An engine is attached to a wagon through a shock absorber of length $1.5\mathrm{m}$. The system with a total mass of $50,000\mathrm{kg}$ is moving with a speed of $36\mathrm{km}/\mathrm{h}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0\mathrm{m}$. If $90\%$ of energy of the wagon is lost due to friction, calculate the spring constant.

A block of mass $1 kg$ is pushed up a surface inclined to horizontal at an angle of 30" by a force of $10\mathrm{N}$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1 .$ If the block is pushed up by $10\mathrm{m}$ along the incline, calculate

(a) work done against gravity

A block of mass $1 kg$ is pushed up a surface inclined to horizontal at an angle of ${30}^{\circ }$ by a force of $10\mathrm{N}$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1 .$ If the block is pushed up by $10\mathrm{m}$ along the incline, calculate

(b) work done against force of friction

A block of mass $1 kg$ is pushed up a surface inclined to horizontal at an angle of ${30}^{\circ }$ by a force of $10\mathrm{N}$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1 .$ If the block is pushed up by $10\mathrm{m}$ along the incline, calculate

Use work done agianst grvaity as $50 J$

(c) increase in potential energy

A block of mass $1 kg$ is pushed up a surface inclined to horizontal at an angle of 30" by a force of $10\mathrm{N}$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1 .$ If the block is pushed up by $10\mathrm{m}$ along the incline, calculate

(d) increase in kinetic energy

A block of mass $1 kg$ is pushed up a surface inclined to horizontal at an angle of 30" by a force of $10\mathrm{N}$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1 .$ If the block is pushed up by $10\mathrm{m}$ along the incline, calculate

(e) work done by applied force.

A curved surface is shown in figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from A which is at a slightly greater height than $C$. With the surface $AB$, ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.

(a) For which ball is total mechanical energy conserved?