How can i answer this question ? Two men carry a weight of 800 Newton. The weight is carried by a stick 1 meter
long. If the weight is 40 cm from one man, what is the force need to be applied by
each man, to keep the stick horizontal?
To find the force needed to keep the stick horizontal, we can use the principle of moments.
The principle of moments states that the sum of the moments acting on an object is equal to zero when the object is in equilibrium.
In this case, the moments created by the weight of the object on one side and the force applied by each man on the other side should balance each other out.
Let's assume that the force applied by the man closer to the weight is F1 and the force applied by the man farther from the weight is F2.
The moment created by the weight is given by the equation:
Moment = Force x Distance
Since the weight is 40 cm from one man and the stick is 1 meter long, the weight is 60 cm from the other man. Therefore, the moment created by the weight is:
Moment = 800 N x 60 cm = 48000 N.cm
To keep the stick horizontal, the sum of the moments created by F1 and F2 needs to be equal to the moment created by the weight.
So, we have the equation:
F1 x 40 cm + F2 x 60 cm = 48000 N.cm
To find the individual forces, F1 and F2, we need to solve this equation.
Since the distances are given in centimeters, it's important to convert them to meters to maintain consistency in units.
40 cm is equal to 0.4 meters, and 60 cm is equal to 0.6 meters.
Now, we have the equation:
F1 x 0.4 m + F2 x 0.6 m = 48000 N.cm
To solve for F1 and F2, we need another equation. Since the stick is horizontal, the sum of the forces in the vertical direction should be equal to zero.
F1 + F2 = 800 N
Now we have a system of two linear equations:
F1 x 0.4 + F2 x 0.6 = 48000
F1 + F2 = 800
We can solve this system of equations to find the values of F1 and F2.
To answer this question, we need to understand the concept of a lever and the principle of moments.
The principle of moments states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments about any point in equilibrium. In this case, the stick acting as a lever is in equilibrium, meaning it is not rotating or moving horizontally.
To find the force needed to be applied by each man, we can apply the principle of moments and set up an equation.
1. Draw a diagram: Draw a simple diagram to visualize the scenario. Label the stick, the weight, and the distances involved.
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^ ^
| |
| W |
| |
|--------|
F F'
2. Assign variables: Assign variables to the unknowns in the equation. Let F represent the force applied by the first man and F' represent the force applied by the second man.
3. Set up the equation: Since the stick is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
Clockwise moment = Weight x Distance
Anticlockwise moment = F x Distance1 + F' x Distance2
F x Distance1 + F' x Distance2 = Weight x Distance
Plugging in the given values:
F x 40 cm + F' x 60 cm = 800 N x 100 cm
4. Convert units if necessary: Convert the distances to meters for consistent units if necessary.
F x 0.4 m + F' x 0.6 m = 800 N x 1 m
5. Solve the equation: Now, you can solve the equation for the forces applied by each man (F and F').
0.4F + 0.6F' = 800
This equation represents a system of linear equations. You can use various methods like substitution or elimination to solve for F and F'.
6. Calculate the forces: Solve the equation to find the values of F and F' that satisfy the equation, giving you the forces needed to be applied by each man to keep the stick horizontal.
Remember to convert the forces back to Newtons if you made any unit conversions earlier.
By following these steps, you should be able to answer the question and determine the force needed to be applied by each man.