Question

A gymnast of mass 46.0kg stands on the left end of a uniform balance beam. The beam is 5.00m long and has a mass of 250kg (excluding the mass of the two supports). Each support is 0.540m from its end of the beam. a) What are the magnitude and the direction of the force on the beam due to left support? Show your work and explain your reasoning. b) What are the magnitude and the direction of the force on the beam due to right support? Show your work and explain your reasoning

Answer 1

To find the force on the beam due to left support, Take moments about right end

F_left*3.92 = 46*9.8*(3.92 + 0.540) + 250*9.8* (3.92/2)

F_left*3.92 = 2010.568 + 4802

F_left = 1737.9 N

b) Similarly, you can take the moment about left support to find force at right support or in a short way, we can just equate vertical forces. Note that two forces (weight of beam and weight of gymnast) acts downwards and force from both supports acts upwards

so, (46*9.8) + (250*9.8) = F_left + F_right

2900.8 = 1737.9 + F_right

F_right = 1162.9 N