Unlocking the Power of Leverage: Maximum Weight Lifted Using the Principle of Moments
How can we determine the largest mass that can be lifted using the principle of moments?
if someone can exert a force of 300N at a distance of 9m from a pivot point, and the mass to be lifted is at a distance of 1m from the pivot, what is the largest mass that can be lifted?
a) 3000kg
b) 275kg
c) 2700kg
d) 30
Answer:
The principle of moments is used to calculate the largest mass that can be lifted. The total moment exerted at a force of 300N 9m from the pivot is 2700 Nm. This can lift a maximum of 270kg, making (b) the right answer.
The largest mass that can be lifted in this scenario can be determined using the principle of moments. The principle of moments states that the total moment exerted by a force is equal to the force multiplied by the distance from the pivot point.
In this case, if a person can exert a force of 300N at a distance of 9m from the pivot, the total moment he can exert is calculated as 300N x 9m = 2700 Nm. This total moment is the maximum weight that can be lifted using the lever.
If the mass to be lifted is located at a distance of 1m from the pivot, the maximum weight that this moment can lift is determined by dividing the total moment by the distance. Therefore, 2700Nm divided by 1m equals 2700N.
To convert this force into mass, we need to consider gravity. Assuming a rough value of 10m/s^2 for gravity, we can calculate the mass as weight divided by gravity. Therefore, 2700N divided by 10m/s^2 equals 270kg. So, the largest mass that can be lifted using the principle of moments in this scenario is 270kg.
By understanding and applying the principle of moments, we can leverage the forces and distances involved to determine the maximum weight that can be lifted efficiently and effectively.