- #1

Thermofox

- 144

- 26

- Homework Statement
- A sphere is connected via a spring, attached to its center, to a block. Initially the block and the sphere are resting on a rough plane, then a constant force F=20N is applied on the sphere. This causes the sphere to start a pure rolling motion.

I need to determine the angular velocity and how much does the spring moves from its resting point when the block starts moving. What I've difficulty with is finding this moment.

ms=3Kg ; mb= 2Kg

R= 30cm

k= 200N/m

μs= 0.5 ; μd= 0.3

- Relevant Equations
- Fs= -kx

ΣF= ma ; Στ= Iα

I know that the block will move only if the force that pushes him is greater than μs
mb g.

The only force that can act on the block is the elastic force (Fs) generated by the expansion of the spring, caused by the rolling sphere, that rolls because a force F is acting on the sphere.

Then can I say that Fs > μs mb g? I've determined this equation by analysing the forces acting on the block and found that:

Fs- Fsf ( static friction force) = 0. I've considered the right direction as positive and put the equation equal to zero because the block is not moving => it has no acceleration.

I don't know how to proceed forward from this point. How can I find the instant, when the block starts moving, if my condition is greater than something? Because all I can find now is that, assuming x is how much did the spring expanded, x >(μs mb g)/k.

The only force that can act on the block is the elastic force (Fs) generated by the expansion of the spring, caused by the rolling sphere, that rolls because a force F is acting on the sphere.

Then can I say that Fs > μs mb g? I've determined this equation by analysing the forces acting on the block and found that:

Fs- Fsf ( static friction force) = 0. I've considered the right direction as positive and put the equation equal to zero because the block is not moving => it has no acceleration.

I don't know how to proceed forward from this point. How can I find the instant, when the block starts moving, if my condition is greater than something? Because all I can find now is that, assuming x is how much did the spring expanded, x >(μs mb g)/k.