What Are the Tensions in the Cables When a Crane Lifts a Load?

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When a crane lifts a load of 500 kilograms with a hook mass of 50 kilograms at a constant acceleration of 2 m/s², the forces acting on both the load and the hook must be analyzed. The tension in the lower cable (T1) is calculated as 10,500 N, while the tension in the upper cable (T2) is 1,050 N. These calculations take into account the gravitational force and the additional force due to acceleration. The analysis demonstrates the relationship between mass, gravitational force, and acceleration in determining cable tensions. Understanding these tensions is crucial for safe crane operation and load management.
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A crane is used to hoist a load of mass m1=500 kilograms. The Load is suspended by a cable from a hook of mass m2=50 kilograms, as shown in the diagram above. The load is lifted upward at a constant acceleration of 2 m/s^2.

a) On the diagrams below draw and label the forces acting on the hook and the forces on the load as they accelerate upward.


b)Determine the Tension T1 in the lower cable and the tension T2 in the upper cable as the hook and load are accelerated upward at 2 m/s^2. Use g=10 m/s^2.
 
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T1 = m1 * g + (m1 + m2) * a = 500 * 10 + (500 + 50) * 2 = 10500 NT2 = m2 * g + (m1 + m2) * a = 50 * 10 + (500 + 50) * 2 = 1050 N
 
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