Sure, we can solve this problem by using the principle of moments for a first-class lever. According to the principle of moments, for a system to be in equilibrium, the moments (torque) on either side of the fulcrum must be equal.
The moment (or torque) is calculated as the product of force and distance from the fulcrum.
The formula we will use is:
[tex]\[ \text{Effort} \times \text{Effort Distance} = \text{Load} \times \text{Load Distance} \][/tex]
Given values:
- Load (\( L \)) = 400 N
- Effort (\( E \)) = 100 N
- Effort Distance (\( E_d \)) = 30 cm (which we will convert into meters since the standard unit of distance is meters)
First, convert the effort distance from centimeters to meters:
[tex]\[ 30 \, \text{cm} = 30 / 100 \, \text{m} = 0.30 \, \text{m} \][/tex]
Now, plug the values into the principle of moments equation and solve for the load distance (\( L_d \)):
[tex]\[ 100 \times 0.30 = 400 \times L_d \][/tex]
[tex]\[ 30 = 400 \times L_d \][/tex]
Rearranging the equation to solve for \( L_d \):
[tex]\[ L_d = \frac{30}{400} \][/tex]
[tex]\[ L_d = 0.075 \, \text{m} \][/tex]
So, the load distance to balance the lever is:
[tex]\[ 0.075 \, \text{meters} \][/tex]
