A machine requires an effort of 3 kN to raise a mass of 2,000 kg. If the load is lifted 1.5 m while the effort moves 12 m, what is the velocity ratio?

To determine the velocity ratio (VR) for the machine described, we utilize the formula that relates the distances moved by the load and the effort. The velocity ratio is defined as the distance moved by the effort divided by the distance moved by the load.

In this case, the effort moves 12 meters while the load is lifted 1.5 meters. Therefore, the calculation for the velocity ratio is:

[

VR = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}} = \frac{12 , \text{m}}{1.5 , \text{m}} = 8

]

This means that for every 1.5 meters the load is lifted, the effort must move 12 meters, leading to a velocity ratio of 8.

Along with this, mechanical advantage (MA) can also be calculated. MA is defined as the ratio of the load force to the effort force. The load can be calculated as:

[

\text{Load} = \text{mass} \times \text{gravity} = 2000 , \text{kg} \times 9.81 , \text{m/s}^2 \approx