Calculating Support Forces on Plank at the Airport

In summary, the conversation is about a question involving support forces at an airport where painters are working on a plank. The plank is 4.0 m long and has a mass of 22 kg, with two legs supporting it at 0.50 m from either end. The question asks for labeled arrows to show the forces acting on the plank, as well as the calculation of the support force at point A when two painters of different masses sit at specific distances from the ends of the plank. The equations involved are torque and force multiplied by distance. The person asking the question is seeking an explanation for solving this problem, as they were absent during the class that covered support forces. The responder advises consulting a textbook and thinking about prior topics such
  • #1
McArthur
1
0

Homework Statement



QUESTION TWO: AT THE AIRPORT
Some painters are working at the airport. They have a uniform plank resting on two supports. The plank is 4.0 m long. It has a mass of 22 kg. The two legs that support the plank are 0.50 m from either end.

(a)The plank is in equilibrium. Draw labelled arrows of appropriate sizes in the correct position showing the forces acting on the plank on the diagram above.

(b)Calculate the support force on the plank at A if a painter of mass 60 kg sits 0.75 m from A, and another painter of mass 75 kg sits at a distance of 0.80 m from B.
Use g = 10 m s–2.


Homework Equations


Torque = Force x Distance


The Attempt at a Solution


I was away when my class covered support forces, so I haven't got the faintest clue how to do it. I'm not so much looking for an answer, because this is not homework, I'm looking for an explanation which I can use to answer this question later in the year :smile:
 
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  • #2
What do you know about Rotational and Translational equilibrium?

Just saying that you were not in the class isn't going to cut it. Support forces aren't a topic that you should be taught as such. It can be deduced from what you've been doing in prior classes. Consult your textbook for Rotational and Translational equilibrium, two dimensional mechanics and try to think of a way to do this problem. We cannot help you with no efforts from your side. The forum guidelines clearly state that.

EDIT: also, this is posted in the wrong forum.
 
  • #3


I am happy to provide an explanation for calculating support forces on a plank at the airport. Firstly, it is important to understand that support forces are the forces that act on an object to keep it in equilibrium, or in other words, to keep it from falling or moving. In this scenario, the two supports are acting as the forces that keep the plank from falling.

To answer part (a) of the question, we need to identify the forces acting on the plank. These include the weight of the plank, the weight of the two painters, and the support forces from the two legs. The weight of the plank can be calculated using the formula W = mg, where W is the weight, m is the mass and g is the acceleration due to gravity (taken as 10 m/s^2). In this case, the weight of the plank would be 22 kg x 10 m/s^2 = 220 N. The weight of the painters can also be calculated in the same way.

To keep the plank in equilibrium, the support forces from the two legs must balance out the weight of the plank and the painters. This can be represented by the equation ΣF = 0, where ΣF is the sum of all the forces acting on the plank. In this case, the support forces would be equal to the weight of the plank and the painters, which is 220 N + (60 kg x 10 m/s^2) + (75 kg x 10 m/s^2) = 1350 N.

To answer part (b) of the question, we need to use the concept of torque, which is the force applied at a distance from a pivot point. In this case, the pivot point would be the support at point A. The torque equation is T = F x d, where T is the torque, F is the force and d is the distance from the pivot point. The total torque acting on the plank must be equal to zero for it to be in equilibrium.

To calculate the support force at A, we need to consider the torque from the weight of the plank and the two painters. The torque from the weight of the plank can be calculated as T1 = 220 N x 2.25 m (distance from A to the center of the plank), which equals 495 Nm. The torque from the weight of the two painters can be calculated as T2 = (60 kg
 

1. How do you calculate the support forces on a plank at the airport?

To calculate the support forces on a plank at the airport, you will need to use the principles of equilibrium. This means that the sum of all the forces acting on the plank must equal zero. First, identify all the external forces acting on the plank, including the weight of the plank, any additional weight placed on the plank, and the reaction forces from the supports. Then, use the equations for summing forces in the horizontal and vertical directions to solve for the support forces.

2. What factors influence the support forces on a plank at the airport?

The support forces on a plank at the airport are influenced by several factors. These include the weight of the plank, the weight of any objects placed on the plank, the angle of the plank, and the location of the supports. Additionally, any external forces such as wind or vibrations can also affect the support forces.

3. Can the support forces on a plank at the airport be calculated using only one support point?

In most cases, the support forces on a plank at the airport cannot be calculated using only one support point. This is because the plank will likely experience both horizontal and vertical forces, and without a second support point, it would be difficult to determine the exact reaction forces from the first support. It is best to use at least two support points to accurately calculate the support forces.

4. How do you account for friction when calculating support forces on a plank at the airport?

Friction can play a significant role in the support forces on a plank at the airport. To account for friction, you will need to use the coefficient of friction between the plank and the supports. This value can be used to calculate the maximum possible frictional force, which can then be subtracted from the total support forces to determine the actual support forces.

5. Are there any safety precautions to consider when calculating support forces on a plank at the airport?

Yes, there are several safety precautions to consider when calculating support forces on a plank at the airport. First, make sure to use accurate measurements and all necessary safety equipment, such as a level and safety harness. Additionally, double-check all calculations and make sure to account for any potential external factors, such as wind or vibration. It is also important to follow proper safety protocols when setting up and using the support points for the plank.

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