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 $1.2m/s^2$ (b) goes up with deceleration $1.2m/s^2$, (c) goes up with uniform velocity, (d) goes down with acceleration $1.2m/s^2$ (e) goes down with deceleration $1.2m/s^2$ and (f) goes down with uniform velocity

Answer 1

Given that,

Mass $m=50kg$

Acceleration $a=1.2m/s^2$

Now, we have

$T-mg=ma$

$T=m(g+a)$

(a).The acceleration is upward

$T=m(g+a)$

$T=\frac{50}{100}(9.8+1.2)$

$T=0.55N$

(b).The acceleration is upward but negative

$T=m(g-a)$

$T=\frac{50}{1000}(9.8-1.2)$

$T=0.43N$

(c).The velocity is constant and therefore acceleration is zero

$T=\frac{50}{1000}\times 9.8$

$T=0.49N$

(d).The acceleration is downward

$T=\frac{50}{1000}(9.8-1.2)$

$T=0.43N$

(e).The acceleration is downward but negative

$T=\frac{50}{1000}(9.8+1.2)$

$T=0.55N$

(f).The velocity is constant therefor acceleration is zero

$T=\frac{50}{1000}\times 9.8$

$T=0.49N$

Hence, this is the required solution