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The mechanical advantage of a pulley system can be analysed using free body diagrams which balance the tension force in the rope with the force of gravity on the load. In an ideal system, the massless and frictionless pulleys do not dissipate energy and allow for a change of direction of a rope that does not stretch or wear.
The free body diagrams of the two hanging masses of the Atwood machine. Our sign convention, depicted by the acceleration vectors is that m 1 accelerates downward and that m 2 accelerates upward, as would be the case if m 1 > m 2. An equation for the acceleration can be derived by analyzing forces.
Block on a ramp and corresponding free body diagram of the block. In physics and engineering, a free body diagram (FBD; also called a force diagram) [1] is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the ...
Examples of rope and pulley systems illustrating mechanical advantage. Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter, and attached to the weight is called a single pulley. It has a mechanical advantage (MA) = 1 (assuming frictionless bearings in the pulley ...
Diagram 3 shows three rope parts supporting the load W, which means the tension in the rope is W/3. Thus, the mechanical advantage is three-to-one. By adding a pulley to the fixed block of a gun tackle the direction of the pulling force is reversed though the mechanical advantage remains the same, Diagram 3a. This is an example of the Luff tackle.
Nine men pull on a rope. The rope in the photo extends into a drawn illustration showing adjacent segments of the rope. One segment is duplicated in a free body diagram showing a pair of action-reaction forces of magnitude T pulling the segment in opposite directions, where T is transmitted axially and is called the tension force.
The swinging Atwood's machine is a system with two degrees of freedom. We may derive its equations of motion using either Hamiltonian mechanics or Lagrangian mechanics. Let the swinging mass be and the non-swinging mass be . The kinetic energy of the system, , is:
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