Question

Gabrielle and Pierre are trying to move a 52 kg box by pushing it across the floor. Gabrielle is pushing with a force of 40 N [east], while Pierre is pushing with a force of 32 N [west]. There is also a friction force of 3 N [west] on the box. Assume the box travels 4 m [east].A. Draw a system diagram and a free-body diagram of the box.B. Calculate the net force in the horizontal direction on the box. In which direction is the net horizontal force?C. Calculate the net force in the vertical direction on the box. In which direction is the net vertical force?D. Remember that net force indicates an acceleration. In which direction is the box accelerating (and hence, moving)?E. Determine the work Gabrielle exerts on the box. Considering the direction the box is going, is the work positive or negative?F. Determine the work Pierre exerts on the box. Considering the direction the box is going, is the work positive or negative?G. Determine the work friction is doing on the box. Considering the direction the box is going, is the work positive or negative?H. Add together Gabrielle’s and Pierre’s work, and the work from the force of friction. If any of the amounts of work were negative, the amount becomes a negative number in the summation. I. What is the net work being done on the box in the horizontal direction?J. What is the net work being done on the box in the vertical direction?

Answer 1

Given:

the mass of the box is

$m=52\text{ kg}$

Gabrielle exert a force in the east direction with a magnitude

$F_1=40\text{ N}$

Pierre exert a force in the west direction with a magnitude

$F_2=32\text{ N}$

A friction of force is in west direction

$f=3\text{ N}$

the distance traveled by the box is

$d=4\text{ m}$

Explanation:

(A)

first, look at the free body diagram

(B)

from the free body diagram we can the net force is

$\begin{gathered} F_{net}=F_1-F_2-f \\ F_{net}=40-32-3 \\ F_{net}=5\text{ N} \end{gathered}$

net force is in east direction.

(C)

from the free body diagram we can write

$\begin{gathered} N-w=F_{net} \\ N-mg=F_{net} \\ N-52\text{ kg}\times9.8\text{ m/s}^2=F_{net} \\ F_{net}=0 \end{gathered}$

because

$N=mg$

(D)

the net force is in the east direction (means horizontal direction), so the box will accelerate in the horizontal direction towards the east.

(E)

work done is given by

$W=F.d$

Gabrielle exert a force in east direction and box is also move in the same direction .

work done by Gabrielle is

$\begin{gathered} W_1=40\times4 \\ W_1=160\text{ J} \end{gathered}$

this work is positive because displacement and force is in the same direction.

(F)

work done by the Pierre is

$\begin{gathered} W_2=-32\times4 \\ W_2=-128\text{ J} \end{gathered}$

work done by Pierre is negative because force and displacement are in opposite directions.

(G)

work done by the friction is

$\begin{gathered} W_3=-3\times4 \\ W_3=-12\text{ J} \end{gathered}$

This work done is also negative because friction and displacement of the box are in opposite directions to each other.

(H)

total work done is

$\begin{gathered} W_{tot}=W_1+W_2+W_3 \\ W_{tot}=160-128-12 \\ W_{tot}=20\text{ J} \end{gathered}$

(I)

net work done by the net force is

$\begin{gathered} W_{net}=F_{net}d \\ W_{net}=5\times4 \\ W_{net}=20\text{ J} \end{gathered}$

this is net work done in the horizontal direction.

(J)

net work done in the vertical direction is zero because net force is zero in the vertical direction and also a box is moved only in the horizontal direction.