A delivery person pulls a 35 kg box across the floor. The applied force exerted on the box is 122.5 N [38o above the horizontal]. The force of kinetic friction on the box has a magnitude of 55.0 N. The box starts from rest. Using the Work-energy theorem, determine the speed of the box after being dragged 1.85 m

To find the speed of the box using the Work-energy theorem, we need to know the work done on the box and the initial kinetic energy.

1. Calculate the work done on the box:
The work done on an object is equal to the force applied to the object multiplied by the distance over which the force is applied. In this case, the distance is given as 1.85 m.
W = F * d

The force applied (F) can be resolved into horizontal and vertical components using the given angle:
F_horizontal = F * cos(angle)
F_vertical = F * sin(angle)

Since the box is dragged along the floor, the vertical component of the applied force does not do any work on the box.

Therefore, the work done on the box is:
W = F_horizontal * d

2. Determine the initial kinetic energy of the box:
Since the box starts from rest, the initial kinetic energy (KE_initial) is zero.

3. Use the Work-energy theorem to find the final kinetic energy and speed of the box:
According to the Work-energy theorem,
Work = Change in kinetic energy
W = KE_final - KE_initial

Since KE_initial is zero, the equation becomes:
W = KE_final

Substituting the values obtained from step 1:
F_horizontal * d = KE_final

And solving for KE_final:
KE_final = F_horizontal * d

4. Calculate the speed of the box:
The final kinetic energy (KE_final) is equal to 1/2 * mass * velocity^2. Rearranging the equation, we can solve for velocity (v):
KE_final = 1/2 * mass * v^2

Substituting the known values:
F_horizontal * d = 1/2 * mass * v^2

Finally, solve for the speed (v):
v = sqrt((2 * F_horizontal * d) / mass)

Plug in the values for the force (F_horizontal), distance (d), and mass of the box, then compute the square root to find the speed of the box after being dragged 1.85 m.