Question

A 25 - kg television set rests on four rubber pads , each having a height of 1 . 0 cm and a radius of 0 . 60 cm . A 200 - N horizontal force is applied to the television set . How far does it move sideways ? The shear modulus of rubber is 2 . 6 x 106 N / m2

Answer 1

Answer:

Thus it moves 1.7 mm sideways

Solution:

As per the question:

Mass of the television, m = 25 kg

Height of the rubber pads, h = 1.0 cm = 0.01 m

Radius, R = 0.60 cm = 0.006 m

Horizontal force, F = 200 N

Shear Modulus of Rubber, G = $2.6\times 10^{6}\ N/m^{2}$

Now,

To calculate the distance moved:

G = $\frac{shear\ stress}{shear\ strain}$

G = $\frac{\frac{Force}{Area}}{\frac{\Delta l}{L}} = \frac{Fl}{A\Delta L}$

where

$\Delta L$ = distance moved

Area of 4 rubber pads, A = $4\times \pi R^{2}$

Now,

$\Delta L = \frac{200\times 0.01}{4\times \pi 0.006^{2}\times 2.6\times 10^{6}} = 1.7\times 10^{- 3}\ m = 1.7\ mm$