Calculate Torque: Homework Solutions

[halo9909]

Homework Statement

Two people are holding up the ends of a 4.55-kg wooden board that is l = 1.90 m long. A m = 5.00-kg box sits on the board, 0.50 m from one end, as shown below. What forces do the two people exert?

Homework Equations

T=F*d

The Attempt at a Solution

4.55*9.8=44.59N
5*9.8=49N
49N+44.59N=93.59N=Total Force

Length(left)=1.4m Length(right)=.5m


I am unsure how do you calculate the force each person exerts, or if I am missing an equation

 

[hage567]

The total force is not just the sum of the weights. If the board is being held up, each person will exert a force on the board in the upwards direction. So you have four forces to sum up, not two. You also need to sum up the torques by picking one point to be your pivot point (it would be convenient to pick one of the points where a person is holding the board). This will give you two equations to work with.

 

[thomate1]

.

To calculate the torque exerted by each person, we can use the formula T = F*d, where T is the torque, F is the force, and d is the distance from the pivot point. In this case, the pivot point is the end of the board where the person is holding it up.

For the person on the left side of the board, the distance from the pivot point to the box is 1.4m, and the force exerted is the weight of the box, which is 49N. Therefore, the torque exerted by the person on the left is T = (49N)*(1.4m) = 68.6 Nm.

For the person on the right side of the board, the distance from the pivot point to the box is 0.5m, and the force exerted is the weight of the board and the box combined, which is 93.59N. Therefore, the torque exerted by the person on the right is T = (93.59N)*(0.5m) = 46.8 Nm.

So the two people are exerting torques of 68.6 Nm and 46.8 Nm, respectively, to hold up the board and the box.