Answer to Question #248457 in Molecular Physics | Thermodynamics for szxi

Question

A boy pushes a box with a mass of 13 kg on a horizontal surface with a constant speed of 2 m/s. The coefficient of kinetic friction between the box and the surface is 0.20. What horizontal force must be applied by the boy to maintain the motion?

Answer 1

If we analyze the whole system we have the following diagram, where we have the balance of forces for the x- and y-axis.

Now, we proceed to find the force that we need to exert on the box so that it moves at a constant speed. This means that the acceleration of the box will be zero, meaning that the sum of the forces acting on the box on both axes has to be equal to zero. Following this hypothesis we have:

$\sum F_y=0= N-m\cdot g \implies N=m\cdot g \\ \sum F_x=0=F_{push}-f_s=F_{push}-\mu\cdot N \\ \implies F_{push}=\mu\cdot N=\mu \cdot m\cdot g$

We proceed to substitute the kinetic friction coefficient, the mass of the box, and the acceleration of gravity to find the force that we have to apply for the box to move at a constant speed:

$F_{push}=(0.20)\cdot (13\,kg)\cdot (9.80\frac{m}{s^2}) \\ \therefore F_{push}=25.48\,N$

In conclusion, the force that has to be applied to maintain the motion is 25.48 N.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.