Examkin

Soru

Zorluk: ZorInclined Planes

A motorized winch is pulling a 1,500 lb1,500\text{ lb} boat and trailer assembly up a concrete boat ramp at a constant speed. The ramp has a total length of 40 ft40\text{ ft} and a vertical drop of 8 ft8\text{ ft} from the parking lot to the water level. If the mechanical efficiency of the ramp system is 80%80\% (due to friction in the wheel bearings and surface resistance), what is the actual effort force, in pounds, the winch must apply to pull the assembly up the ramp?

Cevap: 375 lb

Cevap

The winch must apply an actual effort force of 375 pounds.
To solve this problem, you must integrate the concepts of Ideal Mechanical Advantage (IMA) and mechanical efficiency. First, find the IMA by dividing the ramp's length by its vertical drop (40/8=540 / 8 = 5). In an ideal, frictionless system, the effort force required would be the load divided by the IMA (1500/5=300 lb1500 / 5 = 300\text{ lb}). However, the problem states the system is only 80%80\% efficient due to friction. Efficiency is the ratio of ideal effort to actual effort. To find the actual effort force, divide the ideal effort by the efficiency (300/0.80=375 lb300 / 0.80 = 375\text{ lb}).

Adım Adım Çözüm

1
Calculate the Ideal Mechanical Advantage (IMA).
IMA=5\text{IMA} = 5
The IMA of an inclined plane is found by dividing the length of the slope by the vertical height (40/8=540 / 8 = 5).
2
Calculate the theoretical effort force required under ideal, frictionless conditions.
Theoretical Effort=300 lb\text{Theoretical Effort} = 300\text{ lb}
Theoretical effort force is the load divided by the IMA (1500/5=300 lb1500 / 5 = 300\text{ lb}).
3
Calculate the actual effort force by accounting for the mechanical efficiency.
Actual Effort=375 lb\text{Actual Effort} = 375\text{ lb}
Because the system is only 80%80\% efficient, it requires more force than the ideal scenario. Divide the theoretical effort by the efficiency as a decimal (300/0.80=375 lb300 / 0.80 = 375\text{ lb}).

Anahtar Kavram

Actual Mechanical Advantage and Efficiency of Inclined Planes
Bu soruyu puanla

Konular

Inclined Planes

Bu konudan daha fazla soru