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I'll be very grateful to anyone who could help me with this problem.
I've given it much thought and i couldn't figure it out. I'm trying to get an a in my Physics class so i need extra help.Thanks
a) Use work and energy considerations to find the magnitude of the force that stops the bullet.
b) Assuming that the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment the bullet stops moving.
Lets look at part A, using work and energy to find the frictional force stopping the bullet. Work is defined as change in kinetic energy
where point 1 is the moment the bullet strikes the tree, and point 2 is the moment it stops. Work is also defined as a force acting over a distance
negative because the force is opposite the direction the bullet moves, so it does negative work on the bullet. Kinetic energy is defined as
So K2 = 0 since v2 = 0. This leaves
You know everything except for F, which is what you're looking for. Remember to convert all quantities into meters/kg/seconds so that you get Newtons as your force. This procedure works for all work/energy problems when the object only moves horizontally.
Lets examine the bullet the moment it enters the tree. What is acting on it? There is a frictional force, acting opposite motion. The bullet is decelerating, so there is an acceleration opposite motion (call it a). Apply Newton's second law, sum of forces = mass times accleration:
You know F and m, solve for acceleration. Now apply the kinematic equations which you learned earlier in class (their almost always the first thing taught to you about motion):
where x is distance traveled. You know the velocity it enters the tree with, and you just found the acceleration (remember to plug it in as a negative, and use consistent units!).
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