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Transcribed Image Text:**3. Forces on an Incline:** Find the speed of the crate at the bottom given the coefficient of kinetic friction is 0.10. Use three different approaches.
The diagram illustrates a crate on an incline with an angle of \(30.0^\circ\), with the crate initially at rest (\(\vec{v}_i = 0\)). The incline is 10 meters long. The crate slides down the incline to the bottom where its velocity is \(\vec{v}_f\).
Approaches to solve the problem:
(a) **Kinematics + Dynamics:**
- Use the equations of motion considering the forces acting on the crate along the incline, including gravitational force, normal force, and frictional force.
(b) **Work-Kinetic Energy Theorem:**
- Calculate the work done by all forces and relate it to the change in kinetic energy of the crate.
(c) **Conservation of Energy:**
- Apply the principle of conservation of energy, taking into account the initial potential energy, kinetic energy at the bottom, and the energy lost due to friction.
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