Problem 10 - Master Resource Book in JEE Main Physics

Question

A man squatting on the ground gets straight up and stand. The force of reaction of ground on the man during the process is \(\quad\) [NCERT Exemplar] (a) constant and equal to \(m g\) in magnitude (b) constant and greater than \(m g\) in magnitude (c) variable but always greater than \(\mathrm{mg}\) (d) at first greater than \(m g\), and later becomes equal to \(m g\)

Step-by-Step Solution

Answer

(d) at first greater than \( m g \), and later becomes equal to \( m g \)

Step 1: Understanding the Scenario

The man starts from a squatted position, which involves moving from a crouch to upright standing. During this process, his legs exert a force to push him upwards against gravity, and the ground exerts an equal and opposite force known as reaction force.

Step 2: Applying Newton's Third Law

Newton's third law of motion states that for every action, there is an equal and opposite reaction. As the man is pushing against the ground to stand up, the ground exerts a reaction force on the man.

Step 3: Analyzing Forces at Play

The man needs to overcome gravitational force \( m g \) to stand, and initially, his muscles exert a force greater than \( m g \) to accelerate upwards. This means the reaction force must be greater than \( m g \) at first.

Step 4: Determining Change in Force

Once the man is fully upright and no longer accelerating, there is no net force needed to maintain his standing position. Hence, the reaction force becomes equal to the gravitational force \( m g \) at the end of the process.

Step 5: Conclusion

The reaction force is initially greater than \( m g \) when the man starts standing up, and it equilibrates to \( m g \) once he stands still. This fits option (d) from the given choices.

Key Concepts

Reaction Force

The reaction force is an essential concept in Newton's Third Law of Motion. Imagine you are standing on a flat surface. The ground exerts an upward force on you known as the reaction force. This happens because, as you exert a force downward due to your weight, the ground pushes back with equal strength.

In the scenario of a man squatting and then standing, as he pushes against the ground to rise, the ground responds in kind with a force upward. Initially, this reaction force is greater than simply supporting his weight because it must counteract both the gravitational pull and the upward acceleration of his body.

• At the start of moving up, the reaction force exceeds the man's weight.
• Once the motion stops and he stands still, the reaction force equals the weight of the man.

Understanding this balancing act provides insight into how forces interact in everyday actions, like simply standing or getting up.

Gravitational Force

Gravitational force is the invisible pull that keeps you grounded on Earth. It's a force of attraction that any two masses exert on each other, but here it especially evokes the Earth's pull on your body. The strength of this force can be calculated using the equation:\[F_g = mg\]where \( F_g \) is the gravitational force, \( m \) is mass, and \( g \) is the acceleration due to gravity (approximately 9.8 m/s² on Earth).

When the man in the exercise is squatting, he experiences gravitational force pulling him down. To stand, he must exert an upward force greater than this gravitational pull, thus, overcoming the resistance to motion caused by his own weight.

• This constant gravitational force ensures that the man returns to equilibrium once vertical motion ceases.
• Understanding gravitational force's role is pivotal in predicting how various other forces will act in everyday activities.

Acceleration

Acceleration occurs when an object changes its velocity, either by speeding up, slowing down, or changing direction. In the example of a man getting up from a squat, his velocity changes from zero as he pushes himself upwards.

To achieve acceleration, the force applied must exceed the gravitational force and any other resisting forces. Initially, while standing up, the man's muscles exert a force greater than his weight, causing him to accelerate upward. This process can be illustrated by Newton's second law of motion:\[a = \frac{F_{net}}{m}\]where \(a\) is acceleration, \(F_{net}\) is the net force, and \(m\) is mass. During the ascent, the net force is positive, resulting in upward acceleration.

• Once at the top, with no further vertical motion, acceleration becomes zero as forces equilibrate.
• Understanding acceleration helps in explaining why initial force applied is more than just the weight when initiating movement.

Recognizing how forces result in acceleration helps visualize the dynamics in everyday movements, embedding practical insights into learning about forces.