The two children shown in the figure below are balanced on a seesaw of negligible mass. The first child has a mass of 27.3 kg and sits 1.24 m from the pivot. The second child has a mass of 33 and sits 1.00 m from the pivot. Use the second condition for equilibrium (net r= 0) to calculate the supporting force (in N) exerted by the pivot. (Enter the magnitude.) H m₂ m₂

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**Seesaw Balance Experiment for Educational Purpose**

**Objective:**
Understanding the conditions for equilibrium in a seesaw system with negligible mass using the principles of torque and force balance.

**Description of the Setup and Figure Analysis:**
In the illustrated setup, two children are balanced on a seesaw.

1. **Children's Positions and Masses:**
   - The first child (mass \( m_1 = 27.2 \) kg) sits \( 1.24 \) meters from the pivot point (denoted by \( r_1 \)).
   - The second child (mass \( m_2 = 35 \) kg) sits \( 1.00 \) meter from the pivot point (denoted by \( r_2 \)).

2. **Forces Acting on the System:**
   - The weights of the children exert downward forces (\( W_1 \) and \( W_2 \)):
     - \( W_1 \) = \( m_1 \cdot g \) (gravity's effect on the first child's mass)
     - \( W_2 \) = \( m_2 \cdot g \) (gravity's effect on the second child's mass)
   - \( F_p \) is the supporting force exerted by the pivot, which acts upwards to balance the seesaw system.

**Conditions for Equilibrium:**
To ensure the seesaw remains in equilibrium (net torque is zero), the torques caused by the weights of both children relative to the pivot must be equal and opposite:
\[ W_1 \cdot r_1 = W_2 \cdot r_2 \]

**Steps to Calculate Supporting Force (\(F_p\)):**
1. **Calculate the weights:**
   - \( W_1 = 27.2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \)
   - \( W_2 = 35 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \)

2. **Apply torque equilibrium condition:**
   - Substitute values into the equation \( W_1 \cdot r_1 = W_2 \cdot r_2 \)
   - Simplify to find if torques are balanced.

3. **Calculate the Supporting Force (\( F_p \)):**
   - The sum
Transcribed Image Text:**Seesaw Balance Experiment for Educational Purpose** **Objective:** Understanding the conditions for equilibrium in a seesaw system with negligible mass using the principles of torque and force balance. **Description of the Setup and Figure Analysis:** In the illustrated setup, two children are balanced on a seesaw. 1. **Children's Positions and Masses:** - The first child (mass \( m_1 = 27.2 \) kg) sits \( 1.24 \) meters from the pivot point (denoted by \( r_1 \)). - The second child (mass \( m_2 = 35 \) kg) sits \( 1.00 \) meter from the pivot point (denoted by \( r_2 \)). 2. **Forces Acting on the System:** - The weights of the children exert downward forces (\( W_1 \) and \( W_2 \)): - \( W_1 \) = \( m_1 \cdot g \) (gravity's effect on the first child's mass) - \( W_2 \) = \( m_2 \cdot g \) (gravity's effect on the second child's mass) - \( F_p \) is the supporting force exerted by the pivot, which acts upwards to balance the seesaw system. **Conditions for Equilibrium:** To ensure the seesaw remains in equilibrium (net torque is zero), the torques caused by the weights of both children relative to the pivot must be equal and opposite: \[ W_1 \cdot r_1 = W_2 \cdot r_2 \] **Steps to Calculate Supporting Force (\(F_p\)):** 1. **Calculate the weights:** - \( W_1 = 27.2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \) - \( W_2 = 35 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 \) 2. **Apply torque equilibrium condition:** - Substitute values into the equation \( W_1 \cdot r_1 = W_2 \cdot r_2 \) - Simplify to find if torques are balanced. 3. **Calculate the Supporting Force (\( F_p \)):** - The sum
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