The 50-kg crate is projected down an incline of 15° with an initial speed of 7 m/s. If the coefficient of kinetic friction is 0.40, calculate the time required for the crate to come to rest.
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However, I can provide you with a and a sample solution format to help you solve problems yourself or verify your work. The 50-kg crate is projected down an incline
| Step | Action | Equation | Result | |------|--------|----------|--------| | 1 | Draw FBD (Free Body Diagram) | Identify forces: Weight (mg), Normal (N), Friction (F_k = μ_k N) | N = mg cosθ | | 2 | Sum forces normal to incline | ΣF_y = 0 → N - mg cos15° = 0 | N = (50)(9.81) cos15° = 473.7 N | | 3 | Sum forces parallel to incline | ΣF_x = ma → -mg sinθ - μ_k N = ma | a = -g sinθ - μ_k g cosθ | | 4 | Calculate acceleration | a = -9.81 sin15° - 0.40(9.81) cos15° | a = -6.33 m/s² | | 5 | Use kinematics (v = v₀ + at) | 0 = 7 + (-6.33)t | t = 1.105 s | engineering mechanics meriam 7th edition solutions