00:01
In this problem, we have this situation.
00:06
So we have this horizontal plane and we have a spring like this and we are compressing some mass by an amount delta x.
00:18
And then we are releasing it and when it is free from the spring it will be moving with this speed v and then it will climb through this inclined plane that has this angle theta and we have this gravitational acceleration in the downward direction so with that we have two questions what is the speed here when the mass is free from the spring and what is the distance that it can climb on this inclined plane the maximum distance i mean okay now let us analyze the situation in three parts we have the first part here the second part here and the third part here and i'm going to introduce this height h.
01:21
Okay now let us write down the numerical values of the given quantities.
01:27
So we have g, we know that g is equal to 9 .81 meters per second squared.
01:33
K is given to be 400 newton per meter.
01:37
M is equal to 2 kilograms and its compression this initial compression is 0 .220 meters and this angle is 37 degrees.
01:53
Since we don't have any friction anywhere, we can use the conservation of energy.
02:03
So we will have e1 equal to e2 equal to e3 where e is the total energy.
02:10
At the first point, we are just compressing this spring by holding the mass at rest.
02:19
So we don't have any kinetic energy but we only have the spring potential energy.
02:24
So we have 1 .5k times the compression.
02:28
And if you plug in the numbers, we obtain 9 .68 joules...