What is its linear speed at the bottom of the incline?

AI Thread Summary
The discussion focuses on calculating the linear speed of a spherical object rolling down a 2.25-meter incline, starting from rest. The key equation used is the conservation of energy, relating initial potential energy to final kinetic energy. The participant derived the equation mgh(initial) = 1/2mv^2(final) + 1/20.584mr^2ω^2(final) and simplified it to find the final linear speed. The calculated speed of 5.279 m/s was confirmed as correct, although there was a question about the proper placement of parentheses in the equation. The correct notation for the calculation is sqrt((9.81 m/s^2)(2.25 m)/0.792).
jimmyboykun
Messages
39
Reaction score
0

Homework Statement


A spherical object with a moment of inertia of 0.584mr2 starts from rest rolling down a 2.25-m high incline. If the sphere is rolling without slipping


Homework Equations


I the best equation to use for this problem is k(initial)+u(initial)=k(final)+u(final)


The Attempt at a Solution


I stretch the equation 1/2mv^2(initial)+1/2Iω^(initial)+mgh(initial)=1/2mv^2(final)+1/2Iω^2(final)+mgh(final).

since the object started from rest the initial kinetic energy and the final potential energy is zero, which leads me to this equation

mgh(initial)=1/2mv^2(final)+1/20.584mr^2ω^2(final). As I continue reduce the equations I round up with this.

gh(initial)=0.792v^2(final)

v=sqrt(9.81m/s^2)(2.25m)/0.792

the linear speed I came up with was 5.279m/s.

Did I do this right?
 
Physics news on Phys.org
jimmyboykun said:
v=sqrt(9.81m/s^2)(2.25m)/0.792
The parentheses aren't written correctly there, but the method's fine and I agree with your final answer.
 
haruspex said:
The parentheses aren't written correctly there, but the method's fine and I agree with your final answer.

How would I write the parentheses the correct way?
 
jimmyboykun said:
How would I write the parentheses the correct way?

sqrt((9.81m/s^2)(2.25m)/0.792)
 
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...
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...
Back
Top