Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 129

Block sliding onto a spring. A block with mass \( m = 3.20 \text{ kg} \) starts at rest and slides distance \( d \) down a frictionless \( 30.0^\circ \) incline, where it runs into a spring (Fig. 8.54). The block slides an additional \( 21.0 \text{ cm} \) before it is brought to rest momentarily by compressing a spring, with spring constant \( k = 431 \text{ N/m} \). (a) What is the value of \( d \)? (b) What is the distance between the point of first contact and the point where the block’s speed is greatest?