Do not try to solve the complete motion but use energy considerations where nece

Question

Do not try to solve the complete motion but use energy considerations where necessary. Show all work. Don't forget vectors have magnitude and direction.
M = 6.0 kg, the length of the string, L = 2.0 meters. The point-mass M is pulled away from the vertical as shown and released from rest at an angle theta = 70°.

a) What is the initial tension in the string?
b) What is the initial acceleration of M?
c) What is the tension in the string when theta = 0°?
d) What is acceleration of M when theta = 0°?
e) What is the direction of the average acceleration between theta = 45° and 0°?
f) Sketch the subsequent motion of M if the string is melted when theta = -45°?
g) Sketch the subsequent motion of M if the string is melted when theta = -70°?

Explanation / Answer

a] Force is balanced along the string,

so T = Mg cos 70 degree

= 6*9.8* cos 70 degree

= 20.11 N answer

b] initial acceleration will be tangential to circle a = Mg sin 70 degree/M

= 9.8 sin 70 degree

= 9.21 m/s^2

c] T = Mg cos 0 degree

= 6*9.8* 1

= 58.8 N answer

d] a = Mg sin 0 degree/M

= 0 m/s^2

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