Question

A 23 kg boy sits 1.5 m from the axis of rotation of a seesaw. At what distance from the
axis of rotation must a 21 kg boy be positioned on the other side of the axis to balance the
seesaw?
a) 4.6 m
b) 2.6 m
c) 3.6 m
d) 1.6 m
e) 0.6 m

Answer 1

Answer on Question#41028 – Physics – Mechanics

A 23 kg boy sits 1.5 m from the axis of rotation of a seesaw. At what distance from the axis of rotation must a 21 kg boy be positioned on the other side of the axis to balance the seesaw?

a) 4.6 m

b) 2.6 m

c) 3.6 m

d) 1.6 m

e) 0.6 m

Solution:

$m_1 = 23 \, \text{kg} - \text{mass of the first boy}$;

$d_1 = 1.5 - \text{distance from the first boy to the axis of rotation}$

$m_2 = 21 \, \text{kg} - \text{mass of the second boy}$;

$d_2 - \text{distance from the second boy to the axis of rotation}$

See-saws, or levers are sometimes known as force magnifiers. The further away from the axis we are the less force required to balance the other side.

Equation for the sides of the seesaw:

$$F_1 d_1 = F_2 d_2$$ $$m_1 g \cdot d_1 = m_2 g \cdot d_2$$ $$d_2 = \frac{m_1 g \cdot d_1}{m_2 g} = \frac{m_1 d_1}{m_2} = \frac{23 \, \text{kg} \cdot 1.5 \, \text{m}}{21 \, \text{kg}} = 1.64 \, \text{m}$$

Answer: 21 kg boy must be positioned at the distance 1.64 m from the axis of rotation.

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