Energy conversion of a falling bob

[lingling]

Homework Statement

A bob is hung by a light string and and is pushed sideways. A peg of wood is placed vertically below the point of suspension of the string to hinder the motion of string as shown in the figure below: (please refer to the attachment)

The bob is released. Which of the following statements is/are correct?
(1) The bob has the largest speed when it is vertically below the peg.
(2) The bob cannot reach the original level when it is at the right side of the peg.
(3) The bob possesses same amount of mechanical energy at all time.

A (1) only
B (2) only
C (1) and (3) only
D (2) and (3) only

Homework Equations

The Attempt at a Solution

I attempted option B, but the answer is C.
For statement (1),
I thought when it is vertically below the peg, it loses some energy to the wood, so the speed is lowered.

 

[Hootenanny]

Your attachment will take a while to be approved by the mentors, but I will try to answer your question without.

Can I begin by asking you why you believe that the bob would lose some energy to the peg?

 

[m2003]

Your reasoning for statement (1) is correct. When the bob is vertically below the peg, it experiences a sudden decrease in speed due to the interaction with the peg, resulting in a loss of kinetic energy. However, this does not mean that it has the largest speed at this point. In fact, the bob will have the largest speed at the bottom of its fall, just before it starts to rise again. This is because it has the most potential energy at this point, which is converted into kinetic energy as it falls. So, statement (1) is incorrect.

Statement (2) is also incorrect because the bob will eventually reach its original level, assuming there is no loss of energy due to friction or other factors. This is because the bob's potential energy at the top of its fall is equal to the potential energy it had when it was first released.

Statement (3) is correct. The bob will possess the same amount of mechanical energy (a combination of kinetic and potential energy) at all times, as long as there is no external force acting on it. This is due to the law of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another. Therefore, option C is the correct answer.