Replace the loading by an equivalent resultant force and couple moment acting at point O. Assume F1 = {-420i + 210j + 280k} N and F2 = {-450k} N. Determine the resultant force. Exp... Replace the loading by an equivalent resultant force and couple moment acting at point O. Assume F1 = {-420i + 210j + 280k} N and F2 = {-450k} N. Determine the resultant force. Express the x, y and z components of the resultant force in newtons to three significant figures separated by commas.
Understand the Problem
The problem asks us to find the equivalent resultant force at point O, given two forces F1 and F2 acting on the structure. To solve this, we need to sum the forces F1 and F2, and then express the resultant force in terms of its x, y, and z components. Finally we round to 3 significant figures and list them separated by commas.
Answer
-420, 210, -170
Answer for screen readers
-420, 210, -170
Steps to Solve
- Sum the forces in the i direction
Adding the i components of $F_1$ and $F_2$
$F_{x} = -420 + 0 = -420 \ N$
- Sum the forces in the j direction
Adding the j components of $F_1$ and $F_2$
$F_{y} = 210 + 0 = 210 \ N$
- Sum the forces in the k direction
Adding the k components of $F_1$ and $F_2$
$F_{z} = 280 + (-450) = -170 \ N$
- Write the components separated by commas
Expressing the final answer based on the previous calculations $-420, 210, -170$
-420, 210, -170
More Information
The resultant force is the vector sum of all forces acting on a body. Replacing individual forces with a single resultant force simplifies the analysis of the body's motion or equilibrium.
Tips
A common mistake is to forget to add the corresponding components correctly, especially when one of the forces is zero in a particular direction. Another mistake is misinterpreting the sign of the force components.
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