Question

A parachutist jumps from a plane. Beginning at the point when she reaches terminal velocity (constant velocity during freefall), which of the following is/are true? The jumper is in translational equilibrium. The jumper is not being acted upon by any forces. There is an equal amount of work being done by gravity and air resistance. (A) I only (B) I and III only (C) II and III only (D) I, II, and III

Short answer

(B) I and III only.

Step-by-step solution

Identify Key Concepts

Determine the concepts involved: terminal velocity, translational equilibrium, forces acting on the jumper, and work done by forces.

Analyze Translational Equilibrium

An object is in translational equilibrium if the net force acting on it is zero. At terminal velocity, the gravitational force downward is exactly balanced by the air resistance upward.

Examine Forces Acting on the Jumper

At terminal velocity, even though the net force is zero, there are still forces acting on the jumper: gravity (downward) and air resistance (upward).

Evaluate Work Done by Forces

Work is defined as force applied over a distance. Gravity does work on the parachutist by pulling her downwards, and air resistance does work by pushing upwards. At terminal velocity, these forces do equal amounts of work in opposite directions.

Review Given Statements

Review which of the given statements are true based on the analysis:- Statement I: True, because the jumper is in translational equilibrium.- Statement II: False, as the jumper is still acted upon by gravity and air resistance.- Statement III: True, because the work done by gravity is balanced by the work done by air resistance.

Select the Correct Answer

Based on the true statements, the correct answer is (B) I and III only.

Key concepts

Translational Equilibrium

When we say an object is in translational equilibrium, it means the net force acting on the object is zero. This happens when all the forces acting on the object cancel each other out completely.
An easy way to understand this: imagine you’re pushing a box with a force of 10 N to the right. If someone else pushes the same box with a force of 10 N to the left, the two forces cancel, and the box doesn’t move.

For our parachutist, when she hits terminal velocity, the downward force of gravity (weight) is perfectly balanced by the upward force of air resistance (drag).
Thus, the net force on her is zero. As a result, she doesn't accelerate anymore and continues falling at a constant speed.
This state, where forces are balanced, is called translational equilibrium.
In summary, **Statement I** is true. The jumper is indeed in translational equilibrium.

Forces in Freefall

When an object is in freefall, the forces acting on it depend on its velocity.
Initially, right after the parachutist jumps from the plane, she accelerates downward due to gravity. This is when gravity is the only significant force acting on her.

However, as she falls and her speed increases, air resistance starts to act upward, opposing gravity.
Once she reaches terminal velocity, the forces reach a balance:

• **Gravity (Weight):** This is the force pulling her downward, calculated as her mass times the acceleration due to gravity (\(F_{gravity} = mg\)).
• **Air Resistance (Drag):** This is the force pushing her upward, which increases with her speed until it equals the downward force of gravity. When this balance is achieved, the net force is zero.

It is crucial to note that even though the net force is zero, these forces are still very much acting on her. So, **Statement II** is false. The jumper is indeed acted upon by forces (gravity and air resistance) despite being in translational equilibrium.

Work Done by Forces

Work in physics is defined as a force causing a displacement. It’s calculated as the force times the distance over which it acts, in the direction of that force.
Now, let's consider the jumper at terminal velocity:

• **Gravity:** Gravity does work by pulling the parachutist downward over the distance she falls.
• **Air Resistance:** Air resistance does work by pushing up against her fall, opposing her downward movement.

At terminal velocity, these forces are equal in magnitude but opposite in direction.

This means the parachutist falls at a constant speed, implying no net work is done on her to change her kinetic energy. But, individually, both forces still do work:

• Gravity works to increase potential energy loss by pulling down.
• Air resistance works against this by doing an equal amount of work upwards.

Thus, **Statement III** is true. The work done by gravity is balanced by the work done by air resistance.