I really need help with my physics homework

Question

I've been at this question for hours and I can't figure it out, PLEASE HELP!

A 380.5 N child and a 259.3 N child sit on either end of a 2.9 m long seesaw.

a) How far from the 380.5 N child should the pivot be placed to ensure rotational equilibrium? Disregard the mass of the seesaw. Answer in units of m.

b) Suppose a 330 N child sits 0.158 m from the 380.5 N child. How far from the pivot must a 301 N child sit to maintain rotational equilibrium? Answer in units of m.

Answer 1

Both parts will rely upon the definition of rotational equilibrium:

∑τ = 0

If F is some force applied perpendicularly at a distance d away from some pivot point, then it will cause the following torque:

τ = F * d

It will keep the positive sign so long as the rotation that the force would potentially cause is Counter-ClockWise (CCW).

If the direction of the force and distance would potentially cause ClockWise (CW) rotation, then the produced torque would be as follows:

τ = - F * d

In this problem, all forces are applied perpendicular to their distance from the pivot point, thus, the sense of each torque is the part to be determined in the solution of this problem.

a)

___________x__

↓ Δ |

259.3 ↓

380.5

In the very crude image above, x is the distance in meters from the pivot to where the 380.5 N is being placed at the edge of the seesaw. The full length of the seesaw L is 2.9 m.

Holding true that ∑τ = 0, one must do the following:

0 = (259.3) * ( L - x ) - 380.5 * x ⇒ 0 = (259.3 * L) - (259.3 + 380.5) ( x ) ⇒ x = 259.3 / (259.3 + 380.5) * (2.9 m) x ≈ 1.175 m

Because it is an important distance, let's call the distance from the pivot to the location of the 259.3 N force some distance z.

z = 2.9 - 1.175 z ≈ 1.725 m

b)

____________________

↓ | Δ | |

259.3 ↓ | |

301 ↓ |

330 ↓

380.5

x is the distance from the pivot to the location of the 380.5 N force.

y is the distance from the pivot to the location of the 301 N force.

z is the distance from the pivot to the location of the 259.3 N force.

w is the distance from the pivot to the location of the 330 N force.

From the prompt:

w + 0.158 = x ⇒ w ≈ 1.017 m

The distance that is being looked for is y since all other distances are known.

0 = ( 259.3 ) * ( 1.725 ) + ( 301 ) * ( y ) - ( 330 ) * ( 1.017 ) - ( 380.5 ) * ( 1.175 ) ⇒ 301 y = 335.716

y ≈ 1.115 m

I hope this helps! Message me in the comment section if there's something confusing about this solution or if there is something I did wrong!

Answer 2

a) Equlibrium equation: 380.5x = 259.3(2.9 - x); 380.5x + 259.3x = 259.3·2.9; x = 1.175 m

b) 380.5·1.175 + 330·(1.175 - 0.158) + 301·y = 259.5(2.9 - 1.175); y = 0.222 m