Sphere Under Gravity Problem (Isaac Physics)

In summary, the problem involves a small sphere attached to a fixed point and whirling in a vertical circle under the influence of gravity. The tension in the string is three times higher at the lowest point compared to the highest point. To solve the problem, one must use both energy analysis (conservation) and force analysis (Newton's 2nd law). The equations derived from these analyses will allow for solving the velocities at the top and bottom points, which are represented by different symbols in the equations.
  • #1
bobbricks
32
0
I'm stuck on this problem:
A small sphere is attached to a fixed point by a string of length =30cm , and whirls round in a vertical circle under the action of gravity at such speed that the tension in the string when the sphere is at its lowest point is three times the tension when the sphere is at its highest point.
From: https://isaacphysics.org/questions/sphere_under_gravity

I initially thought it would be constant velocity but that produces the wrong answer and after looking at the hints, I found the velocity at the top is different to the velocity at the bottom.

I've tried using ideas of energy where the Energy at the top=mg0.6+0.5mv2 and Energy at the bottom= 0.5mv2

Also, resolving forces: At the top F=T+mg where F is the centripetal force. At the bottom F=3T-mg.

I've also tried working out the minimum velocity required using a=v2/r where a=9.81 and r=0.3m. I've tried to use Work=forcexdisplacement so F=W/d and d=0.6 and W=energy at the top or W= energy at the bottom, to produce 2 separate equations. Still stuck.
 
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  • #2
You'll need both energy analysis (conservation) and force analysis (Newton's 2nd law) to solve this.

bobbricks said:
I've tried using ideas of energy where the Energy at the top=mg0.6+0.5mv2 and Energy at the bottom= 0.5mv2
Give the velocities at top and bottom different symbols and apply conservation of energy.

bobbricks said:
Also, resolving forces: At the top F=T+mg where F is the centripetal force. At the bottom F=3T-mg.
Good. Apply Newton's 2nd law to top and bottom positions.

That will give you the equations you need to solve for the speeds.
 

1. What is the Sphere Under Gravity Problem?

The Sphere Under Gravity Problem, also known as the "Isaac Physics" problem, is a classic physics problem that involves calculating the motion of a sphere under the influence of gravity. It is often used as a practice problem for students learning about motion and forces.

2. How do you solve the Sphere Under Gravity Problem?

To solve the Sphere Under Gravity Problem, you need to use Newton's laws of motion and the equations of motion for an object under constant acceleration. This involves setting up and solving differential equations for the motion of the sphere, taking into account the forces acting on it such as gravity and air resistance.

3. What are the key assumptions made in solving the Sphere Under Gravity Problem?

When solving the Sphere Under Gravity Problem, there are a few key assumptions that are typically made. These include assuming a spherical object with a uniform mass distribution, neglecting air resistance, and assuming a constant gravitational acceleration. These assumptions help simplify the problem and make it more manageable to solve.

4. How does the mass of the sphere affect its motion in the Sphere Under Gravity Problem?

In the Sphere Under Gravity Problem, the mass of the sphere does not affect its motion as long as its mass distribution is uniform. This is because the acceleration due to gravity is independent of the mass of the object, as stated by Newton's second law of motion (F=ma). However, a larger mass may result in a greater gravitational force, resulting in a different trajectory or speed of the sphere.

5. What are some real-life applications of the Sphere Under Gravity Problem?

The Sphere Under Gravity Problem has many real-life applications, including understanding the motion of objects in free-fall, such as a ball being thrown or a satellite orbiting the Earth. It is also used in industries such as engineering and aerospace to predict the trajectory and motion of objects under the influence of gravity.

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