Answer to Question #259807 in Mechanics | Relativity for AIKA

Question

There are three ways to bring a 2 kg particle from the origin marked as (0,0) to point C with coordinates (5 m, 5m). Path 1 is along OAC, path 2 is along with OBC, and path 3 is OC. Suppose that the force that will do this work has the following component: Fx = 4N and Fy = 3N. Find the work done by this force in each path. Is this force conservative? What is the coefficient of restitution? Show the equation.

Answer 1

Path 1 is along OAC:

$W=5F_y+5F_x=5\cdot 3+5\cdot 4=35$ J

path 2 is along with OBC:

$W=5F_y+5F_x=5\cdot 3+5\cdot 4=35$ J

path 3 is OC:

$W=(F_x+F_y)cos45\degree\sqrt{5^2+5^2}=(4+3)cos45\degree\sqrt{5^2+5^2}=35$ J

A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the path taken.

So, the given force is conservative.

The coefficient of restitution is the ratio of the final to initial relative speed between two objects after they collide:

$e=\frac{|v_1-v_2|}{|u_1-u_2|}$

where u₁, u₂ is the initial velocity of object 1 and object 2,

v₁, v₂ is the final velocity of object 1 and object 2