A diver stands at rest at the end of a massless diving board as shown in Figure P8.16.
(a) If the mass of the diver is 161 kg, and the board is 4 m long, what is the torque due to gravity on the diving board?
I was thinking that T=Frsin(theta)...
but I can't seem to get it right. What would theta be?
never mind... I just figured it out!
To find the torque due to gravity on the diving board, you need to consider the weight of the diver and the distance between the point of rotation (fulcrum) and the center of mass of the diver. The formula you mentioned, T = Frsin(theta), is correct, where T represents torque, F represents the force, r represents the distance, and theta represents the angle between the force vector and the lever arm vector.
In this case, the force is the weight of the diver, which can be calculated using the formula F = mg, where m is the mass of the diver and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, F = 161 kg * 9.8 m/s^2 = 1577.8 N.
Theta represents the angle between the force vector and the lever arm vector. Since the diver is standing at rest, the force of gravity acts straight downward vertically, and the lever arm vector is horizontal. Therefore, the angle theta between them is 90 degrees (or pi/2 radians).
Now, you need to find the lever arm distance (r) between the point of rotation (fulcrum) and the center of mass of the diver. In this case, the lever arm distance is the length of the diving board, which is given as 4 m.
Now, you can calculate the torque by substituting the values into the formula:
T = Frsin(theta)
T = (1577.8 N) * (4 m) * sin(90 degrees)
T = 6311.2 Nm
Therefore, the torque due to gravity on the diving board is 6311.2 Nm.