Answer to Question #182930 in Physics for Andu

Question

14. A sphere with mass 2kg moves in a trajectory where first it has the shape of a triangle and then a half circle. The height of the plane is 1.8m. Frictional forces are absent. weight = 2kg Calculate:

A) The velocity of the sphere at point 2, which is at the bottom of the triangular plane.

B) Mechanical energy at point 3, which is above, in the middle of the semicircle.

Answer 1

A) The velocity at this point can be found from conservation of energy:

$$KE_f=PE_i, \\\space\\\frac12 mv^2=mgh,\\\space\\ v=\sqrt{2gh}=5.9\text{ m/s}.$$

B) The mechanical energy (the sum of potential and kinetic energies at a given point) is constant according to energy conservation principle, so, it is

$$ME=PE_i=mgh=35.28\text{ J}.$$