A particle comes in from the left at 3m/s when still very far away. It\'s mass i

Question

A particle comes in from the left at 3m/s when still very far away. It's mass is 4 kg. As it approaches, it encounters a conservative force with the following PE: 12 AND 10 JOULES

The conservative force is in effect forever.

A) What is the ultimate destiny of the particle if the conservative force is the only force on the particle? (Which way does it exit, and how fast?) (Or is the particle trapped?)

B) Suppose a non-conservative force kicks in for a very short time, while X is just less the zero; its work is Wnc= -16 joules. Now, what is the ultimate destiny?

C) Suppose instead, Wnc= -21 joules. What is the particles ultimate destiny?

D) Is it possible for Wnc= -27 joules? Why or why not?

Explanation / Answer

starting energy = 1/2 m*v^2 = 1/2 * 4* 3^2 = 18 Joule
after energy = 18+12+10=40J
at exit 12+10 energy will be remain so
A) 1/2 m*v^2 = 22
v =sqrt(11)=3.31 m/s right

B)total energy = 22-16 = 6J

1/2 m*v^2 = 6
v= sqrt(3)
=1.732m/s

C) total energy = 22-21 =1J

1/2 m*v^2 = 1

D) its not possible for Wnc greater than total energy of particle
particle will be stop there .

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