if the man in figure 6.13 pulls 1 m of rope downward with a force of 100N, and the load rises 1/7 as high (about 14 cm) what is the maximum load that can be lifted?
To find the maximum load that can be lifted, we need to understand the mechanical advantage of the system.
The mechanical advantage is a measure of how much a machine amplifies or multiplies the input force. In this case, we can use the concept of mechanical advantage to determine the relationship between the force applied by the man and the resulting load that can be lifted.
In figure 6.13, if the man pulls 1 meter of rope downward with a force of 100N, and the load rises 1/7 as high (approximately 14 cm), we can make the following observations:
1. The distance over which the man applies the force is 1 meter, and the load rises only 14 cm. This means that the load moves 1/7th of the distance the man pulls the rope.
2. From the concept of mechanical advantage, we know that for a given displacement, the force required by the machine is inversely proportional to the displacement covered by the load. In simpler terms, if the load is lifted less, the force required to lift it can be greater.
Now, let's set up an equation to find the maximum load that can be lifted:
Force applied by the man / Maximum load = Load displacement / Man's displacement
Using the given values:
100N / Maximum load = 1/7
Now we can solve for the maximum load:
Maximum load = (100N) * (7/1)
Maximum load = 700N
Therefore, the maximum load that can be lifted in this scenario is 700 Newtons.