Torque - Lady on a diving board

[tascja]

Homework Statement

A woman whose weight is w = 500 N is poised at the right end of a diving board with a length of Lw = 3.90 . The board has negligible weight and is bolted down at the left end, while being supported L2 = 1.40 m away by a fulcrum, as figure shows. Find Forces F1 and F2 that the
bolt and the fulcrum, respectively, exert on the board.

Homework Equations

T= rFsin(theta)

The Attempt at a Solution

Since there are two unknown forces, can i solve for them separately, assuming the axis of rotation is different in each?
to solve for F1 i would have that the fulcrum in the axis of rotation, assuming F2 is 0 for acting on the axis of rotation. and for F2 i would have the fulcrum at the bolt...

 

[method_man]

Homework Statement

A woman whose weight is w = 500 N is poised at the right end of a diving board with a length of Lw = 3.90 . The board has negligible weight and is bolted down at the left end, while being supported L2 = 1.40 m away by a fulcrum, as figure shows. Find Forces F1 and F2 that the
bolt and the fulcrum, respectively, exert on the board.

You can calculate momentuma around bolt.
ΣM=0 F₂*1,4 - w*3.9=0
F₂=w*3.9/1,4
After you get F₂, you can easily calculate F₁:F₁=F₂ - w

 

[nlightner]

I would approach this problem by first defining the variables and equations that are relevant to the situation. Torque, as given by the equation T = rFsin(theta), is a measure of the force that causes an object to rotate around an axis. In this case, the axis of rotation is at the fulcrum where the diving board is supported.

To solve for the unknown forces, F1 and F2, we can use the principle of torque equilibrium, which states that the total torque on an object must be equal to zero for the object to be in rotational equilibrium. This means that the sum of the torques acting in the clockwise direction must be equal to the sum of the torques acting in the counterclockwise direction.

In this scenario, we can consider the forces acting on the diving board at two different points - the bolt and the fulcrum. At the bolt, the only force acting is F1, which is the force exerted by the bolt to hold the diving board in place. At the fulcrum, there are two forces acting - F2, the force exerted by the fulcrum to support the diving board, and the weight of the woman, w.

To solve for F1, we can set up the equation for torque equilibrium at the bolt, where the axis of rotation is located. This gives us:

F1*L2 = w*Lw*sin(theta)

Where theta is the angle between the force and the lever arm, which in this case is 90 degrees. This simplifies to:

F1 = w*(Lw/L2)

Substituting in the given values, we get F1 = 500 N * (3.90 m / 1.40 m) = 1428.57 N. This is the force exerted by the bolt to hold the diving board in place.

To solve for F2, we can set up the equation for torque equilibrium at the fulcrum, where the axis of rotation is also located. This gives us:

F2*Lw = w*Lw*sin(theta)

Again, theta is 90 degrees, so this simplifies to:

F2 = w = 500 N

This means that the fulcrum must exert a force of 500 N to balance out the weight of the woman and keep the diving board in equilibrium.

In conclusion, the forces F1 and F2 exerted by the bolt and the fulcr