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**[SOLVED] how to find Fa.....to find other unknowns...?**

**1. Homework Statement**

A mountain bike with mass 13.5 kg , with a rider having mass 63.5 kg, travelling at 32 km/h when the rider applies the brakes, locking the wheels. How far does the bike travel before coming to a stop if the coefficient of friction between the rubber tires and the asphalt road is 0.6?

**2. Homework Equations**

**3. The Attempt at a Solution**

Given:

m1 = 13.5 kg

m2 = 63.5 kg

Velocity Initial = Vi = 32 km/h

Velocity Final = Vf = 0 km/h

friction coefficient = uK = 0.6

Force Natural = mg = (13.5 + 63.5) x 9.81 m/s^2 = 755.37

Force Friction = 755.37 x 0.8 = 453.222

Fn must equal force of gravity because there is no vertical motion.

Applied force must be less than force of friction, because bike is slowing down.

I need to find applied force, so I can use F=ma to find acceleration. Once I get acceleration, I can find displacement. Is my reasoning correct?

thnkx