Object A is stationary while objects B and C are in motion. Forces from object A do 20 J of work on object B and -5 J of work on object C. Forces from the environment do 4 J of work on object B and 8 J of work on object C. Objects B and C do not interact. What are ΔKtot and ΔU if (a) objects A, B, and C are defined as separate systems and (b) one system is defined to include objects A, B, and C and their interactions?

Since these are forces exchanging work I assume they are affecting the kinetic energy of the objects, and not their internal energy. (Internal energy might be affected by heat or work done by shafts).

For object A:

[tex]\Delta K = 5 - 20 = 15 J\\\Delta U = 0[/tex]

For object B:

[tex]\Delta K = 4 + 20 = 24 J\\\Delta U = 0[/tex]

For object C:

[tex]\Delta K = 8 + 5 = 13 J\\\Delta U = 0[/tex]

For all objects consiered as a system:

[tex]\Delta K = 8 + 4 = 12 J\\\Delta U = 0[/tex]

bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-03-15T12:24:58+01:00

The value of ΔKtot for object A, B, and C defined as separate systems are 15 J, 24 J and 13 J respectively. The value of ΔU is zero.

What is work energy theorem?

According to the work energy theorem, the sum of all the forces acting on a body to do a work is equal to the change in the kinetic energy of the body.

a) The value of ΔKtot and ΔU when objects A, B, and C are defined as separate systems.

Forces from object A do 20 J of work on object B and -5 J of work on object C. For this two forces, the kinetic energy works on A will be equal to the sum of this two force in the opposite direction. Therefore,

[tex]\Delta K_A=5+(-20)\\\Delta K_A=15\rm J\\[/tex]

Forces from object A do 20 J of work on object B and forces from the environment do 4 J of work on object B. Thus the kinetic energy,

[tex]\Delta K_B=4+20\\\Delta K_B=24\rm J\\[/tex]

Forces from object A do -5 J of work on object C and forces from the environment do 8 J of work on object C. Thus the kinetic energy,

[tex]\Delta K_C=8+5\\\Delta K_C=13\rm J\\[/tex]

Internal energy in case of separate system will be zero for object A, B and C.

b) The value of ΔKtot and ΔU when one system is defined to include objects A, B, and C and their interactions

As all the system are considered as one system. Thus, the work by environment will be equal to the total internal energy.

AS forces from the environment do 4 J of work on object B and 8 J of work on object C. Thus,

[tex]\Delta K=8+4\\\Delta K=12\rm\; J[/tex]

In this case, the internal energy will also be zero.

Hence, the value of ΔKtot for object A, B, and C defined as separate systems are 15 J, 24 J and 13 J respectively. The value of ΔU is zero.

Learn more about the work energy theorem here;

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