Question

A spring gun of spring constant 90 N/cm is compressed 12 cm by a ball of mass 16g. if the trigger is pulled the velocity of the ball is:
(a) 50 m/s
(b) 90 m/s
(c) 40 m/s
(d) 60 m/s
{ANS: 90 M/s}

Answer 1

here, potential energy stored in spring = kinetic energy of ball

potential energy stored in spring , U = 1/2 Kx²
given, spring constant , K = 90 N/cm = 9000 N/m
compression , x = 12cm = 0.12 m

so, U = 1/2 × 9000 × (0.12)²
= 1/2 × 0.9 × 144

Let velocity of ball is v m/s
so, kinetic energy of ball, K.E = 1/2 mv²
= 1/2 × 16 × 10^-3 × v²


now, 1/2 × 0.9 × 144 = 1/2 × 16 × 10^-3 × v²
0.9 × 144 × 10³/16 = v²
v² = 900 × 144/16
v = 90 m/s

hence, option (b) is correct.

Answer 2

Given:

Spring constant = 90 N /cm

Compression = 12 cm

Mass = 16 g

To find:

The velocity.

Solution:

By formula,

Potential energy = 1 / 2 * spring constant * Compression^

Here,

Converting to the same units,

Spring constant = 9000 N/m

Compression = 0.12 m

Substituting,

We get,

1/2 * 9000 * (0.12)^2

Potential energy = 1/2 * 0.9 * 144

Kinetic energy = 1 / 2 * mass * velocity^2

Substituting,

We get,

Kinetic energy = 1 / 2 * 16 * 10^-3 * velocity^2

Equating both the energies,

Solving for velocity,

1 / 2 * mass * velocity^2 = 1/2 * 0.9 * 144

velocity^2 = 900 * 144 / 16

Hence, Velocity = 90 m / s