Question

Find the distance moved by the wedge when the block reaches the bottom of the wedge?

Answer 1

For this question's answer, we will obtain the block's displacement wrt the wedge's displacement. Then, we will utilize the work performed by the wedge as equal to the work performed by the block. Finally, we will determine the distance travelled by the wedge when the block reaches the bottom of the wedge.

Complete step-by-step solution:
Let x be the distance moved by the wedge.
Mass of wedge, $M = 4kg$
Mass of block, $m = 1kg$
The distance moved by the wedge of mass $4kg$ is x when the block reaches the bottom.
Then, a block of mass $1kg$ is moved by the $(4 - x)$.
We will use the concept of work done.
Work done by a wedge of mass $4kg$ is equal to the work done by a block of mass $1kg$.
Work done by wedge of mass $4kg = 4gx$
Work done by block of mass $1kg = g(4-x)$
Therefore, $4gx = g (4-x)$
$\implies 4x = 4-x$
$\implies 5x =4$
$\implies x = \dfrac{4}{5}$
$\implies x = 0.8m$

Note: A displacement wedge is utilized for estimating displacement and acts using the principle of persistence of eyesight. It is a verification method to confirm that a vibration test system produces what it should be and not something unique due to an inaccurate input sensitivity setup.