(II) A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of 27m/s. What was the average force of air resistance?

Verified step by step guidance

1. Identify the forces acting on the purse: gravity (downward) and air resistance (upward). The net force determines the motion of the purse.
2. Calculate the gravitational force acting on the purse using the formula: $F$_g=mg, where $m$ is the mass of the purse (2.0 kg) and $g$ is the acceleration due to gravity (9.8 m/s²).
3. Determine the net work done on the purse using the work-energy principle: $W$_net=ΔK, where $\Delta K$ is the change in kinetic energy. Use the formula for kinetic energy: $K=\frac{1}{2}m{v}^2$, and calculate the change in kinetic energy from rest to the final speed of 27 m/s.
4. Calculate the work done by air resistance using the relationship: $W$_air=W_net-W_gravity, where $W$_gravity=F_gd (gravitational force multiplied by the distance fallen, 55 m).
5. Determine the average force of air resistance using the formula: $F$_air=W_aird, where $d$ is the distance fallen (55 m).

Key Concepts

Newton's Second Law of Motion

Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). This principle is crucial for analyzing the forces acting on the purse as it falls, including gravitational force and air resistance.

Gravitational Force

The gravitational force acting on an object is the weight of the object, calculated as the product of its mass and the acceleration due to gravity (approximately 9.81 m/s² on Earth). For the purse, this force is essential to determine the net force acting on it during its fall.

Average Force of Air Resistance

Air resistance, or drag, is the force that opposes the motion of an object through the air. To find the average force of air resistance acting on the purse, one must consider the difference between the gravitational force and the net force, which can be derived from the purse's acceleration and final velocity.