Physics of Tension and Forces on Inclined Planes

Problem Setup

• Mass: 10 kg supported by two strings
• Angles: 32° and 82° with the vertical.
• Net Force: 0

Force Equations

• Horizontal Component (Efx):

  • $T<em>1 ext{ cos}(32) + T</em>2 ext{ cos}(82) - mg = 0$

• Vertical Component (Efy):

  • $T<em>1 ext{ sin}(32) + T</em>2 ext{ sin}(82) - mg = 0$

Tension Relations

• Derived Relation:
  • $T<em>1 = k T</em>2$ (where $k$ is some constant factor, e.g., $k=0.7813$)

Resulting Tensions

• Tensions computed regarding $mg$:

  • For vertical equilibrium: where $mg = 98$ N,
  • $T<em>1 ext{ cos}(52) + T</em>2 ext{ cos}(38) = 98$

• Solving leads to:

  • $T_2 = 77.1574 ext{ N}$
  • $T_1 = 0.7813 imes 77.2$

Second Problem Setup

• Box Mass: 160g on an incline (20° above horizontal)
• Constant Velocity implies net force = 0.

Additional Forces

• Man pushes parallel to incline.
• Force Applied is calculated as:
  • $F = mg ext{ sin}(20)$ (ignoring friction).