Projectile hits rod hanging from pivot.

[BOYLANATOR]

Homework Statement

A thin, uniform bar, 2, long and weighing 90N is hanging vertically from the ceiling by a frictionless pivot. It is struck by a small 3kg ball, 1.5m below the ceiling, initially traveling horizontally at 10 m/s. The ball rebounds in the opposite direction with a speed of 6 m/s.

Homework Equations

L_before = L_after

L = Iω

I_rod = $\frac{1}{2}$MR²

I_point = MR²

The Attempt at a Solution

At the point of impact the ball can be thought of as a particle in circular motion about the pivot with radius 1.5m and tangential velocity 10m/s.
The change in velocity is 16m/s. So the effective change in the angular momentum of the ball is

ΔL_ball = I_ball Δω_ball = $\frac{I_ballΔv}{R_ball}$

This is equal to the change in the angular momentum of the rod (opposite direction):

ΔL_rod = I_rod Δω_rod = $\frac{I_ballΔv}{R_ball}$

Insert values for I and rearrange :

Δω_rod = (2*m_ball*r_ball*Δv_ball) / (m_rod*r_ball²)

This gives ω = 3.92 rad/s , the given answer is 5.88 rad/s.

 

[BOYLANATOR]

I obviously used the fraction syntax incorrectly, please let me know what I did wrong. Thanks

 

[ehild]

Homework Statement

A thin, uniform bar, 2, long and weighing 90N is hanging vertically from the ceiling by a frictionless pivot. It is struck by a small 3kg ball, 1.5m below the ceiling, initially traveling horizontally at 10 m/s. The ball rebounds in the opposite direction with a speed of 6 m/s.

Homework Equations

L_before = L_after

L = Iω

I_rod = $\frac{1}{2}$MR²

The formula for the moment of inertia of the rod is not correct.


ehild

 

[haruspex]

I obviously used the fraction syntax incorrectly, please let me know what I did wrong

itex gives up if you put non-itex codes like [s u b] inside. Use ^ for sup and _ for sub.

 

[ehild]

As haruspex said, _ for sub, but enclose subscript between curly thingies {}

$ΔL_{ball} = I_{ball} Δω_{ball} = \frac{I_{ball}Δv}{R_{ball}}$

written as

ΔL_{ball} = I_{ball} Δω_{ball} = \frac{I_{ball}Δv}{R_{ball}}

ehild

 

[BOYLANATOR]

Ah yes. I should stick to deriving the moments of inertia, my memory doesn't serve me well. Thanks.