6N
E. 7.00N

Answer 1

Hint: In this solution, the forces acting on the mass and string upward direction is equal to the all forces acting on the mass and string downward direction. The mass of the body always acts downward.

Complete step by step answer:
Given:
The upward acceleration of the string is$a = 3\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}$.
The mass of the body hanging is$m = 7\;{\rm{kg}}$.
The equation to find the tension in the string is,
The forces acting upward direction are taking as positive and the forces acting downward direction are taking as negative directions.
$ma = + T - mg\\\ \Rightarrow T = ma + mg$
Here, m is the mass of the body, T is the tension in the string, g is the gravitational force.
The standard value of the gravitational force g is $9.8\;{\rm{m/s}}$
Substitute the values in the above equation.
$\Rightarrow T = ma + mg\\\ \Rightarrow T = m(a + g)\\\ \Rightarrow T = 7(3 + 9.8)\\\ \Rightarrow T= 7 \times 12.8\\\ \therefore T= 89.6\;{\rm{N}}$

Therefore, the option is (b) is the correct answer that is $89.6\;{\rm{N}}$.

Note: Here, we should be sure about the signs (positive or negative) while taking the forces. If upward direction is assumed as positive then the downward should be negative, if the upward direction of force is assumed as negative then the downward direction should be taken as positive.