A plank 2.00 cm thick and 15.0 cm wide is firmly attached to the railing of a ship by clamps so that the rest of the board extends 2.00 m horizontally over the sea below. A man of mass 80.0 kg is forced to stand on the very end. IF the end of the board drops by 5.00cm because of the man's weight, find the shear modulus of the wood.

I'm not sure how you find the force in order to complete the shear modulus equation of F/A divided by Delta L/L

To find the force and complete the equation for shear modulus (G), you need to calculate the force applied by the man, the area of the plank, and the change in length caused by his weight.

Let's break down the steps:

1. Calculate the force applied by the man:
The force is equal to the man's weight, which can be calculated using the formula: weight = mass × gravitational acceleration.
Given:
- Mass of the man (m) = 80.0 kg
- Gravitational acceleration (g) = 9.8 m/s^2

So, the man's weight (W) is:
W = m × g = 80.0 kg × 9.8 m/s^2 = 784 N

2. Calculate the area of the plank:
Given:
- Thickness of the plank (h) = 2.00 cm = 0.02 m
- Width of the plank (w) = 15.0 cm = 0.15 m
- Length of the plank extending over the sea (L) = 2.00 m

So, the area (A) of the plank is:
A = w × h = 0.15 m × 0.02 m = 0.003 m^2

3. Calculate the change in length caused by the man's weight:
Given:
- Change in height (delta L) = 5.00 cm = 0.05 m

The change in length (delta L) is negative because the end of the board drops:
delta L = -0.05 m

4. Now, you can plug in the values into the equation for shear modulus (G):
G = (F / A) / (delta L / L)

Substituting the values:
G = (784 N / 0.003 m^2) / (-0.05 m / 2.00 m)

Simplifying:
G = 784 N / 0.003 m^2 / (-0.025 m)

Finally, calculate the shear modulus (G):
G = -125,440 N/m^2

Note: The negative sign indicates that the plank is under compression due to the man's weight.