Dynamics: max horizontal swing of a pendulum

1. Feb 23, 2012

jaredogden

1. The problem statement, all variables and given/known data

In an ore-mixing operation, a bucket full of ore is suspended from a traveling crane which moves along a stationary bridge. The crane is traveling at a speed of 3 m/s when it is brought to a sudden stop. Determine the maximum horizontal distance through which the bucket will swing. (arm length 10m)

2. Relevant equations

KE = 1/2mv2
PE = mgz
Etot = KE + PE + U

3. The attempt at a solution

Since the bucket is traveling with a speed of 3 m/s and has no height E1 = 1/2mv2 and at the highest point the bucket will travel v = 0 m/s E2 = mgz

Therefore since E1 = E2 (law of conservation of energy)
1/2mv2 = mgz
1/2v2 = gz
1/2(3 m/s)2 = (9.81 m/s2)z
z = 0.4587 m

I'm not even sure if I did this the way my professor taught us, I'm just using thermo energy balance equations to be honest. I don't know if there is a way to make a triangle and solve for the x component, or just a complete different way to do this.

2. Feb 23, 2012

kushan

Another way you can try to conserve momentum

3. Feb 23, 2012

jaredogden

I used a triangle to find out that the 10 m arm length minus the 0.4587 m height increase equals a triangle with the vertical leg being 9.54 m and the hypotenuse of 10 m. I then did sin-1(9.54 m/10 m) = 72.55°

Then I did 10cos(72.55°) = 2.9987 m

I know this is the right answer but I don't know if there is another way to find this answer.

4. Feb 23, 2012

kushan

Are masses given ?

5. Feb 23, 2012

jaredogden

No, no masses are given