Question

A man is standing on a spring balance. Reading of spring balance is \(60 \mathrm{~kg} \mathrm{f}\). If man jumps outside balance, then reading of spring balance (A) First increase than decreases to zero (B) Decreases (C) Increases (D) Remains same

Short answer

The correct answer is (A). When the man jumps off the spring balance, he exerts an upward force on it, momentarily increasing the total force acting on the spring and causing the reading to increase. Once he is no longer in contact with the spring balance, the reading will decrease until it reaches zero.

Step-by-step solution

Understanding spring balance working principle

Spring balance is a device used to measure the weight of an object by balancing the force due to the object's weight with the force exerted by the spring. When an object is placed on a spring balance, it compresses the spring, and the reading depends on the equilibrium position of the spring, at which the spring force balances the object's weight. The change in the reading of a spring balance occurs due to a change in the object's weight or force exerted on the spring.

Analyzing the initial situation

Initially, the man is standing on the spring balance, compressing it, and as a result, the spring force balances the weight of the man. At this moment, the reading is 60 kgf.

Evaluating the man's action

The man jumps off the balance. When he does that, he exerts an upward force on the spring balance as he pushes off to jump. This upward force momentarily exceeds his weight, temporarily increasing the total force acting on the spring.

Evaluating the spring balance reading after the man jumps

Once the man jumps off and is no longer in contact with the spring balance, there is no weight acting on the spring balance, and it does not have to counter the man's weight. Therefore, the reading of the spring balance will change during and after the mans' action. Initially, when the man starts pushing off and exerts an upward force, the force on the spring balance increases, causing the reading to increase momentarily. However, as soon as he leaves the balance and is no longer exerting any force on it, the reading of the balance decreases, eventually reaching zero when the spring balance returns to its initial position (uncompressed). Hence the spring balance reading first increases and then decreases to zero.

Choosing the correct answer

Based on our analysis, the correct answer is option (A) - First, the reading will increase and then decreases to zero as the man jumps off the spring balance.

Key concepts

Weight Measurement

Weight measurement is fundamental when using a spring balance. A spring balance measures the force exerted by an object due to gravity. This force is often expressed in units of kilograms-force (kgf) or Newtons (N). When an object is placed on a spring balance, its weight compresses the spring. The reading on the dial or scale gives us a measure of that weight, showing how much force the object applies to the spring.
In the scenario where a man stands on a spring balance, the weight (60 kgf) is what compresses the spring and stabilizes the reading. The balance does not measure the mass directly but rather the force resulting from the mass being acted upon by gravity.
Understanding weight measurement through a spring balance involves physics and mechanics concepts, defining how tools like these help measure gravitational force.

Spring Force

Spring force is a key principle in mechanics where Hooke's Law comes into play. It states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Mathematically, it is expressed as:

• \( F_s = kx \)

Where \( F_s \) is the spring force, \( k \) is the spring constant (stiffness), and \( x \) is the displacement.
In the context of a spring balance, as the man stands on it, the spring compresses until the force exerted by the spring equals the force of the man's weight. This compression is what gives the reading of 60 kgf.
Understanding spring force involves recognizing how springs respond to forces and return to their original state when the force is removed, demonstrating elasticity.

Equilibrium Position

The equilibrium position of a spring balance is the state where the spring is neither extended nor compressed beyond its resting position without any load. At equilibrium, the forces acting on the spring are balanced, meaning that the upward spring force equals the downward weight force.
This balancing point is crucial for accurate weight measurement. When the man is on the balance, the system is at equilibrium. The spring is compressed just enough to counterbalance the man's weight.
If any additional force is applied, like the upward force exerted during a jump, the spring loses this equilibrium momentarily, affecting the reading. Returning to equilibrium only happens when all external forces are removed, demonstrating the spring's return to stability.

Force Exertion

Force exertion involves applying force, leading to a change in motion or state. In the man’s jump from the spring balance, an understanding of force exertion is necessary to predict its effects on the spring and the reading.
During the jump, the man pushes off the balance, exerting an extra upward force which temporarily affects the spring's compression. Initially, this upward force increases significantly, adding to the force of his weight and thus momentarily increasing the reading above 60 kgf.
Once he leaves contact with the balance, the upward force ceases and the spring force alone is left. The lack of any weight force on the spring quickly leads to a reading of zero. This sequence depicts how dynamic interactions between forces influence measurements, demonstrating the transient nature of such exertions.