Question

A rifle fires a 1.06 x 10-2-kg pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by 6.61 x 10-2 m from its unstrained length. The pellet rises to a maximum height of 6.26 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.

Answer 1

k = 2.65 10² N / m

Step-by-step explanation:

As the pellets shoot up we can use energy conservation

Starting point. Compressed spring rifle

Em₀ = Ke = ½ k x²

Final point. Highest point of the path

`Em_(f)` = U = m g y

Energy is conserved

Em₀ = Em_{f}

½ k x² = m g y

k = 2 m g y / x²

Let's calculate

k = 2 1.06 10⁻² 9.8 6.26 / (6.61 10⁻²)²

k = 2.65 10² N / m