A large pendulum swings in the lobby of the United Nations building in New York City. The pendulum has a 91-kg gold-plated bob and a length of 22.9 m. Assume g = 9.81 m/s2.
Part A
How much time does it take for the bob to swing from its maximum displacement to its equilibrium position?
Express your answer to three significant figures and include the appropriate units.

Answer:

44J

Explanation:

Given parameters:

Mass of rock  = 0.22kg

Initial velocity  = 20m/s

Distance moved  = 10m

Unknown:

Initial kinetic energy of the rock  = ?

Solution:

To solve this problem, we need to understand that kinetic energy is the energy due to the motion of a body.

It is mathematically expressed as;

     Kinetic energy  = [tex]\frac{1}{2}[/tex] m v²

m is the mass

v is the velocity

   Kinetic energy  =  [tex]\frac{1}{2}[/tex] x 0.22 x 20²   = 44J

Answer:

3.3kg

Explanation:

Given parameters:

Spring constant = 400N/m

Extension  = 8cm  = 0.08m

Unknown:

Amount of mass the spring is supporting  = ?

Solution:

To solve this problem:

     F  = kE

F is the force

k is the spring constant

E is the extension

  So;

            F  = 400 x 0.08  = 32N

Mass;

       Force  = mass x acceleration due to gravity

          32  = mass x 9.8

  Mass = 3.3kg

The mass the spring is supporting is 3.27 Kg.

We'll begin by calculating the force acting on the spring.

F = Ke

F = 400 × 0.08

F = 32 N

Finally, we shall determine the mass. This can be obtained as follow:

m = F / g

m = 32 / 9.8

m = 3.27 Kg

Therefore, the mass the spring is supporting is 3.27 Kg

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