Question

Breanna is standing beside a merry-go-round pushing 19° from the tangential direction and is able to accelerate the ride and her friends from rest to a frequency of 10 rpm in 9 seconds. Assume the merry-go-round is a uniform disc of radius 2.3 m and has a mass of 750 kg. Rachel (48 kg) and Tayler (46 kg) sit opposite each other on the edge of the ride. What force did Elizabeth push with? (N) (include units with answer) How much work did Elizabeth do? (J) (include units with answer)

Answer 1

Answer

given,

angle of pushing =19°

frequency = 10 rpm

time = 9 sec

radius of disk = 2.3 m

mass of merry-go-round = 750 Kg

Rachel mass = m₁ = 48 Kg

Tayler mass = m₂ = 46 Kg

moment of inertial

$I = \dfrac{1}{2}Mr^2 + (m_1+m_2) r^2$

$I = \dfrac{1}{2}\times 750 \times 2.3^2 + (48+46) 2.3^2$

I = 2481.01 Kg.m²

ω = 10 rpm = $10 \times \dfrac{2\pi}{60}$

ω = 1.05 rad/s

ω₀ = 0

$\alpha= \dfrac{\omega-\omega_0}{t}$

$\alpha= \dfrac{1.05-0}{9}$

α = 0.117 rad/s²

we know,

T = I α

F cos 16° = 2481.01 x 0.117

F = 301.98 N

Work done =

=$\dfrac{1}{2}I\omega^2$

=$\dfrac{1}{2}\times 2481.01\times 1.05^2$

W =1367.66 J