1. The problem statement, all variables and given/known data
The crane shown below has a mass of 4000 kg and a base of 3.4 m. The arm of the crane is 22 m and attaches to the center of the crane. If the arm is placed at an angle of 30°, what is the largest mass that the crane can hold off the ground without tipping?
2. Relevant equations
∑τ = 0 when there is rotational equilibrium.
3. The attempt at a solution
The answer to the question chooses the pivot as the right edge of the body of the crane. When I do this, I get the correct answer (400 kg), but at first I chose the pivot to be at the center of the arm of the crane. When I do this, I get 11cos(30)mg = 11cos(30)(4000)g, which makes m = 4000 kg. I don't know why this method is giving me the wrong answer. I always thought that for rotational equilibrium net torque would equal zero at any point in space. Why should the answer vary with what I choose as the pivot? I guess I could also be omitting a force in calculating the torque, but I don't think I am.
The crane shown below has a mass of 4000 kg and a base of 3.4 m. The arm of the crane is 22 m and attaches to the center of the crane. If the arm is placed at an angle of 30°, what is the largest mass that the crane can hold off the ground without tipping?
2. Relevant equations
∑τ = 0 when there is rotational equilibrium.
3. The attempt at a solution
The answer to the question chooses the pivot as the right edge of the body of the crane. When I do this, I get the correct answer (400 kg), but at first I chose the pivot to be at the center of the arm of the crane. When I do this, I get 11cos(30)mg = 11cos(30)(4000)g, which makes m = 4000 kg. I don't know why this method is giving me the wrong answer. I always thought that for rotational equilibrium net torque would equal zero at any point in space. Why should the answer vary with what I choose as the pivot? I guess I could also be omitting a force in calculating the torque, but I don't think I am.
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