How Do You Calculate the Maximum Angle of Inclination After a Collision?

[psstudent]

Mentor's note: this was originally posted in a non-homework forum, so it doesn't have the homework template.

------------------------------------Hey guys hoping you guys could help me with this

A object (20g) moving horizontally at 100m/s embeds itself in the middle of a block of some wood with a mass of 1kg . the block of wood is suspended by a light vertical string of the length 1m.
This is the drawing he gave in class (the drawing is not drawn to scale) http://imgur.com/HGuPTL8

Calculate:
a)the maximum inclination of the string

b)the maximum angle of inclination of the string after the object collides with the wood.

So the teacher gave this question as part of the homework, now almost no one in my class has been able to get it so far because i don't think we ever discussed max angles of inclination.But I tried part one at least. First we never were thought about angles of inclination but I am just going to assume its the angle of repose. So i figure using the formula angle =archtan(tan inverse) * coefficient of friction.
Now there is no mention of coefficient of friction in this so I assumed it had to be calculate.
We were never thought this but form the name it implies its a ratio of sin to cos.

so because the block was vertically hanged it must be at a 90 degree angle perpendicular to the ground right? so i used 1kgsin90 /1kgcos90 but then i realized its not an inclined plane so then 1kgcos90 would be zero and give me zero as the divisor which can't work.

So i just used the sin part which gave me:
1kgsin90 =1 as my coefficient of friction ,
then using the formula i mentioned before: angle = tan inverse of 1 =45 degrees

this makes sense to me because in parabolic motion at least 45 is the angle you throw at to get the furthest distance so 45 makes sense to be the highest angle of inclination. That's what i thought at least. But as I said we ddint go in depth about this at class so what I wrote above could be completely off.Now for b I really didnt have any idea what to do because I wasn't sure is a) was correct. It says what's the max inclination for the object and wood so I am guessing you do something similar to a but then instead of 1 kg you add the masses together as 1.02kg , but I am not sure where the velocity of the question comes into play.

Any help would be appreciated.

 

[CWatters]

I don't understand the difference between a) and b) but in this type of problem the max angle of inclination is normally the angle the rope makes when the block is at it's highest point.

To calculate how high the block swings you first need to calculate how fast the block and bullet are going just after the collision (eg at the bottom).

The problem statement doesn't provide information about the friction properties of a bullet in a block of wood so you can't work out how much energy is lost as friction/heat. This means you can't apply the theory of conservation of energy to the impact to work out the velocity.

What else is conserved in a collision? What else could you use to work out the initial velocity of the combined block and bullet?

 

[psstudent]

after discussion with someone, i realize the part about friction I ahd was completely off because the object isn't touching. So i can use conservation of momentum to fin dthe momentum of the pendulum after impact, and then us energy =mgh to solve for the max height and use sohcahtoa to find the angle?

 

[CWatters]

That's how I would do it.

 

[psstudent]

Ok so I worked out the max height as 0.2 m. But I am having trouble properly constructing the triangle to find the angle.

 

[haruspex]

Ok so I worked out the max height as 0.2 m. But I am having trouble properly constructing the triangle to find the angle.

Let the suspension point be A, the initial position of the block B, and the position at maximum height C.
Draw a horizontal from C to meet AB at D.
Fill in the lengths that you know. What side lengths do you have for ACD?

 

[psstudent]

Ah ok, I got it , I found the angle to be 36.9 so that's my max inclination after teh object hits. But for part a) which asks for the max inclination before collision, wouldn't it just be 0 ? Because it didnt move?

 

[haruspex]

But for part a) which asks for the max inclination before collision, wouldn't it just be 0 ?

As posted, part a did not specify before or after. Since 'before' is a pointless question, it is natural to assume it means after, but then it's the same as part b. Please check you have quoted questions a and b exactly as worded.

 

[psstudent]

Hey haruspex , i checked the question again and it does indeed say "
the maximum inclination of the string" so what would recommend me doing? Put it as zero? Put it as "unanswerable" or "redundant"?

Thanks !

 

[haruspex]

Hey haruspex , i checked the question again and it does indeed say "
the maximum inclination of the string" so what would recommend me doing? Put it as zero? Put it as "unanswerable" or "redundant"?

Thanks !

I would just give the same answer to both. It's clearly not what the teacher intended to ask, but we can't guess what was intended.

 

[psstudent]

Very true, it seems very poorly worded. Thank you for your help.