Last updated on May 14th, 2022 at 02:20 pm
A pulley is a grooved wheel with a rope, chain, or cable running along the groove. A pulley can change the direction of the input force or increase the output force, depending on whether the pulley is fixed or movable. A system of pulleys can change the direction of the input force and make the output force larger. In this post, we will see how a pulley can be described as a lever as well.
A single fixed pulley is a modified first-class lever or a type 1 lever. The axle of this pulley acts as the fulcrum. The two sides of this pulley are the input arm and output arm. Similarly, a single movable pulley acts as a second-class lever or a type 2 lever. In this case, the fulcrum is at one end of the pulley where the supporting rope makes contact with the pulley.
simple pulley systems – with diagram
Figure 1 below shows 3 types of pulleys with input (effort) and output (load) shown. The thicker arrow beside each pulley points to the direction of the input or effort, and the thinner arrow shows the direction of the movement of the load or output. For 1(a) and 1(b) pulleys, their equivalent lever systems are also shown in figure 1 below.
[Read more about types of pulleys and their operation]
Pulley as type 1 lever
The single fixed pulley in Figure 1a behaves like a type 1 lever. The axis of the pulley acts as the fulcrum, and both lever distances (the radius of the pulley) are equal so the pulley does not multiply force.
It simply changes the direction of the applied force. In this case (figure 1a), as the effort arm equals the load arm, the mechanical advantage or MA of this pulley lever equals 1. Notice that the input distance equals the output distance the load moves.
effort arm = distance between the fulcrum and the input(effort)
load arm = distance between the fulcrum and the output(load)
Pulley as type 2 lever
In Figure 1b, the single movable pulley acts as a type 2 lever. If you observe minutely then you can see that the fulcrum is at the left end of the pulley where the supporting rope makes contact with the pulley.
Input or effort is applied on the right end of the pulley lever.
The load is suspended halfway between the fulcrum and the input end of the lever. Hence, the effort arm is twice the load arm. Each Newton of input will support two newtons of load, so the mechanical advantage is 2.
Mechanical Advantage of a pulley depends on the distances moved by the effort and the load
This mechanical advantage number of a pulley system (MA) is related to the distances moved by the input and the output.
MA of a pulley = (distance travelled by the effort or input) / (distance travelled by the load or output)
Refer to the pulley in figure 1(b): For the pulley with MA equal to 2, to raise the load by 1 m, a person will have to pull the rope up by 2 m.
mechanical advantage of a pulley depends on the number of strands of rope supporting the load – explain
The mechanical advantage for simple pulley systems is the same as the number of strands of rope that actually support the load.
If we say the mechanical advantage of a pulley is 2 then it also means that the load is now supported by 2 strands of rope. This means each strand supports half the load. The force the person applies to support the load is therefore only half of the weight of the load.
In Figure 1a, the load is supported by one strand and the mechanical advantage is 1. In Figure 1b, the load is supported by two strands and the mechanical advantage is 2.
Now let’s see how to use this rule to state the mechanical advantage of the pulley system in figure 1c?
The mechanical advantage of the simple system in figure 1c is 2. Notice that although three strands of rope are shown, only two
strands actually support the load. The upper pulley serves only to change the direction of the force.
Hence, we can say that the mechanical advantage of a pulley equals the number of strands of rope supporting the load.