A workman uses a crowbar to lift a manhole cover. The distance from the end of the crowbar where the workman pushes the crowbar downwards to the pivot is 0.90m. The distance from the pivot to the end of the crowbar where it lifts the manhole cover is 0.05m. Force needed to lift the edge of the manhole cover is 900N.
90:5 mechanical advantage
50N downward push
To determine the force applied by the workman on the crowbar, we can use the principle of moments.
The principle of moments states that the sum of the moments acting on an object must be zero for the object to be in equilibrium.
In this case, we have two forces acting on the crowbar:
1. The force applied by the workman pushing the crowbar downwards (let's call this force F1).
2. The force applied by the manhole cover at the other end (let's call this force F2).
The distances between the forces and the pivot point are given as:
Distance from workman to pivot (d1) = 0.90 m
Distance from manhole cover to pivot (d2) = 0.05 m
According to the principle of moments, we can write the equation:
F1 x d1 = F2 x d2
From the question, we are given:
F2 = 900 N
d1 = 0.90 m
d2 = 0.05 m
Solving for F1, the force applied by the workman:
F1 = (F2 x d2) / d1
= (900 N x 0.05 m) / 0.90 m
= 50 N
Therefore, the force applied by the workman on the crowbar is 50 N.
To find the force exerted by the workman to lift the manhole cover, we can use the principle of moments.
The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.
In this case, we can take moments about the pivot point where the crowbar is located.
Let's assume that the force exerted by the workman is F1, and the force needed to lift the manhole cover is F2.
The clockwise moment about the pivot point is given by: M1 = F1 * distance from pivot to the end of the crowbar where the workman pushes downwards (0.90m).
The anticlockwise moment about the pivot point is given by: M2 = F2 * distance from pivot to the end of the crowbar where it lifts the manhole cover (0.05m).
According to the principle of moments, M1 must be equal to M2.
Therefore, we can set up the equation: F1 * 0.90m = 900N * 0.05m
Simplifying the equation, we have: F1 = (900N * 0.05m) / 0.90m
Calculating the expression, we get: F1 = 50N
Hence, the force exerted by the workman to lift the manhole cover is 50 Newtons.