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Chapter 8: Problem 27

A rod is being used as a lever as shown. The fulcrum is \(1.2 \mathrm{m}\) from the load and \(2.4 \mathrm{m}\) from the applied force. If the load has a mass of \(20.0 \mathrm{kg}\). what force must be applied to lift the load?

Short Answer

Expert verified
Solution: To lift the load, a force of 98.1 N must be applied to the rod.

Step by step solution

01

Convert mass to weight

First, we need to convert the mass of the load (\(20.0 \mathrm{kg}\)) to weight, which is the force acting on the load due to gravity, by multiplying the mass by the acceleration due to gravity (\(g\approx 9.81 \mathrm{m/s^2}\)). Weight of the load \(= m \times g = 20.0 \mathrm{kg} \times 9.81 \mathrm{m/s^2} = 196.2 \mathrm{N}\)
02

Calculate the torque due to the load

We can now calculate the torque due to the load as the product of the weight of the load and the distance from the fulcrum: \(\tau_\text{load} = \text{Weight of the load} \times \text{Distance from the fulcrum} = 196.2 \mathrm{N} \times 1.2 \mathrm{m} = 235.44 \mathrm{Nm}\)
03

Find the applied force

In order to lift the load, the applied force must generate a torque equal in magnitude to that of the load but with an opposite direction. Since we know the distance of the applied force from the fulcrum (\(2.4 \mathrm{m}\)), we can calculate the required force: \(\tau_\text{applied} = \tau_\text{load} = F_\text{applied} \times \text{Distance from the fulcrum}\) \(F_\text{applied} = \frac{\tau_\text{load}}{\text{Distance from the fulcrum}} = \frac{235.44 \mathrm{Nm}}{2.4 \mathrm{m}} = 98.1 \mathrm{N}\) So, to lift the load, a force of \(98.1 \mathrm{N}\) must be applied to the rod.

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