# Conservation of mechanical energy vs sum of forces

Tags:
1. Oct 26, 2014

### 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?

Last edited by a moderator: Oct 26, 2014
2. Oct 26, 2014

### Staff: Mentor

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

3. Oct 26, 2014

### 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/s

According 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