The effort required to lift a 400N load using a crowbar pivoted 20 cm from the tip is 100N. The mechanical advantage is 4, the velocity ratio is also 4, and the efficiency is 100% in a frictionless scenario.
A crowbar is an example of a lever, a simple machine that can amplify an applied force. In this problem, the crowbar is 1 meter long and pivoted 20 cm from the tip where a load of 400N is lifted. To find the effort needed, we apply the principle of moments, which states that the moment about the pivot must be the same for both the effort and the load.
The distance from the pivot to the load is 0.2 m (20 cm), and the distance from the pivot to the point where the effort is applied is 0.8 m (the remainder of the length of the crowbar). The principle of moments gives us:
Effort × Effort Arm = Load × Load Arm
The mechanical advantage (MA) is the ratio of the load to the effort, and ideal MA (IMA) is obtained when we assume no losses due to friction:
IMA = Load Arm / Effort Arm
In this case: IMA = 0.8 m / 0.2 m = 4
To find the actual effort required to lift the load:
Effort = Load / MA
Effort = 400N / 4 = 100N
The velocity ratio (VR) is the ratio of the distance moved by the effort to the distance moved by the load. Since they move proportionally to their respective arm lengths in a lever:
VR = Effort Arm / Load Arm = 4 (same as MA in absence of friction)
The efficiency of a machine is the ratio of the useful output work to the input work. In a frictionless scenario:
Efficiency = (MA / VR) × 100%
Efficiency = (4 / 4) × 100% = 100%