Final answer:
To lift a 400-pound weight with a lever having a 30-inch handle and a 2-inch axle, you would need to apply a force of 26.7 pounds to the handle.
Step-by-step explanation:
Calculating the Force to Lift a Weight with a Lever
When dealing with the physics of levers, we apply the principle of mechanical advantage (MA). The MA is the ratio of the length of the effort arm (dh) to the length of the load arm (da). Given an axle with an effort arm of 30 inches and a load arm of 2 inches to lift a 400-pound weight, we can calculate the force required using the mechanical advantage formula:
MA = dh/da
For this scenario, MA = 30"/2" = 15. As such, the force (F) needed can be determined by dividing the weight (Wt.) by the mechanical advantage (MA):
F = Wt./MA
F = 400 lbs / 15 = 26.7 lbs (to the nearest tenth).
Therefore, to lift a 400-pound weight with a lever having a 30-inch handle and a 2-inch axle, a force of 26.7 pounds must be applied to the handle.
The Complete Question is:
Given the axle below, how much force must be applied to the handle to lift the weight?
[da=2", dh=30", wt.=400lbs]
Force (to the nearest tenth) =