Physics Central Force: find effective potential energy and sketch

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.

Solution Summary

The solution clearly defines the terms of the problem, draws the sketch and calculates the answer.

A particle at rest is attracted toward a center of force according to the relation F=-mk^2/x^33. Calculate the time required for the particle to reach the force center from a distance d.

Physical science (8th edition) by Bill W. Tillery
Parallel Exercises
1. How much work is done when a force of 800.0 Ni s exerted while pushing a crate across a level floor for a distance of 1.5m?
2. A force of 400.0 N is exerted on a 1,250 N car while moving it a distance of 3.0 m. How much work was done on the car?

A particle of mass m moves in one dimension along the positive x axis. It is acted on by a constant force directed toward the origin with magnitude B, and an inverse square law repulsive force with magnitude A/x^2.
a) Find the potentialenergy function U(x)
b) Sketch the energy diagram for the system when the maximum kineti

See attached file for full problem description.
Previously it was considered a force of the form f = ixy + jcx^2 + kz^3, and found a value of "c" from the following list such that this was a conservative force.
Note: there must really be extra 'constants' in front of each term, with magnitude 1 but the proper units (such as

A particle is under the influence of a force F = -kx+(kx^3)/a^3 where k and a are constants and k is positive.
1) Find U(x) the potentialenergy
2) What happens when E (total energy) = (1/4)ka^3

An object on an incline of 30 degrees is towed up the incline by an applied force of 100N. The coefficient of kinetic friction of mu=.35. The mass of the object is 10.0kg.
PART I
1) Draw a sketch
2) Draw a free body diagram
3) What is the weight of the object?
4) What is the acceleration of the object in the y direction?

A block of mass m slides down a frictionless incline. The block is released at height h above the bottom of the loop (see file for drawing of path).
a. What is the force on the inclined track on the block at point A
b. What is the force on the inclined track at point B
c. At what speed does the block leave the track at poin