Question

A smooth block of mass $m$ moves up from the bottom to the top of a wedge which is moving with acceleration $a_{0}$ . Find the work done by the pseudo force measured by the person sitting at the edge of the wedge.

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Accepted Answer

Given,

Mass of block is, $m$

Acceleration of wedge is, $a_{0}$

The observer moving with a wedge will observe a pseudo force $m a_{0}$ in the direction opposite to ${\vec{a}}_{0}$ .

$\Rightarrow {\vec{F}}_{pseudo} = - m \vec{a_{0}}$

And the magnitude of this force is,

$\Rightarrow F_{pseudo} = m a_{0} . . . (1)$

Displacement is given by, ${\vec{s}}_{b, w}$ .

The magnitude of displacement of the block with respect to the observer is, $s_{b, w} = l . . . (2)$ , (See the figure)

Now work done by the pseudo force is given by,

$W_{pseudo} = {\vec{F}}_{pseudo} \cdot {\vec{s}}_{b, w}$

$\Rightarrow W_{pseudo} = F_{pseudo} s_{b, w} \cos (θ)$ ,

where $θ$ is the angle between pseudo force and displacement.

$\Rightarrow W_{pseudo} = F_{pseudo} s_{b, w} \cos (0 °), (∵ θ = 0 °)$

$\Rightarrow W_{pseudo} = F_{pseudo} s_{b, w}$

From $(1)$ and $(2)$ , we have,

$\Rightarrow W_{pseudo} = m a_{0} l$ .

B M Sharma Solutions for Chapter: Work, Energy and Power, Exercise 21: ILLUSTRATION 8.21

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Work, Energy and Power, Exercise 21: ILLUSTRATION 8.21

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