A child pushes a toy box 4.0m along the floor with a force of 6.00N directed downward at an angle of 37.0 degrees to the horizontal.

a. How much work does the child do?
b. Would you expect more or less work to be done if the child pulled upward at the same angle?

a) The work done is the horizontal component of the Force, 6.00 cos 37, multipled by the distance the box moves, 4.0 m.
b) By pulling upwards at 37 degrees with force F, there will be a reduction in the force that the box applies to the floor (which is weight - F sin 37) , and a reduction of the friction force. Less force and less work will be required to move the box at constant speed.

To calculate the work done by the child, we need to consider the formula for work:

Work = Force * Distance * cos(theta)

Where:
- Force is the magnitude of the force applied by the child, which is 6.00N in this case.
- Distance is the distance the box moves, which is 4.0m in this case.
- Theta is the angle between the force and the direction of motion, which is 37.0 degrees in this case.

a) Now, let's calculate the work done by the child:
Work = 6.00N * 4.0m * cos(37.0)
Work = 6.00 * 4.0 * cos(37.0)
Work ≈ 6.00 * 4.0 * 0.7986
Work ≈ 19.16 Joules (rounded to two decimal places)

Therefore, the child does approximately 19.16 Joules of work on the toy box.

b) If the child pulled upward at the same angle of 37.0 degrees, the force applied would have a vertical component in the upward direction. This would result in a reduction in the downward force exerted by the toy box on the floor. Additionally, there would be a reduction in the friction force opposing the motion of the toy box.

As a result, the total force and the amount of work required to move the box at a constant speed would be less when pulling upward. So, we would expect less work to be done in this case compared to pushing downward.