Question

A pendulum bob of mass 50 g is suspended from the ceiling of an elevator. Find the tension in the string if the elevator (a) goes up with acceleration 1.2 m/s², (b) goes up with deceleration 1.2 m/s², (c) goes up with uniform velocity, (d) goes down with acceleration 1.2 m/s², (e) goes down with deceleration 1.2 m/s² and (f) goes down with uniform velocity.

Answer 1

(a) When the elevator goes up with acceleration 1.2 m/s²:



$T=mg+ma$
⇒ T = 0.05 (9.8 + 1.2) = 0.55 N

(b) Goes up with deceleration 1.2 m/s² :


$T=mg+m\left(-a\right)=m\left(g-a\right)$
⇒ T = 0.05 (9.8 − 1.2) = 0.43 N

(c) Goes up with uniform velocity:


$T=mg$
⇒ T = 0.05 × 9.8 = 0.49 N

(d) Goes down with acceleration 1.2 m/s² :



$$\begin{gathered} T+ma=mg \\ \Rightarrow T=m\left(g-a\right) \end{gathered}$$
⇒ T = 0.05 (9.8 − 1.2) = 0.43 N

(e) Goes down with deceleration 1.2 m/s² :

$$\begin{gathered} T+m\left(-a\right)=mg \\ \Rightarrow T=m\left(g+a\right) \end{gathered}$$
⇒ T = 0.05 (9.8 + 1.2) = 0.55 N

(f) Goes down with uniform velocity:



$T=mg$
⇒ T = 0.05 × 9.8 = 0.49 N