The rafters of a roof meet at an angle of 120 degrees. What force is exerted along the rafters by an object weighing 6000nt suspended from the peak?
Woulnt each rafer be supporting 3000N, so the compressive force is given by
cosine60 = 3000/compressive force
and solve for the compressive force. This gives you an idea why in past times flying buttresses were invented...to keep the walls from flying away.
http://www.google.com/images?q=flying+buttresses&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&um=1&ie=UTF-8&source=og&sa=N&hl=en&tab=wi&biw=1219&bih=724
To find the force exerted along the rafters, we need to determine the component of the weight that acts along the slope of the rafters. We can use trigonometry to calculate this.
First, let's consider the triangle formed by the weight, the rafter, and the horizontal line connecting the rafter's endpoints. The angle between the rafter and the horizontal line is 120 degrees. The weight (6000 N) is acting vertically downwards from the peak.
To find the force along the rafters, we need to find the component of the weight that acts along the slope of the rafters. We can use the formula:
Force along rafters = Weight * cos(angle)
In this case, the angle is 120 degrees. Therefore:
Force along rafters = 6000 N * cos(120 degrees)
Now, let's calculate this:
Force along rafters = 6000 N * cos(120 degrees)
To calculate the cosine of 120 degrees, we can use a scientific calculator or an online calculator. The cosine of 120 degrees is -0.5.
Force along rafters = 6000 N * (-0.5)
Force along rafters = -3000 N
Therefore, the force exerted along the rafters by the object weighing 6000 N suspended from the peak is -3000 N. The negative sign indicates that the force is acting in the opposite direction of the weight, which is upward along the slope of the rafters.