Work and Energy
Beginner
mechanical energy and conservation
Spring
Source: High school physics (Chinese)
Problem Sets:
work/energy basic
Problem
A spring in a spring gun has a spring constant $k = 80$ N/m. The trigger holds the spring compressed by 5 cm. A 10 g bullet is placed in the barrel against the spring. The barrel is horizontal.
Find the speed of the bullet as it leaves the muzzle.
$v = 2\sqrt{5}$ m/s
The mechanical energy of the bullet-spring system is conserved. The initial elastic potential energy of the compressed spring is converted into the kinetic energy of the bullet.
$$E_{initial} = E_{final}$$ $$U_{el,i} = K_f$$ $$\frac{1}{2}kx^2 = \frac{1}{2}mv^2$$Solving for the velocity $v$:
$$v = x \sqrt{\frac{k}{m}}$$Substitute the given values, with $m = 10 \text{ g} = 0.01 \text{ kg}$ and $x = 5 \text{ cm} = 0.05 \text{ m}$:
$$v = 0.05 \text{ m} \sqrt{\frac{80 \text{ N/m}}{0.01 \text{ kg}}} = \sqrt{20} \text{ m/s}$$