One type of BB gun uses a spring-driven plunger to blow the BB from its barrel. Calculate the spring constant of its plunger's spring if you must compress it 0.283 m to drive the 0.0500-kg plunger to a top speed of 26.3 m/s. Assume that the barrel of the BB gun is horizontal.

431.83 N/m

Explanation:

Applying the law of conservation of energy,

From the question,

The kinetic energy of the plunger = energy stored in the spring

1/2mv² = 1/2ke² ... Equation 1

Where m = mass of the plunger, v = velocity of the plunger, k = spring constant of the spring, e = compression.

make k the subject of the equation

k = mv²/e² ... Equation 2

Given: m = 0.05 kg, v = 26.3 m/s, e = 0.283 m

Substitute into equation 2

k = 0.05 (26.3²) / 0.283²

k = 34.5845/0.080089

k = 431.83 N/m