Understanding Work
* Work (W) is the energy transferred when a force (F) moves an object over a distance (d).
* Formula: W = F * d
Solving the Problem
We know:
* Input force (F_input) = 2 Newtons
* Input distance (d_input) = 6 meters
* Output force (F_output) = 4 Newtons
We need to find the output distance (d_output).
Assumptions:
* Ideal machine: We're assuming the machine is perfectly efficient, meaning no energy is lost due to friction or other factors.
* Work input = Work output: In an ideal machine, the work done on the machine (input work) equals the work done by the machine (output work).
Calculations
1. Calculate input work:
W_input = F_input * d_input = 2 Newtons * 6 meters = 12 Joules
2. Since work input = work output:
W_output = 12 Joules
3. Calculate output distance:
W_output = F_output * d_output
12 Joules = 4 Newtons * d_output
d_output = 12 Joules / 4 Newtons = 3 meters
Answer: The output distance of the machine is 3 meters.
