Question

A girl and her dog sit on a seesaw. The dog has mass of 20.0 kg and sits 1.5 m from the pivot point and the girl has mass of 65.0 kg. In order to balance the seesaw, the girl should sit at a distance of : (a) 0.5 m (b) 0.64 m (c) 0.46 m (d) 6.04 m

Answer 1

Answer:

(c) d₂ = 0.46 m

Explanation:

We apply Newton's first law to balance moments (M) at the point O at the bottom of the ladder, taking positive the moments that go counterclockwise and negative the moments that go clockwise

ΣMo=0

W₁*d₁ - W₂*d₂ = 0 Equation (1)

W₁ = dog Weight (N)

W₂= girl Weight (N)

d₁ = distance from W₁ to point O

d₂ = distance from W₂ to point O

Data

m₁ =  20.0 kg : dog mass

m₂ = 65.0 kg : girl mass

g = 9.8 m/s² : acceleration due to gravity

d₁ = 1.5 m

We calculate W₁ and W₂ :

W₁=m₁*g=  20.0 kg*9.8 m/s  = 196 N

W₂=m₂*g=  65.0 kg*9.8 m/s  = 637 N

Look at the free body diagram of the seesaw in the attached graphic

In the equation (1):

W₁*d₁ - W₂*d₂ = 0

196*(1.5) - 637*(d₂) = 0

294 = 637*(d₂)

d₂ = 294/637

d₂ = 0.46 m