Math Problem Statement
Solution
To solve this problem, we need to find the net work done on the cargo canister by the three forces during a displacement of 3.50 m. The forces are acting on the canister at given angles, and the formula for work is:
Where:
- is the net force in the direction of the displacement,
- is the displacement (3.50 m), and
- is the angle between the force and the displacement direction.
Steps:
-
Decompose the forces: Since the forces are acting at angles, we need to find the components of each force in the horizontal () and vertical () directions.
-
Force is along the negative x-axis, so:
-
Force is at an angle from the negative x-axis:
-
Force is at an angle from the positive x-axis:
-
-
Calculate the net force in each direction:
-
Find the magnitude of the net force:
-
Calculate the angle of the net force:
-
Find the work done: Since the displacement is along the x-axis, we only need the horizontal component of the net force:
Thus, the net work done on the canister by the three forces is approximately 11.38 joules.
Would you like more details or have any questions?
Here are 5 related questions:
- What is the significance of decomposing forces into components?
- How do angles affect the calculation of work done by forces?
- What would happen if the displacement was in a different direction?
- How would you calculate the work done by individual forces?
- Can the net work be negative in any scenario?
Tip: Always remember to decompose vectors into components before applying them to different directions of motion!
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Math Problem Analysis
Mathematical Concepts
Physics
Work
Vector Decomposition
Trigonometry
Formulas
Work formula: W = F_net * d * cos(θ)
Vector components: Fx = F * cos(θ), Fy = F * sin(θ)
Pythagorean theorem: F_net = √(Fx^2 + Fy^2)
Inverse tangent: θ_net = tan^(-1)(Fy / Fx)
Theorems
Pythagorean Theorem
Trigonometric Ratios
Suitable Grade Level
Grade 11-12
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