Answer to Question #152192 in Physics for Renz Lim Duran

Question #152192
A shopper in a supermarket pushes a loaded cart with a horizontal force of 100 N. The cart has a mass of 30 kg. How far will it move in 3.0 s if the shopper places his 30-N child in the cart before he begins to push it? The coefficient of kinetic friction is 0.2
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Expert's answer
2020-12-21T11:01:13-0500

Let's first find acceleration from the Newtons Second Law of Motion:


FapplFfr=(mcart+mchild)a,F_{appl}-F_{fr}=(m_{cart}+m_{child})a,Fapplμk(mcart+mchild)g=(mcart+mchild)a,F_{appl}-\mu_k (m_{cart}+m_{child})g=(m_{cart}+m_{child})a,a=Fapplμk(mcart+mchild)g(mcart+mchild),a=\dfrac{F_{appl}-\mu_k (m_{cart}+m_{child})g}{(m_{cart}+m_{child})},a=100 N0.2(30 kg+30 N9.8 ms2)9.8 ms2(30 kg+30 N9.8 ms2)=1.1 ms2.a=\dfrac{100\ N-0.2\cdot (30\ kg+\dfrac{30\ N}{9.8\ \dfrac{m}{s^2}})\cdot 9.8\ \dfrac{m}{s^2}}{(30\ kg+\dfrac{30\ N}{9.8\ \dfrac{m}{s^2}})}=1.1\ \dfrac{m}{s^2}.

Finally, we can find the distance traveled by the cart in 3 s from the kinematic equation:


d=v0t+12at2=0+121.1 ms2(3 s)2=4.95 m.d=v_0t+\dfrac{1}{2}at^2=0+\dfrac{1}{2}\cdot 1.1\ \dfrac{m}{s^2}\cdot (3\ s)^2=4.95\ m.

Answer:

d=4.95 m.d=4.95\ m.


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