Two packing crates of masses m1 = 10.0 kg and m2 = 3.20 kg are connected by a light string that passes over a frictionless pulley as in the figure. The 3.20-kg crate lies on a smooth incline of angle 44.0°.
Incomplete.
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To solve this problem, we need to break it down into smaller parts and analyze each part separately. Let's start by analyzing the system and setting up the equations.
1. Draw a Free Body Diagram (FBD) for each crate:
- Crate with mass m1: It is hanging vertically, so the forces acting on it are its weight (mg) and tension (T) in the string.
- Crate with mass m2: It is lying on a smooth incline, so the forces acting on it are its weight (mg) and the normal force (N) perpendicular to the incline.
2. Write down the equations using Newton's second law (ΣF = ma) for each crate:
- Crate with mass m1: T - m1g = m1a (since it is accelerating downwards)
- Crate with mass m2: m2g sinθ - N = m2a (along the incline) and N - m2g cosθ = 0 (perpendicular to the incline)
3. Combine the equations to eliminate the unknown forces:
- From the equation for m2, we can solve for N: N = m2g cosθ
- Substituting this value for N in the equation for m2, we get: m2g sinθ - m2g cosθ = m2a
- Simplifying, we have: m2(g sinθ - g cosθ) = m2a
- Factoring out g, we get: m2(g(sinθ - cosθ)) = m2a
- Canceling out m2, we have: g(sinθ - cosθ) = a
4. Calculate the acceleration (a) using the given value of the angle θ:
- Plug in the value of θ (44.0°) and the acceleration due to gravity (9.8 m/s²) into the equation: g(sinθ - cosθ) = a
- Calculate the value of a.
Once you have determined the value of the acceleration, you can use it to solve the rest of the problem and answer any additional questions.