Question

1. An inventor designs a pendulum clock using a bob with massmat the end of a thin wire of lengthL. Insteadof swinging back and forth, the bob is to move in a horizontal circle with constant speedvwith the wiremaking a fixed angleβwith the vertical direction (Fig 1). This is called a conical pendulum because thesuspending wire traces out a cone.(a) Write the Newton’s equations inxandycomponents.(b) Using part (a) find the tensionFin the wire.(c) Find time periodT(the time for one revolution of the bob) using the expression for centripetal accel-eration.(d) Let bob has a mass of 0.040 kg, the string has lengthL= 0.90 m and circumference of the circle is 0.94m, calculate numerical values of quantities in part a,b and c.

2. What would be the mass of the planet if the launch speed of a projectile is 7910 m/s that rises vertically above the planet of radius R=6.37×106m to an altitude equal to 2R radius before coming to rest momentarily? Use conservation of mechanical energy.

Answer 1