00:01
Neglecting non -conservative forces such as friction, then we can assume that mechanical energy is conserved.
00:07
That means, the sum of the potential and kinetic energy at all points of the path of the object must be the same.
00:13
In this problem, we're given with a spring that as a spring concept of 400 newton per meter is anchored to the bottom of a frictionless incline that is inclined by 30 degrees.
00:25
A 500 gram block is pressed against the spring, thereby compressing it by 10 centimeters.
00:30
The block is then released.
00:32
We wish to find the speed with which the block is launched up the incline.
00:36
So here we're given with k, the force constant of 400 newton per meter, the amount of compression that the spring experienced, which is 10 centimeters, and the mass of the block, which is 500 grams.
00:47
So first is that we will find the elastic potential energy of the spring, as it is pressed by a certain amount.
00:59
So that is solved as one half times k.
01:02
Times x squared we have to make sure that your x is in as a unit of meters so thereby stent centimeters will be divided by 100 since 100 centimeters is 1 meters to convert it into meters which is now becomes 0 .1 meters so you have one half times 400 times 0 .1 squared elastic potential energy of the spring is equal to two juice now as the spring would go back again to its natural length, it would, this elastic potential of the spring would be converted into kinetic energy of the block and the potential energy that the block gains.
01:50
So we have ue equals k plus ug, where k is the kinetic energy and ug is the gravitational potential energy.
02:02
So this is now the significance of conservation of mechanical energy...