To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant 5.25 × 10^3 N m–1. What is the maximum compression of the spring ? Example 5.9 Consider Example 5.8 taking the coefficient of friction, µ, to be 0.5 and calculate the maximum compression of the spring.

Example 5.8 To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant $5.25\times 10^3 Nm^{-1}$ . What is the maximum compression of the spring ? [NCERT Class 11 Example 5.8]

Example 5.9 Consider Example 5.8 taking the coefficient of friction, µ, to be 0.5 and calculate the maximum compression of the spring. [NCERT Class 11 Example 5.9]

$5.25\times 10^3 Nm^{-1}$ corrected as $6.25\times 10^3 Nm^{-1}$

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 m/s. When the stone reaches the floor the distance of the man above the floor will be

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 m/s. When the stone reaches the floor the distance of the man above the floor will be

A) 9.9 m   B) 10.1 m  C) 10 m   D) 20 m

Concepts: Conservation of Linear momentum. Similar to the recoiling of gun. When the man pushes the stone downward the man will get pushed upward. Since there is no external force acting on the system, conservation of linear momentum is valid and center of mass of the whole system remains in the same location.