Question

1. A pendulum of mass 2.0 kg is raised to a height of 0.4 m above the lowest point in its swing and then is released from rest. If air resistance can be ignored, how high will the pendulum swing on the other side of its motion?

1b For the pendulum in the previous problem, how fast will it move at the lowest point in its swing? show work

1cA spring of spring constant 60 N/m is stretched a distance of 0.3 m from its equilibrium position. Calculate the increase in the potential energy of the spring. Show all work or no credit.

Answer 1

1) As it is a simple harmonic motion and a pendulum will have only potential energy at the extreme points. so height of pendulum swing on the other side will be same. The answer is 0.4 m

1a) At lowest point, pendulum as maximum speed. At lowest it has kinetic energy , no potential energy

using conservation of energy

mgh = 1/2*m*v²

gh = 1/2*v²

v = sqrt (2gh)

v = sqrt (2*9.8*0.4)

v = sqrt (7.84) m/s

v = 2.8 m/s

1cA) Potential energy = 1/2*k*x²

  P.E = 0.5*60*0.3²

P.E = 2.7 Joules