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Answer :
A 22 kg, 4 m ladder rests on the side of a house, making a 67 degree angle with the ground. 397.72 Nm is the net torque on the ladder.
To calculate the net torque on the ladder, we can consider the gravitational force acting on the ladder, which will act at its center of mass. The torque due to this force will act perpendicular to the ladder's length.
First, let's find the distance from the pivot point (the point where the ladder touches the ground) to the center of mass of the ladder:
Distance = 0.5 × ladder length = 0.5 × 4m = 2m
Now, let's calculate the gravitational force acting on the ladder:
Force = mass × gravity = 22kg × 9.81m/s² ≈ 215.82N
Next, we'll find the component of the gravitational force perpendicular to the ladder:
Perpendicular force = gravitational force × sin(67°) ≈ 215.82N × 0.9218 ≈ 198.86N
Finally, we can calculate the net torque on the ladder:
Net torque = perpendicular force × distance = 198.86N × 2m ≈ 397.72 Nm
So the net torque on the ladder is approximately 397.72 Nm.
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