A rock of mass 11 kg is tied to a string of length 2.6 m, with the other end of
ID: 1379724 • Letter: A
Question
A rock of mass 11 kg is tied to a string of length 2.6 m, with the other end of the string fastened to the ceiling of a tall room. While hanging vertically, the rock is given an initial horizontal velocity of 2.2 m/s.
(a) Add a coordinate system to the sketch in the figure. Where is a convenient place to choose the origin of the vertical (y) axis? (Do this on paper. Your instructor may ask you to turn in this work.)
(b) What is the potential energy of the rock? (Use the following as necessary: m, g, and h.)
What is the initial kinetic energy of the rock?
(c) If the rock swings to a height h above its initial point, what is its potential energy? (Use the following as necessary: m, g, and h.)
What is its total mechanical energy at that point?
(d) How high will the rock swing? Express your answer in terms of the angle ? that the string makes with the vertical when the rock is at its highest point.
? =
Explanation / Answer
a) the origin will be at the neutral position of the string before velocity is given
b) potential energy = 0
KEi = 0.5*mv^2
KEi = 0.5*11*2.2^2
KEi = 26.62 J
c) the kinetic energy is converted into potential energy
PE at height h = 26.62 J
at that point KE = 0
total ME = PE + KE = 0+26.62
total ME = 26.62 J
d) conservation of energy
PE = KE
0.5*mv^2 = mg*h
0.5*2.2^2 = 9.8*h
h = 0.247 m
h = L*[1-cos(theta)]
0.247 = 2.6*[1-cos(theta)]
0.905 = cos(theta)
theta = 25.176 degrees
e) PE increases linearly as height tincrease
KE falls as the height increases
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