A block of mass $100 \mathrm{g}$ is moved with a speed of $5.0 {\mathrm{ms}}^{-1}$ at the highest point in a closed circular tube of radius $10 \mathrm{cm}$ 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.

A block of mass $m$ sits at rest on a frictionless table in a train that is moving with speed $v_{\mathrm{c}}$ (w.r.t. ground) along a straight horizontal track (figure). A person in the train pushes on the block with a net horizontal force $F$ for a time $t$ in the direction of the car’s motion. 

(i) What is the final speed of the block according to a person on the train?

(ii) What is the final speed of the block according to a person standing on the ground outside the train?

(iii) How much did the kinetic energy of the block change according to the person in the car?

(iv) How much did the kinetic energy of the block change according to the person on the ground?

(v) In terms of $F\mathit{,}\mathit{ }m$ and $t$ how far did the force displace the object according to the person in the car?

(vi) According to the person on the ground?

(vii) How much work does each say the force did?

(viii) Compare the work done to the $KE$ gain according to each person.

(ix) What can you conclude from this computation?

A block having mass $500 \mathrm{g}$ slides on a rough horizontal table, if the friction coefficient between block and table is $0.2$and initial speed of the block is $60 \mathrm{cm} {\mathrm{s}}^{-1}$. Then calculate : 

(i) Work done by frictional force in bringing the block to rest.

(ii) How far does the block move before coming to rest $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$.

The bob of a pendulum is released from a horizontal position $A$ as shown in the figure. If the length of the pendulum is $2 \mathrm{m}$, what is the speed with which the bob arrives at the lowermost point $B$, given that it dissipated $10\%$of its initial potential energy w.r.t. $B$ point against air resistance? $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is $16.0 \mathrm{N}$ when the system is set into motion. Find the decrease in the gravitational potential energy during the first second after the system is released from rest.

The two blocks in an Atwood machine have masses $2.0 \mathrm{kg}$ and $3.0 \mathrm{kg}$. Find the work done by gravity during the fourth second after the system is released from rest. $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$