Consider an ideal pulley system. Pull one end of a rope downward by 1 meter with 50 N of force, and you'll lift a 200-N load a distance of ____________________.

A) 1 meter.
Feedback:
Incorrect!

B) 0.5 meter.
C) 0.25 meter.
D) None of these.

C)

For an ideal pulley system, Force x distance is the same for both ends.

To a larger weight wth less force than the weight, you move it less distance than you pull the other end

To solve this problem, we need to consider the principles of an ideal pulley system. In an ideal pulley system, the force applied to one end of the rope is equal to the force on the load. Additionally, the distance over which the force is applied is inversely proportional to the distance the load is lifted.

In this scenario, we have a force of 50 N applied to one end of the rope, and the load has a weight of 200 N. Since the force applied to the rope is equal to the weight of the load, we can say that these two forces are equal.

Now, we can use the formula for work:

Work = Force x Distance

Let's denote the distance over which the force is applied as x. Since the force applied to the rope is 50 N and the distance is x, we can write:

50 N x = 200 N * D

Here, D represents the distance the load is lifted.

Now, we can solve for D:

50 x = 200 D
D = (50 x) / 200
D = 0.25 x

From this equation, we can see that the distance the load is lifted, D, is equal to 0.25 times the distance over which the force is applied, which we denoted as x.

So, the correct answer is:

C) 0.25 meter.

To solve this problem, we need to understand the concept of an ideal pulley system. In an ideal pulley system, there is no friction, and the pulley is weightless. In this scenario, we have a rope that passes over the pulley, with one end being pulled downward with a force of 50 N. This will cause the load, which is 200 N, to move upward.

The key concept to understand here is that the tension in the rope remains constant throughout the system. This means that the tension at the end being pulled downward with 50 N is also the same tension that lifts the load of 200 N.

Since the load of 200 N is being lifted, we can determine the distance it will move by using the formula:

Work = Force * Distance

We can rearrange this formula to solve for distance:

Distance = Work / Force

The work done in this case is equal to the product of the force and the distance moved by the end being pulled downward, which is 50 N * 1 m = 50 Nm.

Therefore, the distance moved by the load is Distance = 50 Nm / 200 N = 0.25 m.

So, the correct answer is C) 0.25 meter.