Difficult Centripetal Motion Problem

• Arooj
In summary, Tarzan, who has a mass of 80 kg, swings from a vine 20 m long at an angle of 30° with the vertical. If he pushes off with a speed of 2 m/s, the tension in the vine at the lowest point of the swing is approximately 16 N. This is calculated by using the centripetal acceleration formula, Fc = m(v^2)/r, and taking into account the additional force of gravity, 1/2mv^2 + mgh = 1/2mv^2.
Arooj

Homework Statement

Tarzan swings from a vine 20 m long which makes an angle of 30° with the vertical. If he pushes off with a speed of 2 m/s, what is the tension in the vine at the lowest point of the swing? Tarzan has a mass of 80 kg.

Homework Equations

centripetal accelaration force = F
m = mass
v = tangential speed
F=m(v^2)/r

The Attempt at a Solution

F = 80 (2^2)/ 20
F = 16 N

I don't know how to integrate the angle measure into the problem.

The 1/2mv^2 + mgh = 1/2mv^2 looks good. Use it to find the velocity at the lowest point. Then use Fc=m(v^2)/r with that value for v. Another force will add to this to make the total tension.

1. What is centripetal motion?

Centripetal motion is the circular motion of an object that is constantly changing direction, but its speed remains constant. It is caused by a centripetal force that pulls the object towards the center of the circular path.

2. What makes solving centripetal motion problems difficult?

Solving centripetal motion problems can be difficult because it involves understanding and applying various concepts such as circular motion, forces, and vectors. It also requires a good understanding of mathematical formulas and equations.

3. How do I approach a difficult centripetal motion problem?

The key to approaching a difficult centripetal motion problem is to break it down into smaller, more manageable steps. Start by identifying and drawing the relevant forces acting on the object, and then use Newton's laws of motion and other relevant equations to solve for the unknown variables.

4. What are some common mistakes to avoid when solving a difficult centripetal motion problem?

Some common mistakes to avoid when solving a difficult centripetal motion problem include forgetting to include all the relevant forces, using incorrect equations or formulas, and not paying attention to units. It is also important to double-check your work and make sure your final answer makes sense in the context of the problem.

5. How can I improve my skills in solving difficult centripetal motion problems?

Practice is key to improving your skills in solving difficult centripetal motion problems. Work through a variety of problems and make sure to fully understand the concepts and equations involved. You can also seek help from a teacher or tutor if you are struggling with a particular problem or concept.

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