Question

A block of mass 100 g is moved with a speed of 5⋅0 m/s at the highest point in a closed circular tube of radius 10 cm kept in a vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{block},m=100g=0.1\mathrm{kg}, \\ \mathrm{Velocity}\mathrm{of}\mathrm{the}\mathrm{block}\mathrm{at}\mathrm{the}\mathrm{highest}\mathrm{point},\nu =5\mathrm{m}/s \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{circular}\mathrm{tube},r=10\mathrm{cm} \end{gathered}$$

Work done by the block
= Total energy at the highest point − Total energy at the lowest point
$$\begin{gathered} =\left(\frac{1}{2}m{\nu }^2+mgh-0\right) \\ \Rightarrow W=\frac{1}{2}\times \left(0.1\right)\times 25+\left(0.1\right)\times 10\times \left(0.2\right) \\ \mathrm{As},h=2r=0.2\mathrm{m} \\ W=1.25+0.2=1.45\mathrm{J} \end{gathered}$$

So, the work done by the tube on the body is 1.45 joule.