Question

A man inside a sturdy box is fired out of a cannon. Which of following statements regarding the weightless sensation for the man is correct? a) The man senses weightlessness only when he and the box are traveling upward. b) The man senses weightlessness only when he and the box are traveling downward. c) The man senses weightlessness when he and the box are traveling both upward and downward. d) The man does not sense weightlessness at any time of the flight.

Short answer

Answer: The man senses weightlessness when he and the box are traveling both upward and downward.

Step-by-step solution

Option A: Weightlessness during upward motion

Let's consider the situation when the man and the box are traveling upward. The man will sense weightlessness when there is no contact force between him and the box, i.e., when the effective acceleration acting on his body is zero. In this case, the man will be in free-fall, and there won't be any contact force between him and the box. Therefore, the statement in option (a) is a possibility.

Option B: Weightlessness during downward motion

Now, let's analyze the situation when the man and the box are traveling downward. In this case, the acceleration due to gravity will act in the same direction as the motion. The man will still be in free-fall as the downward force and the acceleration due to gravity will be the same. Thus, the contact force between the man and the box will also be zero, contributing to a sensation of weightlessness. Hence, the statement in option (b) is also a possibility.

Option C: Weightlessness during both upward and downward motion

Since we have established that the man can sense weightlessness during both upward and downward motion, this statement considers both cases and is correct.

Option D: No weightlessness during any time of the flight

This statement contradicts our analysis, as we have determined that the man will sense weightlessness during both the upward and downward motion. Therefore, this statement is incorrect.

Final Answer

Based on our analysis, the correct statement regarding the feeling of weightlessness for the man inside the sturdy box when fired out of a cannon is (c) The man senses weightlessness when he and the box are traveling both upward and downward.

Key concepts

Free-Fall Motion

Free-fall motion is a scenario where an object moves under the influence of gravity alone. No other external forces affect it. Imagine dropping a ball from a height. As soon as you release it, it enters a free-fall state. This motion results in the sensation of weightlessness for objects and people inside. Both during the upward and downward movement of the box with the man inside, the lack of contact forces allows free-fall motion to occur.
Thus, the man feels weightless throughout the flight.

• Free-fall occurs when the only force acting on an object is gravity.
• Objects in free-fall experience a sense of weightlessness because no support force is felt.

Contact Force

The contact force is the force exerted when two objects are in contact. It's what you feel when you push against a surface, and it pushes back. In the context of the man inside the sturdy box, contact forces arise when the man interacts with the sides or base of the box.
During free-fall, the box and the man drop at the same rate, negating any contact force. This absence of contact force means he feels as if he is floating, leading to the sensation of weightlessness.

• Contact force occurs when there is direct interaction between two surfaces.
• The absence of contact force, as in free-fall, leads to the sensation of weightlessness.

Gravity and Acceleration

Gravity is a force that pulls objects towards the Earth's center. It's responsible for the acceleration experienced by objects in free-fall. When an object is in free-fall, it accelerates downward at about 9.8 m/s² due to gravity.
This gravitational acceleration ensures that both the box and the man inside it fall together at the same rate. Therefore, they share the same motion without exerting pressure on each other. This synchronous acceleration wipes out all contact force within the box, reinforcing the feeling of weightlessness.

• Gravity causes objects to accelerate downwards at a constant rate of 9.8 m/s².
• Acceleration due to gravity is responsible for the free-fall sensation.