Fisika Study Center

Fisikastudycenter.com,- Physics Olympiads problems series, for beginner, problem 9. Fundamental concepts needed in this problems are Newton law, forces, torque, inertia, and angular acceleration.

Problem 9
Given a figure below. A mass of M = 10 kg and a cylinder of m = 5 kg (M = η m)shown 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, the floor has frictional force. The slop has θ, the M moves down.The cylinder inertia is ½ mR² and it rools without slipping.

Find the acceleration of M, use the acceleration due to gravity g = 10 m/s² dan tan 37° = 0,75
Problem source:
(Fisika Study Center-Modifikasi Soal Fisika Seleksi OSN 2008 Tingkat Provinsi )

Solution
Draw all forces acting on the mass M:

W is M weight , T is the rope tension, and a is the accceleration.
Newton;s second law:


Equation (1)

Take alook the mass m, there are W (weight), where W = mg, T (tension of the rope), f (frictional force) and N (Normal force).

mg sin θ and mg cos θ are the components of W on x axis and y axis respectively, a₂ is the acceleration of m.



The relationship of M and m is:


Equation (3)

Combining equation (1) and (3)

Equation (4)

Combining (4) and (2):

Equation (5)

From the rotation of m:


Equation (6)

:
Combine equation (4) and (5), put into equation (6) to get the result:

and a₁ = 0,5 m s⁻¹

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.



a) The floor has friction force acting on it. What is the acceleration of M that makes the cylinder rolls without slipping? (Show the answer in η, λ, g dan θ)?
Problem source:
(Indonesian Physics Olympiad, Province Level-Soal Fisika Seleksi OSN 2008 Tingkat Provinsi No.2 bagian a )

Answer:


Written bY : Fisika Study Center
Literatures and sources:
-Indonesian Physics Olympiad Problem-Soal Fisika Seleksi OSN 2008 Tingkat Provinsi
-Marthen Kanginan, Fisika SMA Jilid 2, OSN Fisika SMA
-tofi.or.id