Is Gravity Involved in the Motion of a Pendulum After a Collision?

[Maxo]

Homework Statement

Homework Equations

∑F=ma

The Attempt at a Solution

This is a problem that can be solved by looking at impulse and momentum and I understand how the problem is solved in the book but I'm wondering about the reasoning before, if this is the only way to look at it. When I look at the picture of what happens, there is a bullet that hits a pendulum so it moves upwards. I would from looking at this assume that when the object (bullet + ballistic pendulum) moves upwards, there is a force of gravity involved. In the way the task has been solved in the book they didn't draw in a free body-diagram showing the forces acting on the objects. What I'm wondering is wouldn't the force of gravity actually be involved after this collision, when the pendulum moves upwards? And then shouldn't it be drawn in a free body diagram?

 

[dauto]

Yes, gravity should be included in a free body diagram. Is that all you wanted to know?

 

[George Jones]

What I'm wondering is wouldn't the force of gravity actually be involved after this collision, when the pendulum moves upwards?

On the next pages, does the text take gravitational potential energy into account?

And then shouldn't it be drawn in a free body diagram?

I don't see a free-body diagram. The diagram in the image you posted shows velocities (which aren't on free-body diagrams), and not forces (which are on free-body diagrams).

 

[Maxo]

On the next pages, does the text take gravitational potential energy into account?

Yes it does... which makes sense. But I still don't understand why this problem could also have been solved by looking at the forces in a free body diagram? Or could it?

 

[haruspex]

Yes it does... which makes sense. But I still don't understand why this problem could also have been solved by looking at the forces in a free body diagram? Or could it?

I presume your question is only in regard to the motion after the impact.
If you attempt it by forces and accelerations you will obtain the differential equation of motion of a pendulum. Since it would not be acceptable to make the usual SHM approximation, the equation cannot be solved in general. Time as a variable can be eliminated from the equation to produce an answer to this question, but what that is doing, in effect, is deriving the fact that work is conserved by the forces.