A 4 kg block slides 5 m down rough incline (37 deg, mu_k = 0.25). Speed at bottom from rest: (g = 10 m/s^2) <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 350 200" style="max-width:350px;margin:0.5em auto;display:block;"> <title>Block sliding down rough incline with friction</title> <rect width="350" height="200" fill="#faf9f5" rx="6"/> <defs> <marker id="ah-q52-03" markerWidth="8" markerHeight="6" refX="8" refY="3" orient="auto"><polygon points="0 0, 8 3, 0 6" fill="#c6613f"/></marker> <marker id="ah-q52-03b" markerWidth="8" markerHeight="6" refX="8" refY="3" orient="auto"><polygon points="0 0, 8 3, 0 6" fill="#788c5d"/></marker> </defs> <!-- Incline --> <polygon points="40,170 300,170 300,60" fill="none" stroke="#14140f" stroke-width="1.5"/> <!-- Angle arc --> <path d="M265,170 A35,35 0 0,1 286,148" fill="none" stroke="#14140f" stroke-width="1"/> <text x="258" y="162" font-size="10" font-family="sans-serif" fill="#14140f">37°</text> <!-- Block on incline --> <rect x="175" y="90" width="40" height="28" fill="#f0e8e0" stroke="#14140f" stroke-width="1.5" rx="2" transform="rotate(-24.2,195,104)"/> <text x="195" y="108" text-anchor="middle" font-size="9" font-family="sans-serif" fill="#14140f" transform="rotate(-24.2,195,108)">4 kg</text> <!-- Friction arrow (up the incline) --> <line x1="195" y1="118" x2="225" y2="104" stroke="#788c5d" stroke-width="2" marker-end="url(#ah-q52-03b)"/> <text x="225" y="98" font-size="9" font-family="sans-serif" fill="#788c5d">f</text> <!-- Velocity arrow (down the incline) --> <line x1="175" y1="108" x2="145" y2="122" stroke="#c6613f" stroke-width="2" marker-end="url(#ah-q52-03)"/> <text x="140" y="140" font-size="9" font-family="sans-serif" fill="#c6613f">v = ?</text> <!-- Length label --> <text x="240" y="82" font-size="9" font-family="sans-serif" fill="#14140f">5 m</text> <!-- Height dashed line --> <line x1="300" y1="60" x2="300" y2="170" stroke="#788c5d" stroke-width="1" stroke-dasharray="4,3"/> <text x="310" y="120" font-size="9" font-family="sans-serif" fill="#788c5d">h</text> <!-- Labels --> <text x="120" y="185" font-size="9" font-family="sans-serif" fill="#14140f">&#956;&#7496; = 0.25</text> <!-- Ground hatching --> <line x1="35" y1="175" x2="25" y2="170" stroke="#14140f" stroke-width="1"/> <line x1="55" y1="175" x2="45" y2="170" stroke="#14140f" stroke-width="1"/> <line x1="75" y1="175" x2="65" y2="170" stroke="#14140f" stroke-width="1"/> </svg>

2 kg body at 10 m/s hits 3 kg body at rest (elastic). Speed of 3 kg after collision:

Work to stretch spring (k = 100 N/m) from 5 cm to 10 cm:

A 800 kg car starts from rest, constant power 8 kW. Speed after 25 s (no friction):

F = (3x^2 - 2x + 1) N. Work from x = 0 to x = 2 m: