Question

A rifle fires a 3.56 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 4.83 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.

Answer 1

Answer:

k = 773.64 N/m

Explanation:

Given:

mass of the pellet, m = 3.56 x 10² kg

Compression in spring, x = 6.61 × 10⁻² m

Height of rise of the pellet, h = 4.83 m

Now, let k be the spring constant

From the concept of conservation of energy, we get

gravitation potential energy acquired by the pellet will be from the energy provided by the spring

thus,

$mgh = \frac{1}{2}kx^2$

where, g is the acceleration due to the gravity

on substituting the values, we get

$3.56\times10^2\times9.8\times4.83 = \frac{1}{2}k\times(6.61\times10^{-2})^2$

or

1.685 = .002178 × k

k = 773.64 N/m