Two kids create a makeshift seesaw by setting a 4-m long uniform plank on a saw horse. The saw horse is 0.5 m to the left of the center of mass of the plank. The child of mass m1 = 48 kg sits at the left end of the plank. The child of mass m2 = 35 kg sits 1 m to the right of the center of mass of the plank. What is the mass of the plank?

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MechEngineer MechEngineer · Answer 1 · 2019-12-04T11:28:54+01:00

Answer:

39kg

Explanation:

As this system is balanced on the saw horse, the total net torque by the children and plank gravity must be 0

Since child 2 and the plank center of mass are both on the right of the saw horse, their torque is in opposite direction, so so are their signs:

[tex]T_1 - T_p - T_2 = 0[/tex]

[tex]m_1gL_1 - m_pgL_p - m_2gL_2 = 0[/tex]

[tex]m_1L_1 - m_pL_p - m_2L_2 = 0[/tex]

where m1 = 48 kg is the mass of the first child on the left at L1 = 1.5 m

mp is the mass of the plank on the right of the saw horse Lp = 0.5 m

m2 = 35 kg is the mass of the 2nd child on the right at L2 = 1.5 m

Substitute all the parameters above and we get

[tex]48*1.5 - m_p0.5 -35*1.5 = 0[/tex]

[tex]72 - 52.5 = 0.5m_p[/tex]

[tex]19.5 = 0.5m_p[/tex]

[tex]m_p = 39 kg[/tex]