how do i do this?

Question

a 5gram bullet is shot through a 1kg wood block suspended on a string 2.000m long. The center of mass of the block rises a distance of .45cm. Find the speed of the bullet as it emerges from the block if it's initial speed is 450m/s.

Answer 1

First, understand that momentum will be conserved in the collision.

so
450*5/1000=ve*5/1000+vb*1
where ve is the exit speed of the bullet and vb is the speed of the block.

I am assuming the collision occurs very fast

Given the rise of the hanging block, we can compute vb using conservation of energy
.5*1*vb^2=1*9.81*.45/100
vb=sqrt(2*9.81*.45/100)
vb=0.297 m/s

plug in above
450*5/1000=ve*5/1000+0.297
ve=391 m/s

Just for fun, how much energy was lost due to collision?

.5*5*(450^2-391^2)/1000-
9.81*.45/100

124 J lost in the collision.

j

Answer 2

Eh, typical physics trap! The only thing to consider here is the loss of energy, obtained by calculating the energy transferred to the pendulum (this contraption is called a ballistic pendulum, BTW, used to find bullet's velocities).
FORGET about the bullet (type, brand,...).
Since energy is conserved, the initial bullet's energy is the same as the final bullet's energy plus the energy transferred to pendulum. The energy transferred to the pendulum is obtained by knowing it rose 45cm. Simple math.

Answer 3

Since the block rises .0045 m against gravity, its initial velocity must be V1b = √(2gy)
Let p be the suffix for the bullet......
Consevation of momentum gives ∆Vp = V1b*Mb/Mp = √(2gy)*Mb/Mp = √(2*9.8*.0045)*1/.005 = 59.397 m/s

Final Vp = 450-59.397 = 390.6 m/s

Energy considerations alone WILL NOT solve this problem because you don't know how much energy is converted to heat as the bullet goes through the block. Only after having used momentum to get the answer can I now find the heat energy created........

Answer 4

Depends on the type of bullet. A hollow point bullet would flatten and slow considerably. An armor piercing shell would slow less, a silver bullet (used to kill werewolves), would be between the two. You need to ask your teacher the physical characteristics of the bullet itself.

Answer 5

http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html#c1

Find how much energy the pendulum absorbs, the rest remains in the bullet.

Answer 6

dont know