A rifle fires a 2.25 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 8.37 10-2 m from its unstrained length. The pellet rises to a maximum height of 5.49 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.

To determine the spring constant, we can use the principle of conservation of energy. The energy stored in the compressed spring is equal to the gravitational potential energy of the pellet when it reaches its maximum height.

The energy stored in the compressed spring can be determined using the formula for the potential energy stored in a spring:

E_spring = (1/2)kx^2

where k is the spring constant and x is the displacement of the spring from its unstrained length.

The gravitational potential energy when the pellet reaches its maximum height can be determined using the formula:

E_gravity = mgh

where m is the mass of the pellet, g is the acceleration due to gravity, and h is the maximum height.

Since the energy stored in the compressed spring is equal to the gravitational potential energy, we can set the two equations equal to each other and solve for k:

(1/2)kx^2 = mgh

Dividing both sides of the equation by x^2, we get:

(1/2)k = mg(h/x^2)

Finally, solving for k, we can substitute the given values:

k = 2mg(h/x^2)

k = 2 * (2.25 * 10^-2 kg) * (9.8 m/s^2) * (5.49 m) / (8.37 * 10^-2 m)^2

k = 98.9 N/m

Therefore, the spring constant is approximately 98.9 N/m.