Pulleys and Tension Equilibrium in Physics
Learn about pulleys, tension equilibrium, and how to calculate tension and acceleration in a pulley system with objects of different masses. Understand the step-by-step process to solve such problems efficiently.
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Pulleys and Tension Equilibrium
Problem Imagine two objects suspended from a fixed pulley. The mass of object 1 is 1000kg and the mass of object 2 is 1150kg. What is the tension in the rope and the acceleration of object 2? If upwards is the positive y direction for both objects then the acceleration of m1 would be (a1 = a) because m1 accelerates upwards. The acceleration of m2 would be (a2 = a) because m2 accelerates downward. Tension is calculated using the formula ?1= ?1? ?1?1
Step 1 Isolate each side of the pulley and determine the tension in the rope. Because acceleration of mass 1 is in the upwards (positive) direction this can be written as ?1= ?1? + ?1? Because acceleration of mass 2 is in the downward (negative) direction this can be written as ?2= ?2? ?2? The equilibrium rule requires these two equations to be equal to each other ?1? + ?1? = ?2? ?2?
Step 2 Rearranging to get acceleration on one side and gravity on the other would give ?2 ?1? = ?2+ ?1? Solving for acceleration would give ?2 ?1 ?2+?1 ? = ? 1150?? 1000?? 1150??+1000??9.8 ? ?2=0.68 ? ?2 Mass m2 accelerates downward (and mass m1 accelerates upwards) at 0.68m/s2.
Step 3 Tension can then be obtained from either equation ?1? + ? = ?1 ? ?2+ 0.68 ? ?2= 10,500? 1000?? 9.8 Or ?2? ? = ?2 ? ?2 0.68 ? ?2= 10,500? 1150?? 9.8
