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.
B) 0.5 meter.
C) 0.25 meter.
D) None of these.
B) 0.5 meter.
In an ideal pulley system, the mechanical advantage is equal to the number of sections of rope supporting the load. In this case, there are two sections of rope supporting the load.
According to the principle of mechanical advantage, the force exerted by the load is equal to the force applied at one end of the rope divided by the mechanical advantage.
So, the force exerted by the load can be calculated as follows:
Force exerted by the load = Force applied at one end of the rope / Mechanical advantage
Force exerted by the load = 50 N / 2 = 25 N
Now, we can use the formula for work:
Work = Force x Distance
Given that the force exerted by the load is 25 N, we can calculate the distance lifted by the load:
Work = 25 N x Distance
Since the work done is equal to the force exerted multiplied by the distance, we can rearrange the formula to solve for distance:
Distance = Work / Force
Distance = 200 N x 1 m / 25 N
Distance = 8 meters
Therefore, the 200-N load will be lifted a distance of 8 meters.
So, the correct answer is: D) None of these.
To solve this problem, we need to understand the concept of an ideal pulley system. In an ideal pulley system, the pulleys are considered to be massless and frictionless. This means that no energy is lost due to the weight of the pulleys or the friction between the rope and the pulleys.
In an ideal pulley system, the tension in the rope is always the same throughout the system. This means that the force applied at one end of the rope will be transmitted equally to the load being lifted.
In this problem, we are given that we pull one end of the rope downward by 1 meter with 50 N of force. The load being lifted has a weight of 200 N.
Since the tension in the rope is the same throughout the system, the load being lifted will experience an upward force of 50 N. This upward force will be equal to the weight of the load, so we can say that the load will be lifted with a force of 200 N.
To calculate the distance the load is lifted, we can use the formula:
Work = Force x Distance
The work done on the load is equal to the force applied (200 N) multiplied by the distance the load is lifted (D).
Work = 200 N x D
We know that the work done on the load is equal to the work done by pulling the rope downward, which is equal to the force applied (50 N) multiplied by the distance the rope is pulled downward (1 meter).
Work = 50 N x 1 meter
Since the work done is the same in both cases, we can set the two equations equal to each other:
200 N x D = 50 N x 1 meter
Simplifying the equation, we get:
D = (50 N x 1 meter) / 200 N
D = 0.25 meter
Therefore, the correct answer is C) 0.25 meter.