Dynamics: max horizontal swing of a pendulum

[jaredogden]

Homework Statement

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)

Homework Equations

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

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.

 

[kushan]

Another way you can try to conserve momentum

 

[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.

 

[kushan]

Are masses given ?

 

[jaredogden]

No, no masses are given