Kinematics Rolling motion off a cliff

In summary, the conversation discusses a problem involving a smooth rolling object on an inclined plane that falls from a roof. The problem is solved using conservation of energy and free fall equations, but the last part of the problem involves finding the angle of inclination and the distance traveled horizontally. The conversation also mentions a solid sphere with negligible mass and radius, and the use of quadratic equations to solve the problem. Finally, the conversation ends with the problem being solved and the individual feeling embarrassed for making it out to be more difficult than it was.
  • #1
Varaia
7
0
So I'm sure most everyone has come across the problem where you have a smooth rolling object on an inclined plain that rolls off a roof or something and falls some distance x away from the roof. I can solve that because it usually gives me the distance along the incline and the angle of inclination and we assume conservation of energy and then use free fall equations and blah blah blah. What I can't seem to do is solve the last part of this problem where I'm given:
A solid sphere of of negligable mass and radius so I=2/5M(Rsquared)
Smooth rolling so we assume r(omega)=Vcom
From an initial height of H=6.0 m along a very wavy descent to a final height of h=2.0 m where it falls off the edge and
using the conservation of energy and plugging our stuff in
at the end of the roof the Vcom= 5.29 m/(s) and the average speed=7.23m/s (found first part easy)
I assume that the acceleration is constant (gravity) but that only comes into play on the last part because the normal force cancels it out while it is on the crazy ramp.
so now where do I go from here to find the angle so I can calculate t and then calculate the distance it fell horizontally d to point A that is directly below the edge of the 2.0m roof. The answer is 4.8m but when I can't find my all my values to plug into my quadratic equation it is kinda pointless. I know it is some simple relation that I can't remember. I would like to use the freefall relationships but without my angle it doesn't mean anything. Is there an easier way?
x(not)=0 Vx(not)=Vcos(theta) y=h=2.0m Vy(not)=-Vsin(theta)
y=h-(Vsin(theta))t -1/2g(t(squared))
Distance=Vcos(theta)t
 
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  • #2
The angle at which it leaves the roof? If that isn't given somewhere in the geometry of the situation, there isn't any way to calculate it. Exactly what is given?

And what in the world do you mean by "the distance it fell horizontally d to point A that is directly below the edge of the 2.0m roof"? If it feel to a point directly below the roof isn't the horizontal distance 0? Or do you not really mean "directly below"?
 
  • #3
If some how one can find the distance it traveled along the roof , the angle of inclination can be found since we know the vertical displacement of the center of mass.
 
  • #4
Here is the problem and I attached a picture (you'll love my mad photoshop skills)
In the picture a solid ball rolls smoothly from rest (starting at height H=6.0m) until it leaves the horizontal section at the end of the track at height h=2.0m. How far horizontally from point A does the ball hit the floor?

If anyone has spent the money to buy the student solutions manual to the 7th ed of Halliday/Resnicks Fundamentals of Physics this problem is in there as #9 in Chp 11

I should know how to do it by tomorrow and then I'll post the process because dang this was a tuffie.
 

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  • #5
Got it! and boy do I feel dumb

:-p So it was a much easier problem than I was making it out to be, had to go back all the way to Chp 3 for simple horizontal motion equation and then figured it out from there. Thanks for helping.
 
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Related to Kinematics Rolling motion off a cliff

1. What is kinematics rolling motion off a cliff?

Kinematics rolling motion off a cliff is a type of motion where an object rolls off a cliff or incline without any external force acting on it, except for the force of gravity.

2. What factors affect the kinematics rolling motion off a cliff?

The factors that affect kinematics rolling motion off a cliff include the initial velocity of the object, the angle of the incline, the mass and shape of the object, and air resistance.

3. What is the equation for calculating the velocity of an object in kinematics rolling motion off a cliff?

The equation for calculating the velocity of an object in kinematics rolling motion off a cliff is v = √(2gh), where v is velocity, g is the acceleration due to gravity, and h is the height of the cliff.

4. How does the angle of the incline affect the kinematics rolling motion off a cliff?

The angle of the incline affects the kinematics rolling motion off a cliff by changing the acceleration of the object. A steeper incline will result in a greater acceleration and a faster rolling motion, while a shallower incline will result in a slower rolling motion.

5. What is the difference between kinematics rolling motion and regular rolling motion?

Kinematics rolling motion off a cliff is a specific type of rolling motion where the object is not subject to any external forces except for gravity. Regular rolling motion, on the other hand, occurs when an object rolls on a surface with friction and is subject to external forces such as pushing or pulling. In kinematics rolling motion off a cliff, the object's motion is solely determined by its initial conditions and the force of gravity.

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