physics questions p5?

65 ....  see image....

63a) Period = 2pi√(l/g)

P = 2pi√(2.23/9.8)

P = 2.99722 ~= 2.99

63b)

Total energy = kinetic energy at the bottom OR potential energy at the max position. We don't know maximum height so let's find kinetic energy at the bottom.

KE = (mv^2)/2

KE = 6.74*(2.06^2)/2

KE = 14.3009 J

63c)

You know kinetic energy at bottom = potential energy at the top.

14.3009 = m*g*(vertical height)

14.3009 = 6.74 * 9.8 * h

h = 0.2151

h = position at the bottom - vertical component of string at the top

0.2151 = 2.23 - 2.23*cos(θ)

cos(θ) = 0.90291

arccos(0.90291) = 25.4567 DEGREES

first. your previous question took a LOT of time. So will be brief this time. a)  T = 2*pi() * sqrt( L/g).    b) Ek = 1/2 m v^2  c) mgh = Ek but h = L*(1-sin(theta) ) = L *(1-theta) for small angles  -> theta = 1-( Ek/(MgL) )