## Physics Olympiads Series Problem 20

- Category: Olympiads
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physics.fisikastudycenter.com, physics olympiads series problem 20. Inclined plane, force, statics friction and newton's laws.

**Problem 20**

A mass m = 10 kg is held at rest on an inclined planed, whose slope is θ = 53°, by means of a horizontal force F (see Figure).

The coefficient of statics friction is μ = 0.2, find the maximum F allowed before the body starts to move up the plane, use the acceleration due to gravity g = 10 m ⋅ s^{−2} and tan 53°= 4/3

**Solution**

We take the x - direction up the slope and y-direction normal to it.

At the moment when the mass begins to move, F = F_{max} and the resultant forces are :

Σ F_{x} = F_{max} cos θ − mg sin θ − μ_{s} N

0 = F_{max} (0.6) − (10)(10)(0.8) − (0.2) N

0.6 F_{max} = 80 + 0.2 N*Equation (1)*

Σ F_{y} = N − F_{max} sin θ − mg cos θ

Both forces must vanish, so we can use the second equation to write

N = F_{max} sin θ + mg cos θ

N = F_{max} (0.8) + (10)(10)(0.6)

N = 0.8 F_{max} + 60 *Equation (2)*

and then from combining (1) and (2) we get:

* Literatures: -Physics with Answers, A.R King and O. Regev -Mekanika I, Yohanes Surya*