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Zorluk: ZorLevers and Fulcrums

A worker is using a wheelbarrow, which acts as a second-class lever, to transport materials. The wheel's axle serves as the fulcrum. The empty wheelbarrow has a downward weight of 200 N200 \text{ N}, with its center of gravity located 0.5 m0.5 \text{ m} horizontally from the axle. A load of bricks weighing 800 N800 \text{ N} is placed in the tray so that its center of gravity is 0.4 m0.4 \text{ m} horizontally from the axle. The worker lifts upward at the ends of the handles, which are located 1.2 m1.2 \text{ m} horizontally from the axle.

Assuming the wheelbarrow is in a horizontal position, what is the minimum upward force required to lift the rear supports off the ground?

Cevap: 350 N

Cevap

The minimum upward force required to lift the wheelbarrow is 350 N.
The correct answer is derived by applying the principle of moments (torque). Because there are two separate masses acting on the lever, their torques must be calculated independently and summed. The wheelbarrow contributes 100 N⋅m100 \text{ N}\cdot\text{m} of torque and the bricks contribute 320 N⋅m320 \text{ N}\cdot\text{m}. Balancing the total 420 N⋅m420 \text{ N}\cdot\text{m} torque over a 1.2 m1.2 \text{ m} lever arm requires exactly 350 N350 \text{ N} of effort.

Adım Adım Çözüm

1
Calculate the torque from the empty wheelbarrow.
τcart=100 N⋅m\tau_{cart} = 100 \text{ N}\cdot\text{m}
The intrinsic weight of the lever system applies a downward force that must be accounted for.
2
Calculate the torque from the added load.
τload=320 N⋅m\tau_{load} = 320 \text{ N}\cdot\text{m}
The load applies an additional independent downward force at its specific distance from the fulcrum.
3
Sum the downward torques.
τtotal=420 N⋅m\tau_{total} = 420 \text{ N}\cdot\text{m}
In equilibrium, the total clockwise torque must be balanced by the total counterclockwise torque.
4
Divide the total torque by the effort distance to find the effort force.
Feffort=350 NF_{effort} = 350 \text{ N}
Torque equals force times distance. Rearranging 420=F×1.2420 = F \times 1.2 isolates the required lifting force.

Anahtar Kavram

Torque Equilibrium and Composite Loads in Second-Class Levers
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Konular

Levers and Fulcrums

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