Question

balancing torques keisha (35 kg) and allie (43 kg) want to balance on a 2.5-m-long seesaw. where should they place the pivot point of the seesaw? assume the seesaw is massless. 1. analyze and sketch the problem
knowns
$m_k = $
$m_a = $
$r_k + r_a = $
unknown
$ = ?$
$ = ?$

1. solve for the unknowns

find the two forces.
keisha:
allie:

Explanation:

Step1: Fill in known values

$m_K = 35\ \text{kg}$, $m_A = 43\ \text{kg}$, $r_K + r_A = 2.5\ \text{m}$
Unknowns: $r_K = ?$, $r_A = ?$

Step2: Set torque balance equation

Torque balance: $m_K g r_K = m_A g r_A$
Cancel $g$: $m_K r_K = m_A r_A$

Step3: Substitute $r_A = 2.5 - r_K$

$35r_K = 43(2.5 - r_K)$
Expand: $35r_K = 107.5 - 43r_K$

Step4: Solve for $r_K$

$35r_K + 43r_K = 107.5$
$78r_K = 107.5$
$r_K = \frac{107.5}{78} \approx 1.38\ \text{m}$

Step5: Solve for $r_A$

$r_A = 2.5 - 1.38 = 1.12\ \text{m}$

Step6: Calculate weights (forces)

Keisha's force: $F_K = m_K g = 35 \times 9.8 = 343\ \text{N}$
Allie's force: $F_A = m_A g = 43 \times 9.8 = 421.4\ \text{N}$

Answer:

Knowns: $m_K = 35\ \text{kg}$, $m_A = 43\ \text{kg}$, $r_K + r_A = 2.5\ \text{m}$
Unknowns solved: $r_K \approx 1.38\ \text{m}$ (distance from Keisha to pivot), $r_A \approx 1.12\ \text{m}$ (distance from Allie to pivot)
Forces: Keisha = $343\ \text{N}$, Allie = $421.4\ \text{N}$
The pivot should be placed 1.38 meters from Keisha and 1.12 meters from Allie.