# Fisika Study Center

## Physics Olympiads Series Problem 12

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Problem 12
A mechanical system consisting of four masses m1, m2, m3 and m4. See the figure.

A horizontal force F is now applied to cart m4 as shown. The size of F is such that m1, m2 and m3 remain at rest relative to m4. Ignore the mass and frictional forces of string and pulley, find the magnitude of F and the system acceleration ! Use g = 10 m/s2 and the four masses respectively are 0,3 kg, 0,4 kg, 0,5 kg and 2,8 kg!
Problem source: Fisika Study Center-Modification of 3rd International Physics Olympiad 1969, Brno, Czechoslovakia, Problem 1

Solution
Analyze the four masses as a system moving on x axis with accelerations a1 = a2 = a3 = a3 = a4 = a, Apply Newton's law

Analyze m3 at vertical direction, y axis, in equilibrium conditions.The acting forces on m3 are W = mg and te string tension, T23.

Analyze m1 at x axis, horizontal direction, the acting force is the string tension T12.

Analyze m2, the acting forces are strin tensions T12 and T23.

Combining equation 4 and 2 and 3, and then equation 1 to get the result.

Try This
Figure 1 shows a mechanical system consisting of three carts A, B and C of masses m1 = 0.3 kg, m2 =0.2 kg and m3 = 1.5 kg respectively. Carts B and A are connected by a light taut inelastic string which passes over a light smooth pulley attaches to the cart C as shown. For this problem, all resistive and frictional forces may be ignored as may the moments of inertia of the pulley and of the wheels of all three carts. Take the acceleration due to gravity g to be 9.81 m s−2.

1. A horizontal force F is now applied to cart C as shown. The size of F is such that carts A and B remain at rest relative to cart C.
a) Find the tension in the string connecting carts A and B.
b) Determine the magnitude of F.
2. Later cart C is held stationary, while carts A and B are released from rest.
a) Determine the accelerations of carts A and B.
b) Calculate also the tension in the string.
Kunci:
1) 2.94 N dan 29.4 N
2) 5.89 m s−2 dan 1.18 N
Sumber Soal: 3rd International Physics Olympiad 1969, Brno, Czechoslovakia, Problem 1

Prepared bY : Fisika Study Center
Sumber-sumber:
-Soal International Physics Olympiad 1969, Brno, Czechoslovakia
-Mekanika 1, Yohanes Surya
-Marthen Kanginan, OSN SMA
-tofi.or.id

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