How Do You Calculate Initial Bullet Speed in a Ballistic Pendulum Scenario?

[rbrow039]

Homework Statement

A 7.0-g bullet is fired into a 1.5-kg ballistic pendulum. The bullet emerges from the block with a speed of 200 m/s, and the block rises to a maximum height of 12 cm. Find the initial speed of the bullet.

Now I think this is an imperfect inelastic collision because the bullet does not lodge itself in the pendulum. So I assumed since it was inelastic I could ignore conservation of kinetic Energy.

Homework Equations

Conservation of Momentum
Conservation of Energy

The Attempt at a Solution

m1v1i +m2v2i=(m1 + m2)vf
(.007kg x v1i)+0=(1.507kg)vf

(PE + KE)collision=(PE + KE)top
0 + (.5 x 1.507 x vf^2)= mgh + .5mv^2
0 + (.5 x 1.507kg x vf^2) = (1.5 kg x 9.81m/s^2 x .12m) + (.5 x .007kg x 200^2)
vf^2=(1.7658J + 140J)/(.7535kg)
vf=13.716m/s

(.007kg x v1i)=1.507kg x 13.716m/s
v1i = 2952 m/s
Now I know this is not the answer because the answer is given as 530m/s but I can't for the life of me figure out what went wrong with the energy calculation. (I'm assuming that's where the big boo boo happened)

 

[alphysicist]

Hi rbrow039,

Homework Statement

A 7.0-g bullet is fired into a 1.5-kg ballistic pendulum. The bullet emerges from the block with a speed of 200 m/s, and the block rises to a maximum height of 12 cm. Find the initial speed of the bullet.

Now I think this is an imperfect inelastic collision because the bullet does not lodge itself in the pendulum. So I assumed since it was inelastic I could ignore conservation of kinetic Energy.

Homework Equations

Conservation of Momentum
Conservation of Energy

The Attempt at a Solution

m1v1i +m2v2i=(m1 + m2)vf

I don't believe this formula is correct; this formula applies to a perfectly inelastic collision (where both objects stick together and move with the same speed vf after the collision). As you remarked, these objects do not stick together after the collision. What would the conservation of momentum equation be for this case? (And notice they give you the speed of the bullet right after the collision.)

(.007kg x v1i)+0=(1.507kg)vf

(PE + KE)collision=(PE + KE)top
0 + (.5 x 1.507 x vf^2)= mgh + .5mv^2
0 + (.5 x 1.507kg x vf^2) = (1.5 kg x 9.81m/s^2 x .12m) + (.5 x .007kg x 200^2)

With the change to the conservation of momentum equation for the collision, do you see how to correct your energy equation?