Answer to Question #152192 in Physics for Renz Lim Duran

Question

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

Answer 1

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

$$F_{appl}-F_{fr}=(m_{cart}+m_{child})a,$$ $$F_{appl}-\mu_k (m_{cart}+m_{child})g=(m_{cart}+m_{child})a,$$ $$a=\dfrac{F_{appl}-\mu_k (m_{cart}+m_{child})g}{(m_{cart}+m_{child})},$$ $$a=\dfrac{100\ N-0.2\cdot (30\ kg+\dfrac{30\ N}{9.8\ \dfrac{m}{s^2}})\cdot 9.8\ \dfrac{m}{s^2}}{(30\ kg+\dfrac{30\ N}{9.8\ \dfrac{m}{s^2}})}=1.1\ \dfrac{m}{s^2}.$$

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

$$d=v_0t+\dfrac{1}{2}at^2=0+\dfrac{1}{2}\cdot 1.1\ \dfrac{m}{s^2}\cdot (3\ s)^2=4.95\ m.$$

Answer:

$d=4.95\ m.$