A uniform horizontal beam weighing 136 kg is 10.4 m long and is supported by columns at each end. A vertical load of 1275 kg is applied to the beam x metres from the right end. Find x so that the reaction at the left column is 540 kg. Round your answer to 2 decimal places
sum moments about the right end.
1275x+136(10.4/2)-L*10.4=0
let L be 540, solve for x.
I am also helpless
To find the value of x, 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 rotational equilibrium.
In this case, the moment of the weight of the beam about the left column is balanced by the moment of the vertical load about the right column.
The moment of a force about a point is given by the formula:
Moment = Force * Distance
First, let's find the moment of the weight of the beam about the left column. The weight of the beam can be calculated by multiplying its mass (136 kg) by the acceleration due to gravity (9.8 m/s^2):
Weight of the beam = mass * acceleration due to gravity
= 136 kg * 9.8 m/s^2
= 1332.8 kg m/s^2
The distance between the left column and the vertical load is given as x. The distance between the left column and the right end of the beam is 10.4 m - x. Therefore, the moment of the weight of the beam about the left column is:
Moment of the weight of the beam = Weight of the beam * Distance from the left column
= 1332.8 kg m/s^2 * (10.4 m - x)
Next, let's find the moment of the vertical load about the right column. The moment of a force is again calculated by multiplying the force by the distance. The distance between the vertical load and the right column is x. The force is the weight of the vertical load:
Moment of the vertical load = Force * Distance
= Vertical load * Distance from the right column
= 1275 kg * x
According to the principle of moments, the moments of the weight of the beam and the vertical load must be equal:
Moment of the weight of the beam = Moment of the vertical load
From this equation, we can set up our equation to solve for x:
1332.8 kg m/s^2 * (10.4 m - x) = 1275 kg * x
Now, we can solve for x:
1332.8 kg m/s^2 * 10.4 m - 1332.8 kg m/s^2 * x = 1275 kg * x
1332.8 kg m/s^2 * 10.4 m = 1275 kg * x + 1332.8 kg m/s^2 * x
13876.32 kg m/s^2 = (1275 kg + 1332.8 kg m/s^2) * x
13876.32 kg m/s^2 = 2607.8 kg m/s^2 * x
x = 13876.32 kg m/s^2 / 2607.8 kg m/s^2
x ≈ 5.32
Therefore, the value of x that will result in a left column reaction of 540 kg is approximately 5.32 meters.