Work and Energy of wrecking ball

In summary, the conversation discusses a problem involving a wrecking ball swinging on a 10.0-m cable on a vertical circular arc. The crane operator initially gives the ball a speed of 6.00 m/s at the lowest point of its swing and then stops providing assistance. The question is to determine the speed of the ball when the cable makes an angle of 30.0° with respect to the vertical. The solution involves using gravitational potential energy and constructing an isosceles triangle to find the height of the ball.
  • #1
kaspis245
189
1

Homework Statement


A wrecking ball swings at the end of a 10.0-m cable on a
vertical circular arc. The crane operator manages to give the ball a
speed of 6.00 m/s as the ball passes through the lowest point of its
swing and then gives the ball no further assistance. Friction and
air resistance are negligible. What speed v does the ball have
when the cable makes an angle of 30.0° with respect to the
vertical?

Homework Equations


Gravitational potential energy

The Attempt at a Solution


image.jpg


The answer must be 3.1 m/s
 
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  • #2
When calculating r + k, note that the base of the triangle is not 5 m.

You might try a different construction. Draw a horizontal auxiliary line from the final position of the ball over to the vertical string at the initial position.
 
  • #3
Sorry, I saw my mistake xD .

If I draw a line from initial to final position, I get an isosceles triangle. Still I don't know how to find the hight.
 
  • #4
Here's the horizontal line I was suggesting.
 

Attachments

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  • #5
Solved it, thanks!
 

Related to Work and Energy of wrecking ball

What is a wrecking ball?

A wrecking ball is a heavy, spherical object that is used to demolish large structures by swinging it into the structure repeatedly until it collapses.

How does a wrecking ball work?

A wrecking ball works by utilizing the principles of work and energy. When the ball is swung, it gains kinetic energy which is then transferred to the structure upon impact, causing damage. The repeated swinging of the ball increases the amount of work done on the structure, eventually leading to its collapse.

What factors affect the work and energy of a wrecking ball?

The work and energy of a wrecking ball are affected by its mass, velocity, and the height from which it is dropped. A heavier ball has more potential energy and can do more work upon impact. A higher velocity also increases the kinetic energy of the ball, making it more effective in demolishing structures.

How is the work and energy of a wrecking ball calculated?

The work done by a wrecking ball is calculated by multiplying the force of impact by the distance over which it is applied. The energy of the ball can be calculated using the equation E=1/2mv^2, where m is the mass and v is the velocity of the ball.

What are some safety precautions that need to be taken when using a wrecking ball?

When using a wrecking ball, it is important to ensure that the surrounding area is clear of people and objects. The operator should also be trained and experienced in handling the ball. Adequate safety gear should be worn and the ball should be regularly inspected for any damage. Proper communication and coordination between the operator and other workers is also crucial to ensure safety.

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