Question

A pendulum bob of mass 50 g is suspended on a string from the ceiling of an elevator which is moving downwards with an acceleration 1.5 ms-2. Draw the free body diagram using the non-inertial frame of reference and determine the tension in the string. (Take g = 10 ms-2)

Answer 1

Answer on Question #65500, Physics / Mechanics | Relativity

A pendulum bob of mass 50 g is suspended on a string from the ceiling of an elevator which is moving downwards with an acceleration 1.5 ms-2. Draw the free body diagram using the non-inertial frame of reference and determine the tension in the string. (Take g = 10 ms-2)

Find: T - ?

Given:

$$m = 50 \times 10^{-3} \text{ kg}$$ $$a = 1.5 \text{ m/s}^2$$ $$g = 10 \text{ m/s}^2$$

Solution:

Newton's Second Law:

$$\vec{F} = m\vec{a} \quad (1)$$ $$\text{Of} \quad (1) \Rightarrow m\vec{g} + \vec{T} = m\vec{a} \quad (2),$$

where $m\vec{g}$ is gravity force, $\vec{T}$ is tension force

Projections on axis OY: $mg - T = ma$ (3)

$$\text{Of} \quad (3) \Rightarrow T = m(g - a) \quad (4)$$ $$\text{Of} \quad (4) \Rightarrow T = 0.425 \text{ N}$$

Answer:

0.425 N

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