A 1640-kg lift truck with rubber tires is skidding on wet concrete with all four wheels locked. Calculate the acceleration of the truck, given that the coefficient of kinetic friction is 0.5.

Question

anonymous · Answer

Find normal force = 1640kg x 10ms^-2 = 16400N
coefficient of friction is a decimal representation of the fraction of normal force which will oppose movement of the truck, so, 16400*0.5 = 8200N
F = MA, rearranging a = f/m, a being acceleration of truck, f being force due to friction and m being mass of truck
this gives a = 8200N / 1640kg = 5ms^-2

homeworksucks · Answer

So I'm getting all that, but my textbook says the formula, after simplification is, $$a=-\mu _{k} g$$ Why is the coefficient negative?

anonymous · Answer

Oh yeah I was wrong, answer should be -5ms^-2. Its negative because the resulting force opposes the motion of the object, resulting in 'negative' acceleration.

anonymous · Answer

If the coefficient was positive, we would have a force in the same direction as the motion of the object, which would act to accelerate the object in the direction which it is currently moving.

homeworksucks · Answer

So.. are we always supposed to infer this from the question?

anonymous · Answer

Yup, it helps to think about this intuitively. A friction force always OPPOSES the motion of the object. If the friction force was positive, then it would aid the motion of the object. This means that the force produced by friction must always be negative.

homeworksucks · Answer

Sorry if I'm being difficult, but does that mean I can use the negative coefficient whenever I'm solving for acceleration?