Calculating Forces and Torques in a Basic Equilibrium Problem

[Matt Armstrong]

Homework Statement

A sturdy wooden plank, 4 meters in length and having a mass of 42 kg, is rests on 2 supports placed 1.2 meters from each end. Suppose a man of 72 kg stands 1 meter from the right end of the board. What are the upward forces on each board?

|---L----R-M--|

Where L is the left support, R is the right support, and M is the man.

Homework Equations

ΣFy = 0

Στ = 0

τ_R = F_R * .8, τ_L = F_L * .8

Total gap between supports is 1.6 meters.

Weight of man = 705.6 N

Weight of board = 411.6 N

The Attempt at a Solution

Each support is located .8 meters away from the board, and thus I have written out those equations above. I know that the torque produced by the man is equal to his weight, as he is 1 meter away from both the center and the edge of the board, and I am assuming the torque of the board is also equal to its weight. I also know that in problems similar to this, like cantilevers, the force of the left support will actually be downward, instead of upward.

I know that if I have the force of the right support, I can figure out the support of the left. At first, I tried to figure the force of the right support out by adding the torques of the man and board together and then solving for F_R, but in hindsight I am not confident that is the correct way to go about it.

 

[DoItForYourself]

Hello,

As I can see, you have written the ΣF_y=0 equation but you have not used it.

 

[haruspex]

the force of the left support will actually be downward

It's a support. By definition, it can only exert an upward force on the plank.

adding the torques of the man and board together and then solving for F_R

Sounds good. Please post your attempt.

you have written the ΣFy=0 equation but you have not used it.

There being no horizontal forces, there are only two equations available. Doesn't matter whether they are two torque equations or one torque and one linear.

 

[Matt Armstrong]

Sounds good. Please post your attempt.

.8*F_R = T_M + T_B = 705.6 + 411.6 = 1117.2 -> 1117.2/.8 = 1396.5 = F_R

1396.5 + F_L - F_M - F_B = 0, with F_L resulting as -279.3, but it needs to be an upward force?

 

[Chestermiller]

You are aware that, when you calculate moments, you need to multiply by the moment arm, correct?