A box of negligible mass rests at the left end of a 1.80 -m, 27.5 -kg plank (see

Question

A box of negligible mass rests at the left end of a 1.80-m, 27.5-kg plank (see figure). The width of the box is w = 74.5 cm, and sand is to be distributed uniformly throughout it. The center of gravity of the nonuniform plank is x = 47.5 cm from the right end. What mass of sand should be put into the box so that the plank balances horizontally on a fulcrum placed just below its midpoint? (The origin is at the fulcrum and +x to the right.)
kg

A box of negligible mass rests at the left end of a 1.80-m, 27.5-kg plank (see figure). The width of the box is w = 74.5 cm, and sand is to be distributed uniformly throughout it. The center of gravity of the nonuniform plank is x = 47.5 cm from the right end. What mass of sand should be put into the box so that the plank balances horizontally on a fulcrum placed just below its midpoint? (The origin is at the fulcrum and +x to the right.)

Explanation / Answer

Mass of plank from centre
= (1.80/2) - 0.475
= 0.425 m

Mass of sand from centre
= -(1.80/2) + (0.745/2)
= - 0.9 + 0.3725
= - 0.5275 m

The torque applied by each mass will cancel out each other.

27.5 * 0.425 - 0.5275 * M = 0

11.6875 = 0.5275 M

M = 22.16 Kg

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.