A construction supervisor of mass M = 83.7 kg is standing on a board of mass m = 30.5 kg. The board is supported by two saw horses that are a distance of 4.50 m apart. If the man stands a distance x1 = 1.30 m away from saw horse 1 as shown, what is the force that the board exerts on that saw horse?
Set the total moment about saw horse 2 equal to zero. Call the upward force at saw horse 1 "F1".
F1*4.50 = Mg(4.50 - 1.30) + mg(2.25)
Solve for F1. The number 2.25 meters appears because the weight of the board acts through the center of gravity.
I still don't quite understand how you got 2.25 meters...
2.25 m is the location of midpoint of the board, where the board's weight acts. That is measured from saw horse 2. I am assuming that the saw horses are at the ends. If a figure (which you did not provide) says otherwise, use the appropriate distance.
ok so i solved all that out and it said i was wrong and told me this
There are two forces acting on the saw horses. One is due the weight of the board. This is evenly distributed between the two saw horses, because the board is placed symmetrically on them.
The other force acting on the saw horse is due to the weight of the man. If the man was standing exactly in the middle, his weight would also be distributed evenly over both saw horses. However, he is standing off to one side, and so his weight gets distributed proportionally to the distances of the man to the saw horses.
To do the math, it is perhaps easiest to use the top of saw horse 2 as the pivot points for calculating the torques on the board. (They have to add up to zero!).
To find the force that the board exerts on saw horse 1, we can use the concept of torques. Torque is the rotational equivalent of force and is defined as the cross product of the force and the lever arm.
1. First, calculate the total weight of the system, which includes the weight of the supervisor and the weight of the board:
Total weight = Weight of supervisor + Weight of board
Total weight = M * g + m * g
where M is the mass of the supervisor, m is the mass of the board, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Next, determine the lever arm of the total weight with respect to saw horse 1. The lever arm is the perpendicular distance between a rotation point and the line of action of the force. In this case, the rotation point can be considered as the center of the saw horse.
Lever arm of total weight = x1 + (0.5 * 4.50)
where x1 is the distance of the supervisor from saw horse 1, and 0.5 * 4.50 is half the distance between the two saw horses.
3. Calculate the torque exerted by the total weight on saw horse 1. Torque is the product of the force and the lever arm.
Torque = Total weight * Lever arm
4. Finally, find the force exerted by the board on saw horse 1 using the equation:
Force = Torque / Lever arm
By following these steps and plugging in the given values (M = 83.7 kg, m = 30.5 kg, x1 = 1.30 m, and the acceleration due to gravity g = 9.8 m/s^2), you can calculate the force that the board exerts on saw horse 1.