"A one meter board with uniform density, hangs in static equilibrium from a rope with tension T. A weight hangs from the left end of the board 0.2m away in distance. What is the mass of the board"

To find the mass of the board, we can use the concept of torque balance. Torque is the measure of how effectively a force can rotate an object. In static equilibrium, the net torque acting on the system is zero.

The torque due to the weight hanging at the left end can be calculated by multiplying the weight (force) by the distance from the pivot point (which is the left end of the board):

Torque_left = (Weight) * (Distance)

Since we know the distance is given as 0.2m, we can substitute this value.

Now, the board is in equilibrium, so we need to consider the torque provided by the tension in the rope. The tension acts at the pivot point (left end) of the board and creates an equal and opposite torque.

Torque_right = (Tension) * (Distance)

Given that the board is one meter long, the distance from the pivot point (left end) to the right end is 0.8m. We can substitute this value as well.

Since the board has uniform density, we can assume that the mass is distributed evenly throughout its length. To find the mass of the board, we need to calculate the weight of the board.

Weight = Mass * Gravity

The weight acting at the left end of the board is equal to the weight acting at the right end (since the board is in equilibrium). Therefore, we can equate the torque equations:

(Weight) * (0.2m) = (Tension) * (0.8m)

We can substitute the weight as "Mass * Gravity":

(Mass * Gravity) * (0.2m) = (Tension) * (0.8m)

Simplifying the equation, we find:

0.2 * Mass * Gravity = 0.8 * Tension

Next, we can cancel out the gravitational constant (9.8 m/s^2):

0.2 * Mass = 0.8 * Tension

To isolate Mass, we can rearrange the equation:

Mass = (0.8 * Tension) / 0.2

Finally, substituting the given tension value, we can solve for the mass of the board.

You know the center of mass of the board is at the midpoint. Sum moments around the rope connection to get the mass of the board.