Answer to Question #146467 in Physics for Michele

Question

Two objects are connected by a light rope in between and are placed on a table. The mass of object 1 is m1=2.00 kg and object 2 has a mass m2= 3.00 kg. Both objects have the same coefficients of kinetic friction of 0.100 with the table top. A horizontal force F= 8.00 N is applied to object 1 in the direction parallel to the rope, and as a result, the two objects move together at the same acceleration on the table.
a) find the friction forces acting on object 1 and 2
b) find the acceleration of the system
c) find the tension in the rope
d) suppose the rope is not light and the mass of the rope cannot be ignored. what will be the effects on the acceleration and the tension? explain.

Answer 1

a)

$$F_{1f}=\mu m_1g=(0.1)(2)(9.8)=1.96\ N\\F_{2f}=\mu m_2g=(0.1)(3)(9.8)=2.94\ N$$

b)

$$(m_1+m_2)a=F-F_{1f}-F_{2f}\\(2+3)a=8-1.96-2.94\\a=0.62\frac{m}{s^2}$$

c)

$$T=m_2a=(3)(0.62)=1.86\ N$$

d) Acceleration and tension will decrease.