Question

If no friction acts on a diver during a dive, then which of the following statements is true? A) The total mechanical energy of the system increases. B) Potential energy can be converted into kinetic energy but not vice versA) . C) (KE+ PE) beginning = (KE + PE) end . D) all of the above

Answer 1

If no frictional work is considered, then the energy of the system (the driver at all positions is conserved.

Let
position 1 = initial height of the diver (h₁), together with the initial velocity (v₁).
position 2 = final height of the diver (h₂) and the final velocity (v₂).

The initial PE = mgh₁ and the initial KE  = (1/2)mv₁²
where g = acceleration due to gravity,
m = mass of the diver.
Similarly, the final PE and KE are respectively mgh₂ and (1/2)mv₂².
PE in position 1 is converted into KE due to the loss in height from position 1 to position 2.
 
Therefore
(KE + PE) ₁ = (KE + PE)₂

Evaluate the given answers.
A) The total mechanical energy of the system increases.
     FALSE

B) Potential energy can be converted into kinetic energy but not vice versa.
     TRUE

C) (KE + PE)beginning = (KE + PE) end.
     TRUE

D) All of the above.
     FALSE

Answer 2

Option (C) is correct .i.e. ${(KE + PE)_{initial}} = {\left( {KE + PE} \right)_{final}}$.

Further Explanation:

For an isolated system, the total mechanical energy is always conserved if no friction or resisting or drag force is considered.

${\text{Total}}\,{\text{mechanical}}\,{\text{energy}}\,{\text{ =}}\,{\text{constant}}$       ………. (1)

Therefore, option (A) is incorrect.

Also, both the potential energy and the kinetic energy are Inter-convertible. As the diver dives and follows a parabolic path, jumps up with some initial velocity and thus has a significant amount of kinetic energy and at the highest point the vertical component of the velocity becomes zero and whole of the kinetic energy get converted into potential energy then as it moves through space downwards the potential energy decreases and the diver gets its kinetic energy back.

Therefore, option (B) is incorrect.

The sum of the kinetic energy and the potential energy of the system initially will remain equal to the sum of the kinetic energy and the potential energy at the final stage of the system.

Now, from equation (1),

$\begin{aligned}\text{kinetic energy+potential energy}&=\text{mechanical constant}\\KE+PE&={\text{constant}}\\{\left( {KE + PE} \right)_{initial}}&={\left( {KE + PE} \right)_{final}}\\\end{aligned}$

Therefore, option (C) is correct.

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Answer Details:

Grade: high school

Subject: Physics

Chapter: mechanics

Keywords:

kinetic energy, potential energy, mechanical energy, diver, dive, velocity, conservation of mechanical energy, constant, total energy of system.