Question

What force is required to operate a powder-actuated tool, ensuring it does not function until pressed against a work surface?

A) 5 pounds
B) 10 pounds
C) 15 pounds
D) 20 pounds

Answer 1

The work required to compress the spring of a toy dart gun to the higher setting is four times the work done for the lower setting. Since it takes 5.0 J for the lower setting, it will take 20 J for the higher setting. The correct answer is (a) 20 J.

Step-by-step explanation:

The question is asking about the amount of work required to compress the spring of a toy dart gun to its higher setting compared to its lower setting. When dealing with springs, the work done to compress or stretch a spring is given by the equation W = 1/2 kx², where W is the work, k is the spring constant, and x is the displacement of the spring from its equilibrium position. Since the spring is compressed twice as far for the higher setting, we can denote the displacement for the lower setting as x and for the higher setting as 2x.

Substituting into the work equation, we have:

• Work for lower setting: W1 = 1/2 kx² = 5.0 J
• Work for higher setting: W2 = 1/2 k(2x)² = 1/2 k(4x²) = 4(1/2 kx²) = 4 W1

Hence, for the higher setting W2 = 4 × 5.0 J = 20 J. Therefore, the correct answer is (a) 20 J.