A 10 m long steel beam which weighs 700 kg lies on a roof. The beam sticks out 4,5 m over the edge of the roof. How far can a person weighing 80 kg go out on the beam (on the part sticking out over the edge of the roof) without the beam tipping over?
The answer is supposed to be 4,375 m
I translated this question from Swedish to English, so once again – please excuse any grammar mistakes.
2. Relevant equations
M = F * r
m1*x1 =m2*x2 or m1g*x1 =m2g*x2
3. The attempt at a solution
I started by trying to figure out where the center of gravity (I think that´s what it´s called in English) is for the beam. Let this point = X1/2, assuming this point is in the middle of the beam.
Also let m1 = the weight of the beam = 700 kg
m2= the weight of the man = 80 kg
x2= the length of the beam exceeding the edge of the roof
I then also assumed that the man wasn´t moving, and set up an equation as follows:
m1*(X1/2) = m2*X2
Plugging in the numbers above and solving for X1
results in X1 = 1,03 m
Is this reasonable?
I then figured the man would be moving anywhere between 4,5 – X2, and that the force acting on the man is 80 kg * 9,82 =785,6 N, such that the momentum is given by 785,6 (4,5 – X2) = 3535,2 – 785,6X2
The force acting on the beam is Fbeam = 700 * 9,82 = 6874 N, and under the assumption that 1,03 m is correct, we get a momentum of 6874 N * 1,03 m=7080,22
Setting 3535,2 – 785,6X2 = 7080,22 and solving for X2 results in X2 = -4,673 m, which is obviously wrong!