Accelerating a Uniform Sphere Down an Incline

AI Thread Summary
To find the acceleration of a uniform sphere rolling down a 30-degree incline, start with the potential energy equation, mgh, and the kinetic energy equations for both translational and rotational motion. The initial kinetic energy is zero since the sphere starts from rest. After calculating the velocity at the end of the slope, use the relationship s = v^2/(2a) to determine the acceleration of the center of mass. The discussion highlights the importance of correctly applying energy conservation principles and understanding the motion equations to solve for acceleration.
physikx
Messages
10
Reaction score
0

Homework Statement


A uniform sphere rolls down a 30 degree incline θ from height h. Initially, the solid is at rest. Find the acceleration for the center of the mass of the solid.

I am not sure where to start with this problem. I started with the energy formulas, but I am not sure how to find the acceleration of the center of mass from there. I just need a guide on what formulas or setup to use, thanks!

Homework Equations


Translational and rotational motion equations

The Attempt at a Solution


K_i=mghsin30
K_f=1/2mv^2+1/2Iω^2

then I solved for v:
v=radical(10/7*ghsin30)
 
Last edited:
Physics news on Phys.org
Hi, physikx,

The potential energy is mgh (h is the height of the (slope). Correct your result for v.

V is the speed of the CM at the end of the slope. Find the length travelled, and use the relation s=v^2/(2a) to determine the acceleration of the CM.

ehild
 
Hey ehid,

Thank you so much for the help! I was able to setup the problem and get the answer. I really appreciate the guidance.

Peace
 
You are welcome.

ehild
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Acceleration of a uniform solid sphere rolling down incline
Replies
1
Views
3K
Ring and solid sphere rolling down an incline - rotation problem
Replies
8
Views
3K
Acceleration of system related to rolling motion and pulley
Replies
35
Views
4K
Sphere rolling down incline then up incline?
Replies
5
Views
2K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
2K
Which sphere reaches the bottom of the inclined plane first
Replies
19
Views
4K
Why is the direction of kinetic/static friction up a ramp?
Replies
7
Views
1K
How to Determine Angular Velocity of a Rolling Sphere on an Inclined Plane?
Replies
11
Views
3K
Should I Consider the Electric Field Outside a Uniformly Charged Sphere?
Replies
2
Views
3K
Sphere rolling down an incline problem.
Replies
7
Views
5K

Hot Threads

Recent Insights

Back
Top