(b) 3 particles are moving on a plane surface, connected to each other, write no of constraint forces and degrees of freedom.

Consider a solid sphere (e.g., a planet) with mass M and radius R. The volume mass density for this planet is given by r2 p(r) = for rR where A is a constant with the units of kg/m'.

A simple pendulum is given an initial tangential velocity such that it swings in acomplete circle around its fulcrum. Assume:● The string is 32 meters long● The bob has mass M Determine: (A) The minimum velocity atthe top ofthe loop. Now assume the mass passesthrough the top of the loop with theminimum found in part (a), above; Determine: (B) the velocity at an angle of 30 degrees from the vertical(i.e.: at 30 degrees up from a position fully at the bottom of the loop).

A particle of mass m = 1.50 kg moves along one dimension and is subject to a single force, whose potential energy function is given by U(x) = x4 – 2x2 + 4 (where U is measured in Joules and x is measured in meters). At the moment when the particle is located at position x = 1.50 m, its speed is v = 2.50 m/s. %3D