Answer:
40 inches
Step-by-step explanation:
Woman + sit = 145 lb + 5 lb = 150 lb
Distance from the fulcrum to the left side = 60 in
Moment of the force on the left side:
Son + sit = 95 lb + 5 lb = 100 lb
Distance from the fulcrum to the son's seat = 60 in
Moment of the force:
Daughter + sit = 70 lb + 5 lb = 75 lb
Distance from the fulcrum to the daughter's seat = x
Moment of the force:
Since left and right sides are balanced, moments should be equal on both sides.
This is shown as:
So, the daughter should sit at 40 in distance from the fulcrum.
Answer:
[tex]\large \boxed{\text{40 in from the fulcrum}}[/tex]
Step-by-step explanation:
An object is in rotational equilibrium when the net torque applied to it is zero.
For example, if a seesaw is not rotating, you know the torque on each side is balanced.
The counterclockwise torque of the woman equals the sum of the clockwise torques of her son and daughter.
The formula for torque τ is
τ = Fr,
where
F = the turning force and
r = the distance from the fulcrum
Thus, we can write
[tex]F_{\text{w}}r_{\text{w}} = F_{\text{s}}r_{\text{s}} + F_{\text{d}}r_{\text{d}}[/tex]
Data:
Each person has a 5 lb seat, so they are exerting 5 lb in addition to their weight.
Fw = 150 lb; rw = 60 in
Fₛ = 100 lb; rₛ = 60 in
Fd = 75 lb; rd = ?
Calculation:
[tex]\begin{array}{rcl}F_{\text{w}}r_{\text{w}} &=& F_{\text{s}}r_{\text{s}} + F_{\text{d}}r_{\text{d}}\\\text{150 lb $\times$ 60 in} & = & \text{100 lb $\times$ 60 in} + \text{75 lb} \times r_{\text{d}} \\\text{9000 in} & = & \text{6000 in}+ 75 r_{\text{d}}\\\text{3000 in} & = &75 r_{\text{d}}\\ r_{\text{d}} & = & \dfrac{\text{3000 in}}{75}\\\\& = & \textbf{40 in}\\\end{array}\\\text{The daughter should sit $\large \boxed{\textbf{40 in from the fulcrum}}$}[/tex]
Check:
[tex]\begin{array}{rcl}150 \times 60 &=& 100 \times 60 + 40 \times 75\\9000 & = & 6000 + 3000\\9000 & = & 9000\\\end{array}[/tex]
It checks.
