Suppose the pendulum bob in the figure(Figure 1) has a mass of 0.32 kg and is mo

Question

Suppose the pendulum bob in the figure(Figure 1) has a mass of 0.32 kg and is moving to the right at point B with a speed of 2.3 m/s . Air resistance is negligible.

Figure 1 (Point B is perdendicular straight down from the attachment site with Point A to the right by 35 degrees (Point A is also 1.2 m away from attachement site))

A) What is the bob's kinetic energy at point B?

B) At some point the bob will come to rest momentarily. Without doing an additional calculation, determine the change in the system's gravitational potential energy between point B and the point where the bob comes to rest.

C) Find the maximum angle the string makes with the vertical as the bob swings back and forth. Ignore air resistance.

Explanation / Answer

a)
m = 0.32 Kg
v = 2.3 m/s
At Pont B , Bob has Kinetic Energy = 1/2 * mv^2
K.E = 1/2 * 0.32 * 2.3^2
K.E = 0.846 J

(b)
Using Energy Conservation,
At the point where the bob will come to rest, all the kinetic energy at Point B, will be converted to Potential Energy.
Therefore,
Change in the system's gravitational potential energy between point B and the point where the bob comes to rest = 0.846 J

(c)
Potential Energy = m*g*h
P.E = 0.32 * 9.8 * (1.2 - 1.2 * cos())

For Maximum Angle,
0.32 * 9.8 * (1.2 - 1.2 * cos())= 0.846
cos() = 0.930/1.2
= 39.2o

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