Question

A spring gun is made by compressing a spring in a tube and then latching the spring at the compressed position. A 4.97-g pellet is placed against the compressed and latched spring. The spring latches at a compression of 3.90 cm, and it takes a force of 9.12 N to compress the spring to that point.

Answer 1

given,

mass of pellet = 4.97 g

the compression distance = 3.90 cm = 0.039

Force to compress the spring = 9.12 N

we know,

F = k x

9.12 = k x 0.039

k = 233.85 N/m

conservation of energy:

`(1)/(2)k x^2 = m g x + (1)/(2)mv^2`

`(1)/(2)* 233.85 * 0.039^2 = 0.00497 * 9.81 * 0.039 + (1)/(2)* 0.00497 * v^2`

`0.1778 = 0.0019 + 0.002485 v^2`

v = 8.41 m/s

b) conservation of energy:

`(1)/(2)k x^2 = m g h`

`(1)/(2)* 233.85 * 0.039^2 =0.00497* 9.81 * h`

`h = 3.64\ m`