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An apple falls from a tree and feels no air resistance. Asit is falling, which of these statements about it are true?

(a) Onlyits momentum is conserved;

(b) Only its mechanical energy isconserved;

(c) Both its momentum and its mechanical energy are conserved;

(d) Its kinetic energy is conserved.

Short Answer

Expert verified

(a) The statement is not true.

(b) The statement is true.

(c) The statement is not true.

(d) The statement is not true.

Step by step solution

01

Definition of mechanical energy

The combination of kinetic energy, or energy of motion, and potential energy, or energy stored in a system as a result of the arrangement of its components, is known as mechanical energy.

02

Step 2:The law of conservation of energy:

The sum of kinetic, potential, and internal energies is always conserved.

∆K+∆U+∆Uint=0

03

Step 3:Discussion for part (a)

Since external force gravity is acting on the system, so the net external force on the system is not zero so momentum will not be conserved.

Hence this statement is not true.

04

Step 4:Discussion for part (b)

Since gravity is a conservative force therefore total mechanical energy (kinetic energy + potential energy) of the system will be conserved.

Hence the statement is true.

05

Step 5:Discussion for part (c)

Since external force gravity is acting on the system, so the net external force on the system is not zero so momentum will not be conserved.

Since gravity is a conservative force therefore total mechanical energy (kinetic energy + potential energy) of the system will be conserved.

Therefore, Mechanical energy is conserved but momentum is not conserved

Hence the statement is not true.

06

Step 6:Discussion for part (d)

Since gravity is a conservative force therefore total mechanical energy (kinetic energy + potential energy) of the system will be conserved,sothere is a change in Kinetic energy,but total energy is conserved.

Hence the statement is not true.

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