Mechanics problem, how does the friction affect the movement of an object

[sandercock]

hi

just a general question, i was setting up an experiment the other day where a spring launched a cube with a mass of 176g with 30N of force along a 85cm surface with friction coefficient of 0.27 (according to the teacher), i got the answer but that's because my class mates helped me in my group, and i didnt really understand how to work out how far the object went (we measured the distance but we had to present calculations), i have handed it in but i just want to understand it better (and we got the wrong measurment anyway).

Can any1 help?

Thanx

 

[rock.freak667]

You know that the frictional force is related to the cube's normal reaction by F_R=μN.

If you utilize conservation of energy, the change in kinetic energy of the body is equal to the work done against friction. And the work done against friction is simply obtained from the definition of work, F_Rd. You'd want to find 'd'.

 

[sandercock]

cool thanx!

But how do i work out the velocity? You need that to work out the kinetic energy right?

ke=0.5MV^2

as i have the mass, but don't know the distance or time so can't work out V?

 

[rock.freak667]

cool thanx!

But how do i work out the velocity? You need that to work out the kinetic energy right?

ke=0.5MV^2

as i have the mass, but don't know the distance or time so can't work out V?

Well actually since you are using a spring, the maximum energy the spring stores will be converted to kinetic energy. So essentially it is the same as the change in potential energy of the spring.

 

[sandercock]

Yea i starting to get it now, so using the conservation of energy, the change in kinetic energy then equals the work done, and u take away the total work done by friction in the opposite direction (which i worked out to be 6.885N), then do the equation:

work=force(friction) * distance

which when switched around is

30N (force exerted from spring) = 6.885 * (x)

(x) = 30/6.885
distance = 4.357m

right?
haha i just want to understand it correctly

 

[rock.freak667]

Yea i starting to get it now, so using the conservation of energy, the change in kinetic energy then equals the work done, and u take away the total work done by friction in the opposite direction (which i worked out to be 6.885N), then do the equation:

work=force(friction) * distance

which when switched around is

30N (force exerted from spring) = 6.885 * (x)

(x) = 30/6.885
distance = 4.357m

right?
haha i just want to understand it correctly

no no.

Did you measure how much the spring is compressed by ? OR were you given the spring constant? Else you will need to find either one using F=kx.

If you were then you can just use E=1/2kx². This will be the total energy of the system.

Now all of that energy is used up when the block is overcoming friction. Such that 1/2kx²= Work done by friction.

 

[sandercock]

yea i got given the spring constant to be 200N\M, and the spring was compressed 15 cm, so the total potential energy was 30N right?

 

[rock.freak667]

yea i got given the spring constant to be 200N\M, and the spring was compressed 15 cm, so the total potential energy was 30N right?

Check that over.

1/2(200)(0.15)²

 

[sandercock]

ohh right

2.25N

that makes more sense..so the distance traveled is...

27cm? according the the work=force*distance equation?

 

[jack action]

You are mixing force and energy. The unit for a force is Newton. The unit for energy is joule.

The problem you have is one based on the conservation of energy. The energy stored in a spring is:

Es = ½*k*x²

The energy needed to push the cube (the work done) is equal to the force times the distance traveled:

W = F*d

Where the force is the friction force, which is equal to µ*m*g.

Since energy is conserve, both equations should be equal, hence:

d = (½*k*x²) / (µ*m*g)