A 1.2 kg block is hung from a vertical spring, causing the...

A $1.2 \mathrm{~kg}$ block is hung from a vertical spring, causing the spring to stretch by $2.4 \mathrm{~cm}$. How much farther will the spring stretch if a $0.60 \mathrm{~kg}$ block is added to the $1.2 \mathrm{~kg}$ block?

Key Concepts

Additional Mass Effects

Adding extra mass to a spring-mass system increases the gravitational force on the spring, causing further extension. The additional displacement can be calculated using the spring constant and the new total force applied, according to Hooke's Law.

Spring Constant Determination

The spring constant (k) is a measure of a spring’s stiffness and can be determined by analyzing the equilibrium condition where the gravitational force equals the spring force. Once k is known, it can be used to predict how the spring will behave when additional forces are applied.

Equilibrium in Spring-Mass Systems

In a spring-mass system, equilibrium occurs when the downward gravitational force on the mass is balanced by the upward restoring force of the spring. This balance allows for the calculation of the spring constant and the prediction of additional displacement when extra mass is added.

Gravitational Force

Gravitational force is the weight of an object and is calculated by multiplying its mass by the acceleration due to gravity. This force is the primary factor causing the spring to stretch in a vertical spring-mass experiment.

Hooke's Law

Hooke's Law states that the force exerted by a spring is proportional to the displacement from its equilibrium position, expressed as F = kx. This principle is used to determine the relationship between the applied force (such as weight) and the resulting stretch or compression in the spring.

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