Calculating Forces and Torques in a Basic Equilibrium Problem

  • Thread starter Matt Armstrong
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That is, I'm not sure where the 0.8 comes from.Also, please try to organize your equations in a more orderly fashion. It's difficult to follow what you're doing without any organization.In summary, a sturdy wooden plank with a length of 4 meters and a mass of 42 kg is supported by two supports placed 1.2 meters from each end. A man with a mass of 72 kg stands 1 meter from the right end of the plank. Using the equations ΣFy=0 and Στ=0, the upward forces on each support can be calculated. The torque produced by the man is equal to his weight, and the torque of the plank is also equal to
  • #1
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.
 
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  • #2
Hello,

As I can see, you have written the ΣFy=0 equation but you have not used it.
 
  • #3
Matt Armstrong said:
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.
Matt Armstrong said:
adding the torques of the man and board together and then solving for F_R
Sounds good. Please post your attempt.
DoItForYourself said:
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.
 
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  • #4
haruspex said:
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?
 
  • #5
You are aware that, when you calculate moments, you need to multiply by the moment arm, correct?
 

Related to Calculating Forces and Torques in a Basic Equilibrium Problem

1. What is a basic equilibrium problem?

A basic equilibrium problem is a type of question that involves calculating the equilibrium constant (K) for a chemical reaction. It typically asks for the concentration of reactants and products at equilibrium, given the initial concentrations and the value of K. The solution to a basic equilibrium problem involves setting up an ICE table and using the equilibrium expression to solve for unknown quantities.

2. How do I know if a problem is a basic equilibrium problem?

A problem is considered a basic equilibrium problem if it involves a reversible chemical reaction and asks for the equilibrium concentrations of reactants and products. It may also mention the equilibrium constant (K) or provide initial concentrations of reactants and products.

3. What is the purpose of solving a basic equilibrium problem?

The purpose of solving a basic equilibrium problem is to understand the relationship between the concentrations of reactants and products in a chemical reaction at equilibrium. It allows scientists to predict the direction of a reaction and the amount of product formed under certain conditions.

4. What are some common mistakes when solving basic equilibrium problems?

One common mistake when solving basic equilibrium problems is not properly setting up an ICE table. Another mistake is not using the correct value of K, which can vary depending on the units used for concentration. Additionally, forgetting to account for the stoichiometric coefficients of reactants and products when calculating equilibrium concentrations can lead to incorrect answers.

5. How can I improve my problem-solving skills for basic equilibrium problems?

The best way to improve your problem-solving skills for basic equilibrium problems is to practice, practice, practice. Make sure you understand the concepts behind equilibrium, such as Le Chatelier's principle and the equilibrium constant expression. It is also helpful to seek guidance from a teacher or tutor if you are having trouble with a specific problem or concept.

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