Answer to Question #150700 in Physics for Erica

Question #150700
A 5 kg object is pushed along a horizontal plane by a force of 20 N. if the velocity is 20 m/sec at the foot of the plane and the coefficient of kinetic friction between the plane and the object is 0 25. how far the plane will the object go ?
1
Expert's answer
2020-12-17T07:26:51-0500

Let's first find the acceleration of the object from the Newton's Second Law of Motion (we assume that when object reaches the velocity of 20 m/s at the foot of the plane, it releases and the only force of friction acts on it):


Fk.fr.=ma,-F_{k.fr.}=ma,μkmg=ma,-\mu_k mg=ma,a=μkg=0.259.8 ms2=2.45 ms2.a=-\mu_kg=-0.25\cdot 9.8\ \dfrac{m}{s^2} = -2.45\ \dfrac{m}{s^2}.

The sign minus means that the object decelerates.

Then, we can find the distance traveled by the object until it finally stops:


v2=v02+2ad,v^2=v_0^2+2ad,d=v022a=(20 ms)22(2.45 ms2)=81.6 m.d=\dfrac{-v_0^2}{2a}=\dfrac{-(20\ \dfrac{m}{s})^2}{2\cdot (-2.45\ \dfrac{m}{s^2})}=81.6\ m.

Answer:

d=81.6 m.d=81.6\ m.


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