Question

A car of mass 1000 kg moving with a speed $18 \mathrm { kmh } ^ { - 1 }$ on a smooth road and colliding with a horizontally mounted spring of spring constant$6.25 \times 10 ^ { 3 } \mathrm { Nm } ^ { - 1 }$. The maximum compression of the spring is:

• A. 1 m
• B. 2 m
• C. 3 m
• D. 4 m

Answer 1

Answer: (B)

2 m

Answer 2

Here,

$\mathrm { m } = 1000 \mathrm {~kg} , \mathrm { v } = 18 \mathrm {~km} \mathrm {~h} ^ { - 1 } = 18 \times \frac { 5 } { 18 } \mathrm {~ms} ^ { - 1 } = 5 \mathrm {~ms} ^ { - 1 }$

$\mathrm { k } = 6.25 \times 10 ^ { 3 } \mathrm { Nm } ^ { - 1 }$

At maximum compression $\mathbf { x } _ { \mathrm { m } }$ the kinetic energy of the car is converted entirely into the potential energy of the spring.

$\therefore \frac { 1 } { 2 } \mathrm { mv } ^ { 2 } = \frac { 1 } { 2 } \mathrm { kx } _ { \mathrm { m } } ^ { 2 }$ or $\mathrm { x } _ { \mathrm { m } } = \sqrt { \frac { \mathrm { m } } { \mathrm { k } } } \mathrm { v }$

Substituting the given values, we get

= 0.4 × 5 m = 2 m