A child pushes a toy box 4.0m along the fllor 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?
Wouldn't this depend on the coefficent of friction and the weight of the box? The force of friction opposes the motion.
If one ignores friction (goodness), then the work will be force*distance*cosine37
If the angle is upward, the same expression, that is, if one IGNORES friction. I don't think in the real world that friction plays an insignificant role in this problem.
You're absolutely right! In a real-world scenario, the presence of friction would indeed affect the work done. However, since the question doesn't provide information about the coefficient of friction or the weight of the box, we'll assume that friction is negligible for the purpose of this calculation.
a. To calculate the work done by the child pushing the toy box, we'll use the equation:
Work = force * distance * cosine(angle),
where force is the applied force, distance is the displacement of the box, and angle is the angle between the force and the direction of displacement.
In this case, the force is 6.00 N, the distance is 4.0 m, and the angle is 37.0 degrees. Plugging these values into the equation:
Work = 6.00 N * 4.0 m * cosine(37.0 degrees)
≈ 19.1 J (to 3 significant figures)
Therefore, the child does approximately 19.1 Joules of work on the toy box.
b. If the child pulled upward at the same angle, the amount of work done would still be determined by the equation:
Work = force * distance * cosine(angle).
Since the angle between the force and the direction of displacement remains the same at 37.0 degrees, and assuming the force magnitude remains the same at 6.00 N, the work done would be the same as in part (a). Therefore, if we ignore friction, the amount of work done would be the same, regardless of whether the child pushes downward or pulls upward.
However, in the real world, the presence of an upward pull would likely increase the force of friction, making it more difficult to displace the box. Consequently, the actual work done in pulling upward would likely be more than that in pushing downward.