Conservation of mechanical energy vs sum of forces

[Donovan]

When do one use the principle of conservation of mechanical energy to find the velocity of a mass, and when would you use the sum of forces equals to the mass times acceleration, and there after use a ds=v dv in order to find the velocity.

The specific question related to this is a spring fixed to a mass which is pulled up a slope by a constant force. They want the final velocity. I already have the force in terms of distance that the spring applies of the mass. I have the constant force etc.

I used sum of F's = ma and a ds = v dv in order to find velocity. In the memo however They used conservation of energy: T1 +V1 +U1-2 = T2 +V2. My answer is different to the memo. Should'nt the answer be the same? and if not? Whats the two cases that splits these two methods of approach?

 

[berkeman]

When do one use the principle of conservation of mechanical energy to find the velocity of a mass, and when would you use the sum of forces equals to the mass times acceleration, and there after use a ds=v dv in order to find the velocity.

The specific question related to this is a spring fixed to a mass which is pulled up a slope by a constant force. They want the final velocity. I already have the force in terms of distance that the spring applies of the mass. I have the constant force etc.

I used sum of F's = ma and a ds = v dv in order to find velocity. In the memo however They used conservation of energy: T1 +V1 +U1-2 = T2 +V2. My answer is different to the memo. Should'nt the answer be the same? and if not? Whats the two cases that splits these two methods of approach?

Yes, the answers should be the same. Can you post the detailed work for both methods? We can help to find the error(s). :-)

 

[Donovan]

Question: calculate speed of block at final position.
GIven: block on slope of 15 degree incline attached to spring; spring applies force down the slope with stiffness of 450 N/m; frictional coefficient= 0.28 kinetic and 0.3 static; constant force of 150N applied up the slope; final position has spring stretched to 0.2m; initial position has string unstretched and block velocity of 0 m/s.

Calculated: work done by applied force=30J ; work done by frictional force= -4,327; potential energy of spring in final position = 9J.

According to work energy theorem (memo):
T1+V1+U1-2=T2+V2
0+0+30-4,327=0.5 * (80/9) * (V squared)+9+4,141
V=1,753 m/sAccording to sum of forces:
sum of F = ma
150-80sin15 - 21,64-450x=80a
a=1,346 - 5,625x

since a ds=v dv

integrate...
1,346*0,2-(5,625/2)*(0.2 squared)=0,5*(V squared)
V=0,56 m/s

Thanks for the help