Not sure if I have the correct angle and mass for this sum of forces

In summary, the conversation discusses balancing forces east-west and north-south using the given equations and distances on a vertical plate mounted on a horizontal axis. The forces in consideration are the weights of the masses placed at specific distances from the origin. The conversation also addresses the possibility of balancing moments and questions the relevance of horizontal forces in this scenario. It is determined that only vertical forces are acting in this situation.
  • #1
dougiehazard
2
0
Homework Statement
Balance the following face plate if the masses are as follows:A = 2.8 kg, B = 3.5 kg, C = 4.2 kg, D = 4.8 kg, E = ?(What angle and mass should E be placed to balance the other 4 masses
angle.PNG

Balance the forces east-west:

3.5kg*sin45º + 4.2kg*cos30º - 4.8kg*sin30º - E*cosΘ = 0

E*cosΘ = 3.712 kg
balance north-south:

2.8kg + 3.5kg*cos45º - 4.2kg*sin30º - 4.8kg*cos30º + E*sinΘ = 0

E*sinΘ = 0.982
EsinΘ / EcosΘ = 0.982 / 3.712

tanΘ = 0.2645

Θ = 14.8º ◄
E = 3.712kg / cos14.8º = 3.84 kg ◄
If that's not right, then you want to balance the moments.
balancing east west:

3.5kg*0.35*sin45º + 4.2kg*0.315*cos30º - 4.8kg*0.6*sin30º - E*0.2*cosΘ = 0

E*cosΘ = 2.86 kg
and north-south

2.8kg*0.35 + 3.5kg*0.35*cos45º - 4.2kg*0.315*sin30º - 4.8kg*0.6*cos30º + E*0.2*sinΘ = 0

E*sinΘ = 6.55 kg
EsinΘ / EcosΘ = 6.55 / 2.86

tanΘ = 1.706

Θ = 59.6º ≈ 60º
E = 6.55kg / sin59.6º = 7.6 kg
 
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  • #2
I assume you are asking which approach is correct.
Are we to understand that the plate is mounted vertically on a horizontal axis through the origin, and that the numbers in the diagram are distances of the masses from the origin?
What forces act where?
 
  • #3
forces are the weight id assume and yes the number are distances in the diagram
 
  • #4
dougiehazard said:
forces are the weight id assume
Then why are you considering a horizontal balance of forces?
Does any other force act vertically?
 

1. How do I determine the correct angle for a sum of forces?

The correct angle for a sum of forces can be determined using trigonometric functions such as sine, cosine, and tangent. These functions use the lengths of the sides of a triangle to calculate the angle. You can also use a protractor to measure the angle directly.

2. What is the importance of having the correct angle in a sum of forces?

The correct angle is crucial in a sum of forces because it determines the direction of the resultant force. If the angle is incorrect, the calculated resultant force will also be incorrect, leading to inaccurate predictions and calculations.

3. How do I calculate the mass for a sum of forces?

The mass for a sum of forces can be calculated using the formula F=ma, where F is the resultant force, m is the mass, and a is the acceleration. Rearranging the formula, you can also calculate the mass by dividing the resultant force by the acceleration.

4. What happens if the mass used in a sum of forces calculation is incorrect?

If the mass used in a sum of forces calculation is incorrect, the calculated resultant force will also be incorrect. This can lead to inaccurate predictions and calculations, and may also affect the overall accuracy of the experiment or study.

5. How can I ensure that I have the correct angle and mass for a sum of forces?

To ensure that you have the correct angle and mass for a sum of forces, it is important to double-check your calculations and measurements. You can also compare your results with known values or use multiple methods to confirm your findings. Additionally, seeking guidance from a colleague or mentor can help verify the accuracy of your calculations.

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