Max Distance Up Ramp for Rotating Sphere

  • Thread starter Thread starter physicos
  • Start date Start date
  • Tags Tags
    Exercise Rotation
AI Thread Summary
The discussion revolves around calculating the maximum distance a uniform solid sphere travels up a ramp at an angle of 27.6° after rolling without sliding. In the first scenario, where the ramp is frictionless, the initial kinetic energy is incorrectly equated, leading to an erroneous conclusion about the distance. For the second scenario, with sufficient friction preventing sliding, the calculations confirm that the approach is correct, allowing for both linear and rotational motion to stop instantaneously. The correct formula for the distance in the first case is derived as l = v²/(2g*sinθ), clarifying the misunderstanding. Overall, the key takeaway is the distinction between the two scenarios and the importance of accurately accounting for energy types.
physicos
Messages
46
Reaction score
1
A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle θ = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if :
1-
the ramp is frictionless, so the sphere continues to rotate with its initial angular speed until it reaches its maximum height.
→ I used : Ki+Ui=Kf+Uf
and concluded that Ki=7/10* m*v² =mglsinθ
so l = (7/10 *m*v²)/(mg*sinθ).

is it true ?
2-
the ramp has enough friction to prevent the sphere from sliding so that both the linear and rotational motion stop (instantaneously).
→ I concluded the same as the first case : means l = (7/10 *m*v²)/(mg*sinθ).
is it correct ?
 
Physics news on Phys.org
physicos said:
A uniform solid sphere of mass M and radius R is rolling without sliding along a level plane with a speed v = 2.30 m/s when it encounters a ramp that is at an angle θ = 27.6° above the horizontal. Find the maximum distance that the sphere travels up the ramp if :
1-
the ramp is frictionless, so the sphere continues to rotate with its initial angular speed until it reaches its maximum height.
→ I used : Ki+Ui=Kf+Uf
and concluded that Ki=7/10* m*v² =mglsinθ
so l = (7/10 *m*v²)/(mg*sinθ).

is it true ?
Nope.

2-
the ramp has enough friction to prevent the sphere from sliding so that both the linear and rotational motion stop (instantaneously).
→ I concluded the same as the first case : means l = (7/10 *m*v²)/(mg*sinθ).
is it correct ?
It turns out this one is correct. Obviously the two cases are different, so you need to figure out where you messed up in the first part of the problem.
 
Where did the 7/10 come from?

Does the sphere have rotational kinetic energy?
 
The sphere has both rotational and transitional kinetic energy
 
vela said:
Nope.It turns out this one is correct. Obviously the two cases are different, so you need to figure out where you messed up in the first part of the problem.

FOR THE FIRST CASE :

Kf+Uf=Ki+Ui
so 1/2m*v²f+1/2*I*w²+mg*l*sinθ=1/2*m*v²+1/2*I*w²
so It becomes : mg*l*sinθ=1/2*m*v²so l = v²/2*g*sinθ

Is it correct now ?
 
That part looks right to me.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Finding the distance of a peg so that a pendulum can circle around it
Replies
2
Views
878
What Is the Effect of Friction on the Height of a Sphere Rolling Down a Ramp?
Replies
2
Views
2K
Wooden sphere rolling on a double metal track
2
Replies
97
Views
5K
Period and Velocity of Oscillating Sphere Attached to Spring
Replies
10
Views
2K
Why Do We Use Ramp Length Instead of Height in Rolling Sphere Calculations?
Replies
3
Views
1K
How Does Rotational Inertia Affect the Motion of a Sphere on a Moving Ramp?
Replies
2
Views
4K
Dynamics/kinematics of rotating sphere
Replies
4
Views
2K
I need opinions on a Projectile Motion problem that I made up
Replies
11
Views
2K
Block Sliding Down a Ramp that is Free to Slide
Replies
4
Views
7K
Finding r of a Jovian-synchronous orbit and escape velocity
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top