Question

Question: Figure 7.48 is a portion of a graph of energy terms vs, time for a mass on a spring, subject to air resistance. Identify and label the three curves as to what kind of energy each represents. Explain briefly how you determined which curve represented which kind of energy.

Short answer

Answer

Curve Ahas potential energy $U=U_g+U_s$, curve Bhas kinetic energy Kand the curve Chas total energy$E=K+U$ .

Step-by-step solution

Definition of Energy

The energy is the capacity to perform work in physics. The potential energy, kinetic energy, thermal energy, electrical energy, chemical energy, nuclear energy, and other kinds of energy are all examples of potential energy. There is also heat and work (energy transmitted from one body to another).

Analysing all the labels of the curve 

Let the mass is initially motionless.

The potential energy can only exist in the initial condition when both gravitational and elastic exists.

From the given graph, the curve A has the system's potential energy.

As the system is initially motionless so, the total energy of the system in curve Ais equals to the potential energy at this time that is $U=U_g+U_s$.

The mass acquires kinetic energy when potential energy falls due to the stretching (or compressing) of the spring.

From the given figure, the curve Bis designated as the system's kinetic energy.

The equilibrium position is reached when U is at its lowest and K is at its highest.

From the given figure, the curve C has been determined as the system's total energy.

Therefore, it is concluded that, Curve Ahas potential energy$U=U_g+U_s$ , curve Bhas kinetic energy Kand the curve Chas total energy $E=K+U$.