The height of a tower is measured by attaching a simple pendulum to its ceiling,

Question

The height of a tower is measured by attaching a simple pendulum to its ceiling, whose length is barely enough to stay off the floor. The pendulum is let go from a small angle at a height of 0.2 m above the floor, and takes 15 s to return to the same location it started from.

a.) How tall is the tower?
_________ m

b.) How fast is the mass travelling at its lowest point?
__________ m/s

c.) What angle did the pendulum string make with the vertical when it was released?
_________ degrees
(Does this seem "small" to you?)

Explanation / Answer

the period appears to be 15 s

T = 2pi sqrt( L / g )
15 = 2pi sqrt ( L / 9.81)
(15/2pi)^2 = L / 9.81
L = 55.91 m

conservation of energy
PE at start = KE at bottom
it's all GPE at the release point and all KE at the bottom of the swing)
m*g*h = 1/2*m*v^2
v = sqrt( 2*g*h )
v = 1.98m/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.