Equilibrium and impulsive forces (crane and demolition ball problem)

[rotiff]

Homework Statement

The Attempt at a Solution

I tried to find the acceleration using F= ma

Resultant force = Tension - mg
so a = (10295.2-8730)/890 = 1.758 m/s^2 but I don't think it works that way...

please help.

 

[Vespa71]

The height which from the ball falls, and its mass, gives a potential energy to the ball. This results in an identical kinetic energy at 0-level. The angle and length of rope should give the height. Then impulse can be calculated.

 

[rotiff]

I don't think so, because at the vertical position the total energy would equal kinetic energy + some potential energy therefore mgh = 0.5 mv^2 + mgh

And both velocity & height are missing from the right side of the equation.

 

[Vespa71]

I think the height can be calculated by angle and length, but possibly that is not what is asked for. My reply might be uninformative. Tension is not a topic of mine. Nor is geometry, really.

 

[rotiff]

Can you please attempt it? I have solved other parts of this question and I will see if your calculated height fits in with the rest.

 

[Vespa71]

At vertical position, the ball can fall no further in this system: equals no potential energy

 

[rotiff]

I tried it and the final velocity came up as 17 m/s, I know this is wrong because in the next part it says SHOW that the final velocity just before impact = 6.7 m/s

 

[rotiff]

This is ridiculous... I'm sure the answer should be fairly easy.

 

[Vespa71]

The 32deg. form the top of a triangle. The two other angles are 180-32=148 deg. combined, or 74 deg. each. Find length of base of triangle. Probably some cosinus or sinus calculating. I don't know. Then there's another small triangle below, whith 90 and 90-74=16 deg. angles. Base from other triangle is one side, short side of this small triangle is your heigth, and basis for potential/kinetic energy

 

[rotiff]

Thank you but I still think there is some other solution that jiggles with Newton's laws. If someone figures it please post.

 

[rotiff]

has anyone got any idea, please? At this point I tried everything and I just can't get my answer to fit both a final velocity of 6.7 m/s and a reasonable height

 

[rotiff]

I figured this and thought I'd post the solution:

Height at elevated position = 15 cos 32 = 12.72m

Therefore h = 15-12.72 = 2.28m