Questions: Multiple Choice Question Identify the correct equation that represents the principle of work and energy for a rigid body. U1+2=T1-T2 U1+2=T1/T2 T1+U1-2=T2 U1-2=T1+T2

Multiple Choice Question Identify the correct equation that represents the principle of work and energy for a rigid body. U1+2=T1-T2 U1+2=T1/T2 T1+U1-2=T2 U1-2=T1+T2

Transcript text: Multiple Choice Question Identify the correct equation that represents the principle of work and energy for a rigid body. $U_{1+2}=T_{1}-T_{2}$ $U_{1+2}=\frac{T_{1}}{T_{2}}$ $T_{1}+U_{1-2}=T_{2}$ $U_{1-2}=T_{1}+T_{2}$

Solution

Solution Steps

Step 1: Understand the Principle of Work and Energy for a Rigid Body

The principle of work and energy for a rigid body states that the work done by all external forces acting on a body is equal to the change in kinetic energy of the body. This can be expressed mathematically as:

\[ U_{1-2} = T_2 - T_1 \]

where:

$ U_{1-2} $ is the work done by external forces from state 1 to state 2,
$ T_1 $ is the initial kinetic energy,
$ T_2 $ is the final kinetic energy.

Step 2: Analyze the Given Options

Let's analyze each of the given options to see which one matches the principle of work and energy:

$ U_{1+2} = T_1 - T_2 $: This equation suggests that the work done is equal to the negative change in kinetic energy, which is incorrect.
$ U_{1+2} = \frac{T_1}{T_2} $: This equation is not dimensionally consistent with the principle of work and energy.
$ T_1 + U_{1-2} = T_2 $: This equation can be rearranged to $ U_{1-2} = T_2 - T_1 $, which matches the principle of work and energy.
$ U_{1-2} = T_1 + T_2 $: This equation suggests that the work done is equal to the sum of the initial and final kinetic energies, which is incorrect.

Step 3: Identify the Correct Equation

Based on the analysis, the correct equation that represents the principle of work and energy for a rigid body is:

\[ T_1 + U_{1-2} = T_2 \]