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.
.25
To solve this problem, we can use the concept of mechanical advantage in a pulley system. Mechanical advantage is the ratio of the output force to the input force.
In an ideal pulley system, the mechanical advantage is equal to the ratio of the number of supporting ropes to the load being lifted. The mechanical advantage formula for a pulley system is:
Mechanical Advantage = Number of supporting ropes / Load Being Lifted
In this case, we have one end of the rope being pulled downward by a force of 50 N, and a load of 200 N being lifted. The mechanical advantage can be calculated as:
Mechanical Advantage = 1 (the number of supporting ropes) / 200 N (the load being lifted) = 1/200
Now, we know that mechanical advantage is also equal to the ratio of the distance the input force moves to the distance the load moves. This can be expressed as:
Mechanical Advantage = Distance the input force moves / Distance the load moves
We are given that the input force moves downward by 1 meter. Let's assume the distance the load moves is "x" meters.
Therefore, we can write the equation:
1/200 = 1 meter / x
To solve for "x", we can cross-multiply:
1 * x = 200 * 1 meter
x = 200 meters
So, the load will be lifted a distance of 200 meters.
However, looking at the answer choices provided, none of them match the calculated answer of 200 meters. Therefore, the correct answer would be D) None of these.