Question1 Forces
19. Two ropes are attached to a tree, and forces of and are applied. The forces are coplanar (in the same plane).
(a) What is the resultant (net force) of these two force vectors? (b) Find the magnitude and direction of this net force.
Studdy Solution
STEP 1
1. Two forces, and , are applied to a tree.
2.
3.
4. The forces are coplanar.
5. We need to find the resultant force vector and its magnitude and direction.
STEP 2
1. Calculate the resultant force vector.
2. Determine the magnitude of the resultant force.
3. Determine the direction of the resultant force.
STEP 3
Calculate the resultant force vector by adding the corresponding components of and .
Combine the components and the components:
STEP 4
Determine the magnitude of the resultant force using the Pythagorean theorem.
Calculate the squares and sum them:
STEP 5
Determine the direction of the resultant force by calculating the angle with respect to the positive axis using the tangent function.
Calculate using the inverse tangent function:
The direction of the resultant force is approximately above the positive axis.
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