Question

A gymnast weighs 450 N. She stands on a balance beam of uniform construction which weighs 250 N. The balance beam is 3.0 m long and is supported at each end. If the support force at the right end is four times the force at the left end, how far from the right end is the gymnast

Answer 1

x = 9.32 cm

Step-by-step explanation:

For this exercise we have an applied torque and the bar is in equilibrium, which is why we use the endowment equilibrium equation

Suppose the counterclockwise turn is positive, let's set our reference frame at the left end of the bar

- W l / 2 - W_{child} x + N₂ l = 0

x =
`(-W l/2 + n_2 l)/(W_(child))` 1)

now let's use the expression for translational equilibrium

N₁ - W - W_(child) + N₂ = 0

indicate that N₂ = 4 N₁

we substitute

N₁ - W - W_child + 4 N₁ = 0

5 N₁ -W - W_{child} = 0

N₁ = ( W + W_{child}) / 5

we calculate

N₁ = (450 + 250) / 5

N₁ = 140 N

we calculate with equation 1

x = -250 1.50 + 4 140 3) / 140

x = 9.32 cm