A pulley system is attached to a massless board as shown below. The board pivots only at the pivot point. A 10 kg mass M sits exactly in the middle of the board. If the angle $θ$ is $6 0^{\circ}$ , what is the force F (in N) necessary to hold the board in the position shown?
Take g = 10 m/s².

Question

A pulley system is attached to a massless board as shown below. The board pivots only at the pivot point. A 10 kg mass M sits exactly in the middle of the board. If the angle $θ$ is $6 0^{\circ}$ , what is the force F (in N) necessary to hold the board in the position shown?

Take g = 10 m/s².

TestHub · Accepted Answer

Take g = 10 m/s²

The string pulls the free end of the board upward with 2F, at distance ℓ from the pivot

Weight Mg acts at the middle, at distance ℓ/2

For equilibrium, torque about the pivot is zero:

$M g \frac{ℓ}{2} = 2 F ℓ$

$F = \frac{M g}{4} = \frac{10 \times 10}{4}$

$F = 25 N$

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