How far does a cylinder roll after being released from an incline?

In summary, a 10kg solid cylinder is released from rest on a 10m high ramp at a 37 degree angle. It rolls without slipping down the incline and then across a rough 1m long table that is 2m above the ground. The friction is ignored. The task is to calculate how far from the base of the table the cylinder lands. Using kinematics, Newton's Second Law, and conservation of energy, it is possible to determine the horizontal distance the cylinder will travel after leaving the table.
  • #1
amegirl24
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0

Homework Statement


A solid cylinder of mass 10 kg is at rest atop a 10m high ramp inclined at an angle of 37 degrees. The cylinder is released and rolls, without slipping, down the incline. Then, the cylinder rolls across a rough 1-m long table that is 2m above the ground. Finally, the cylinder rolls off of the table. Calculate how far from the base of the table the cylinder lands.

The friction is to be ignored because it allows the cylinder to roll, and doesn't hinder the motion.


Homework Equations




The Attempt at a Solution


I've tried using kinematics, Newtons 2nd and conservation of energy, but
I can't figure out how far the cylinder lands plays into it.
 
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  • #2
Welcome to PF!

amegirl24 said:
… I can't figure out how far the cylinder lands plays into it.

Hi amegirl24! Welcome to PF! :wink:

The cylinder leaves the table with a horizontal velocity. Use ordinary projectile equations to find where it lands. :smile:
 

FAQ: How far does a cylinder roll after being released from an incline?

1. What factors affect the speed of an object when rolling down an incline?

The speed of an object rolling down an incline is affected by the angle of the incline, the mass and shape of the object, and the presence of any external forces such as friction or air resistance. The steeper the incline, the faster the object will accelerate. Objects with greater mass or a less aerodynamic shape will roll slower than lighter or more streamlined objects. Friction and air resistance can also slow down the speed of an object as it rolls down an incline.

2. How does the height of an incline affect the speed of an object rolling down it?

The height of an incline has a direct impact on the potential energy of an object at the top of the incline. The higher the incline, the higher the potential energy. As the object rolls down the incline, this potential energy is converted into kinetic energy, resulting in a higher speed. Therefore, the higher the incline, the faster the object will roll.

3. Is the acceleration of an object rolling down an incline constant?

No, the acceleration of an object rolling down an incline is not constant. As the object rolls down, its speed increases, resulting in a higher acceleration. However, as the object reaches the bottom of the incline, its speed will eventually become constant, resulting in a constant acceleration. This is due to the conversion of potential energy to kinetic energy and the presence of external forces such as friction and air resistance.

4. How does the angle of an incline affect the acceleration of an object rolling down it?

The angle of an incline has a direct effect on the acceleration of an object rolling down it. The steeper the incline, the greater the acceleration of the object. This is because a steeper incline results in a greater component of the object's weight acting down the incline, resulting in a larger force and therefore a higher acceleration. A shallow incline will result in a smaller component of the object's weight acting down the incline, resulting in a lower acceleration.

5. Can an object roll up an incline?

Yes, an object can roll up an incline if it has enough initial kinetic energy to overcome the force of gravity pulling it down. This can be achieved by giving the object an initial push or by having it roll down a higher incline before reaching the incline it needs to roll up. However, the object will eventually slow down and roll back down the incline due to the force of gravity. In order for an object to roll up an incline and stay there, it would need to have a constant external force pushing it up, such as a motor or a person pushing it.

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