potential energy and energy conservation

Question

wyzant wont let me upload the figure, so I provided the link to it here

https://www.flipitphysics.com/Content/smartPhysics/Media/UserData/ebfae213-ad62-da58-2e01-ff6f3e3c551b/pendulum.jpg

The pendulum shown to the left consists of a bob of mass of 0.31 kg, attached to a string of length L = 1 meters. It is moving to the right with a speed of 4.33 m/sec at point A. What we'd like to know is what the the velocity of the bob when it reaches point B which is 34 degrees from vertical.

There are two different ways to look at this problem, each of which will give us the same answer. Let's look at each separately. (For all of the questions below, let's start by defining the potential energy of the bob to be zero at point A.)

First, lets look at the question in terms of the work energy theorem. (W_TOT=ΔKE)

1)

What is the initial kinetic energy of the bob at point A?

KE_A =

 J 

2)

What is the work done by on the bob by gravity as it moves from point A to point B?

W_GRAV =

 J  

3)

What is the work done by on the bob by the force of tension from the string attached to the bob as it moves from point A to point B?

W_TEN =

 J  

4)

What is the total work done on the bob as it moves from point A to point B?

W_TOT =

 J 

5)

What is change in kinetic energy of the bob as it moves from point A to point B?

ΔKE =

 J 

6)

What is kinetic energy of the bob at point B?

KE_B =

 J 

7)

What is velocity of the bob at point B?

v_B =

 m/sec 

8)

Now, lets look at the problem in terms of mechanical energy. That is,ME=U+KE and ΔME=W_non-con. (Recall we are defining the potential energy to be zero at point A.) What is the kinetic energy of the bob at point A?

KE_A =

 J 

9)

What is the potential energy of the bob at point A?

U_A=

 J 

10)

What is the mechanical energy of the bob at point A?

ME_TOT-A=

 J 

11)

What is work done by non-conservative forces as the bob moves from point A to point B?

W_non-con=

 J 

12)

What is the mechanical energy of the bob at point B?

ME_TOT-B=

 J 

13)

What is the potential energy of the bob when it reaches point B?

U_B =

 J 

14)

What is the kinetic energy of the bob when it reaches point B?

KE_B =

 J 

15)

What is the speed of the bob at point B?

v=

 m/sec

Answer 1

I am going to give you three hints, and will come back later to provide a complete answer.

Hint #1 The force of tension in this problem is perpendicular to the displacement, hence its work is zero.

Hint #2 Gravity is the conservative force, hence its work is independent on the path. Moreover it’s work only depends on the vertical component of the displacement, the horizontal component of the displacement is irrelevant, because it is perpendicular to gravity.

Hint #3 Use the trigonometry of the right triangle to determine the vertical component of the displacement.

Best!