Frictionless In-line Skates: Calculating Distance Required for Final Kinetic Energy

To solve this problem, we can utilize the work-energy principle to determine the distance required to achieve the desired final kinetic energy. Let's break down the steps involved in calculating this distance:

Work-Energy Principle

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the constant force applied to the student will result in an increase in kinetic energy.

Initial and Final Energy

Given that the student starts from rest, her initial kinetic energy is zero. Therefore, the initial energy (E₀) is equivalent to zero.

The final energy (E_f) is specified as 355 J, which represents the desired kinetic energy of the student after being pushed by the constant force.

Calculating Distance

By applying the work-energy principle, we can express the relationship between initial energy, final energy, and the work done by the force:

E₀ = E_f - W

Since the work done (W) by the force is equal to the final kinetic energy (E_f), we can simplify the equation as follows:

W = E_f

Using the formula for work (W = force x distance) and rearranging the equation, we can determine the distance (d) required to achieve the final kinetic energy:

d = E_f / F

Substituting the given values:

d = 355 J / 44 N = 8.0 m

Conclusion

In conclusion, the student must be pushed a distance of 8.0 meters by her friend with a constant force of 44 N in order to achieve a final kinetic energy of 355 J. This calculation highlights the application of the work-energy principle in determining the mechanical work required to change the kinetic energy of an object.