Question 273: Work, Energy and Power & Circular Motion

Question

A block of mass '$$\mathrm{m}$$' (as shown in figure) moving with kinetic energy E compresses a spring through a distance $$25 \mathrm{~cm}$$ when, its speed is halved. The value of spring constant of used spring will be $$\mathrm{nE} \,\,\mathrm{Nm}^{-1}$$ for $$\mathrm{n}=$$ _________.

Accepted Answer

$$\Delta KE = {W_{all}}$$
So $${E \over 4} - E =  - {1 \over 2}K 	imes {(0.25)^2}$$
$${{3E} \over 4} = {1 \over 2}K 	imes {1 \over {16}}$$
$$ = K = 24E$$

Work, Energy and Power & Circular Motion

A block of mass '$\mathrm{m}' (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 \mathrm{~cm} when, its speed is halved. The value of spring constant of used spring will be \mathrm{nE} \,\,\mathrm{Nm}^{-1} for \mathrm{n}=$ _________.

Integer / Numeric Answer Type