Physics Olympiads Series Problem 10
- Category: Olympiads
- Written by fisikastudycenter
Fisikastudycenter.com,- Physics Olympiads problems series, for beginner, problem 10. Fundamental concepts needed in this problems are Newton law, forces, torque, inertia, and angular acceleration.
Problem 10
Given a figure below. A mass of m1 = 10 kg and a cylinder of m2 = 5 kg. See figure below. Ignore the mass and frictional force of the pulley. The inner radius of cylinder is r = 0.25 m and the outer is R = 0.5 cm. Assume the string and cylinder as a yo-yo, ignore the floor frictional force. The slop has θ, the m1 moves down.The cylinder inertia is ½ mR2. 
Find the acceleration of m1 and m2, use the acceleration due to gravity g = 10 m/s2 and sin 37° = 0,6
Problem source:
(Fisika Study Center-Modifikasi Soal Fisika Seleksi OSN 2008 Tingkat Provinsi )
Solution
Tinjauan gaya-gaya yang bekerja pada m1 sebagai berikut: 
Two forces acting on m1, the m1 weight (W), and string tension (T), a1 is the acceleration of m1.
Applying Newton's second law:
Equation (1)
Take alook at m2, sketch all forces acting on m2, the m2 weight, where W = mg, string tensioni (T),and normal force(N), no frictional force. 
mg sin θ and mg cos θ are the components of W on X axis, and Y axis, a2 the acceleration of m2.
Equation (2)
The relationship of a1 and a2
Equation (3)
Rotation of m1, where Σ τ = I α
Equation (4)
Combining 3 and 4 equations
Equation (5)
Combining 2 and 3
Equation (6)
Combining 1 and 5
Equation (7)
Combining equation 6 and equation 7, we'll getn a1 and a2
Result
Try This!
A mass of M kg and a cylinder of m kg (M = η m)shown below. Ignore the mass and frictional force of the pulley. The inner radius of cylinder is r and the outer is R (r = λR). Assume the string and cylinder as a yo-yo. The slop has θ, the M moves down.The cylinder inertia is ½ mR2. 
b) The floor has no frictional force. Find the acceleration of M (show youranswer in η, λ, g and θ)?
Problem source:
(Soal Fisika Seleksi OSN 2008 Tingkat Provinsi #2 part b -Indonesian physics olympiad, province level)
prepared bY : Fisika Study Center
Literatures:
-Soal Fisika Seleksi OSN 2008 Tingkat Provinsi
-Marthen Kanginan, Fisika SMA Jilid 2, OSN Fisika SMA
-tofi.or.id