Question #20244

a child is sitting on a swing .its minimum and maximum heights from the ground are 0.75m and 2m resp. its maximum speed will be

Expert's answer

T - kinetic energy

U - potential energy

The Law of Conservation of Energy:

T+U = const

U = mgh

T = (mv^2)/2

T_max+U_min = 0 + U_max

(m*(v_max)^2)/2 = mg(h_max - h_min)

v_max = sqrt(2g(h_max - h_min) = sqrt(2*10*1.25) = sqrt(25) = 5 m/s

Answer : v_max = 5 m/s

U - potential energy

The Law of Conservation of Energy:

T+U = const

U = mgh

T = (mv^2)/2

T_max+U_min = 0 + U_max

(m*(v_max)^2)/2 = mg(h_max - h_min)

v_max = sqrt(2g(h_max - h_min) = sqrt(2*10*1.25) = sqrt(25) = 5 m/s

Answer : v_max = 5 m/s

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