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allyferrell
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Homework Statement
A plank having mass 3.7 kg rides on top of two identical solid cylindrical rollers each having radius 5.5 cm and mass 2.9 kg. The plank is pulled by a constant horizontal force of 6 N applied to its end and perpendicular to the axes of the cylinders(which are parallel). The cylinders roll without slipping on a flat surface. There is also no slipping between the cylinders and the plank.
1.) Find the acceleration(linear) of the plank(m/s^2).
2.) Find the frictional force acting acting on the plank(N).
M=3.7 kg
m=2.9 kg
r=.055 m
F=6 N
α = angular acceleration
a=linear acceleration
Homework Equations
τ=Fr
I=(1/2)m(r^2)
Ʃτ=Iα
F=ma
Frictional force(static) = force applied
The Attempt at a Solution
torque of one wheel: τ=Fr = 6*.055 = .33 N
Ʃτ=Iα = (1/2)*(2.9)*(.055^2)*α →
.33=.00438625α → α(of one wheel)=75.2351907 rad/s^2
a=αr = 75.2351907*.055 = 4.13793103 m/s^2
Ʃa(both wheels and board)= (4.13793103*2) + a of board
F=ma→ 6=(3.7 + 2.9 +2.9)a → a of board = .631578947 m/s^2
∴ Ʃa = 8.27586207 + .631578947 = 8.90744102 m/s^2