Rolling ball down slope at specific time

AI Thread Summary
A uniform solid ball with a diameter of 0.5m and mass of 0.1 kg rolls down a slope, and the goal is to find the velocity equation over time, starting from rest. The discussion involves using energy equations, including kinetic and potential energy, but the challenge is incorporating time as a variable. Attempts include using the moment of inertia and relating rotational kinetic energy to linear velocity. The moment of inertia is calculated as 2MR^2/5, and the relationship between height and time is expressed as h = 1/2*g*sin(theta)*t^2. The thread seeks assistance in substituting these values to derive a solution before the deadline.
havetolovemus
Messages
1
Reaction score
0

Homework Statement


A uniform solid ball rolls down a slope. If the ball has a diameter of .5m and a mass of .1 kg find the following:

The equation which describes the velocity of the ball at any time, given that it starts from rest.


Homework Equations



I've tried using energy equations, thus: 1/2 Iw^2+1/2Mv^2+mgh = constant (Kf +Uf = Ki + Ui) but that doesn't have "t" as a variable. I have also tried θ-θi=1/2(ωi+ω)t. But that didn't end up taking the radius or mass into consideration.

The Attempt at a Solution



More or less stated in the relevant equations. This is due in a few hours, so anything is much appreciated. Thank you in advance!
 
Physics news on Phys.org
Moment of inertia of the sphere is 2MR^2/5 and v = R*w.
So the rotational kinetic energy is given by 1/2*I*w^2 = 1/2*2M*R^2/5*v^2/R^2 = M*v^2/5.
And h = 1/2*g*sin(theta)*t^2.
Substitute these values in the relevant equation to solve for t.
 

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

Question About Momentum: Ball Rolling up a Curved Ramp
Replies
12
Views
1K
Ball rolling down a slope problem: Find an expression for time taken
Replies
8
Views
5K
A ball climbing a ramp while "rolling the wrong way"
Replies
32
Views
3K
How to find distance when a ball rolls slope with angle?
Replies
1
Views
1K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
2K
Is this formula for a ball rolling down a ramp incorrect?
Replies
10
Views
3K
3 balls rolling down different-shaped inclined platforms
Replies
8
Views
2K
Mechanics: A bowling ball is thrown and rolls with slipping
Replies
8
Views
4K
Why Is Deriving the Motion Formula for Hoops More Complex?
Replies
4
Views
982
Ball rolling down a slope ending with a loop
Replies
12
Views
2K

Hot Threads

Recent Insights

Back
Top