Question

A 1 kg block collides with a horizontal light spring of force constant 2 N/m. The block compresses the spring m from rest position. Assuming that the coefficient of kinetic friction between the block and the horizontal surface is 0.25. What was the speed of the block at the instant of collision?

• A. 10 m/s.
• B. 7.2 m/s
• C. 6.7 m/s
• D. 7.9 m/s

Answer 1

The correct option is B 7.2 m/s

When the block compresses the spring let x be the amount of compression.

i.e. x = 4m

Let v be the velocity of the lock when it collides with the spring.

Loss in K.E. of the block = gain in elastic potential energy + work done against friction

$\left(\frac{1}{2}\right)$mv${}^2$ - 0 = $\left(\frac{1}{2}\right)$kx${}^2$ + $\mu$mgx,

$\left(\frac{1}{2}\right)$mv${}^2$ = $\left(\frac{1}{2}\right)$ × 2 × 4${}^2$ + 0.25 × 1 × 9.8 × 4,

v${}^2$ = 2 × 4${}^2$ + 0.25 × 1 × 9.8 × 4 × 2 = 51.6,

v = $\sqrt{51.6}$ = 7.2m/sec