Part1: Determine the magnitude of the component of F directed along the axis of AB. Set F = 480 N
.
Express your answer to two significant figures and include the appropriate units.
Part2: Determine the magnitude of the component of F directed along the axis of AC
.
Express your answer to two significant figures and include the appropriate units.
session.masteringengineering.com/problemAsset/2071764/4/Hibbler.ch2.p7.jpg
PartA: AB=480sin(60)/sin(75)=
PartB: AC=450sin(45)/sin(75)=
To determine the magnitudes of the components of F directed along the axes of AB and AC, we will use the dot product formula and the projection formula.
Part 1: Component of F along the axis of AB
To find the component of vector F along the axis of AB, we need to find the dot product of F and the unit vector along AB.
1. Find the unit vector along AB:
To find the unit vector along AB, we need to subtract the initial point from the terminal point: AB = B - A. Then divide AB by its magnitude to get the unit vector uAB.
2. Calculate the dot product:
The dot product of F and uAB can be calculated using the formula: F · uAB = |F| |uAB| cosθ, where |F| is the magnitude of F and θ is the angle between F and uAB.
3. Determine the magnitude of the component:
The magnitude of the component of F along the axis of AB is given by: |F|cosθ.
Part 2: Component of F along the axis of AC
To find the component of vector F along the axis of AC, we will follow similar steps as in Part 1.
1. Find the unit vector along AC:
To find the unit vector along AC, we need to subtract the initial point from the terminal point: AC = C - A. Then divide AC by its magnitude to get the unit vector uAC.
2. Calculate the dot product:
The dot product of F and uAC can be calculated using the formula: F · uAC = |F| |uAC| cosθ, where |F| is the magnitude of F and θ is the angle between F and uAC.
3. Determine the magnitude of the component:
The magnitude of the component of F along the axis of AC is given by: |F|cosθ.
Now, to actually calculate the magnitudes of the components of F along AB and AC, we would need the values of the vectors AB, AC, and the angles θ1 and θ2. The provided image link does not give these values, so you would need to refer to the actual problem or any accompanying information to obtain the necessary data. Once you have the values, you can plug them into the formulas mentioned above to find the magnitudes of the components.