Marble rolling

A marble of mass M and radius R is rolled up a plane of angle A. If the initial velocity of the marble is Vo, what is the distance L it travels up the plane before it begins to roll back down? Ans clue: If Vo were to equal 3m/s, A=30, then l=1.3m

Yo-yo tension and force

A yo-yo of mass M has an axle of radius b and a spool of radius R. Its moment of inertia can be taken to be MR^2/2 and the thickness of the string can be neglected. The yo-yo is released from rest. a) What it the tension in the cord as the yo-yo descends and as it ascends? b)The center of the yo-yo descends distance h before the string is fully unwound. Assuming that it reverses direction with uniform spin velocity, find the average force on the string while the yo-yo turns around.

Mass hitting a vertical plank

A plank of length 2l and mass M lies on a frictionless plane. A ball of mass m and speed Vo strikes its end (the plank is standing vertical and the ball strikes the top from the left). Find the final velocity of the ball, Vf, assuming that mechanical energy is conserved and that Vf is along the original line of motion. b)Find Vf assuming that the stick is pivoted as the lower end. Ans clue: If m=M, then part a has Vf=3Vo/5 and part b would equal Vf=Vo/2

Central Force

A particle of mass 50g moves under an attractive central force of magnitude 4r^3 dynes. The angular momentum is equal to l,000 g*cm/s. a) Find the effective potential energy. b) Indicate on a sketch of the effective potential the total energy for circular motion. c) The radius of the particle's orbit varies between ro and 2ro. Find ro. Ans c) ro is about 2.8 cm

Central Force

A particle of mass 50g moves under an attractive central force of magnitude 4r^3 dynes. The angular momentum is equal to l,000 g*cm/s. a) Find the effective potential energy. b) Indicate on a sketch of the effective potential the total energy for circular motion. c) The radius of the particle's orbit varies between ro and 2ro. Find ro. Ans c) ro is about 2.8 cm