00:01
All right, so we have these two blocks.
00:03
One block of the mass of m, which is 950 grams, on top of a second block that has a mass of 3 m's, three times that amount.
00:11
And they're both resting on a frictionless surface.
00:14
We have a coefficient of friction between the blocks of 0 .2, and we're going to stretch those blocks to a distance of 2 .5 centimeters.
00:23
Now for part a, we're just looking for an expression, mathematically, in terms of the acceleration.
00:30
So we want what the maximum acceleration is when we release these two blocks, assuming that they stick together.
00:37
And for this, we can use hooke's law, where the net force is acting on the two blocks.
00:45
And since we're assuming they stick together, we can treat them as a single block with a mass of 4 m.
00:51
That net force is equal to the sum of all the forces acting on it.
00:55
And the only force acting on it when it's released will be the force due to the spring, or hooke's law.
01:00
So the net force will be 4 m times the acceleration.
01:06
And thanks to hooke's law, we know that the spring is going to apply a force of k times the distance that the spring has been stretched, so k times d.
01:19
And so now we can solve this for the acceleration just by dividing by 4 m.
01:24
So we have k d divided by 4, and that's our expression for the acceleration.
01:31
This will be the maximum acceleration that the block system will feel, because as it's moving back towards equilibrium, the d is going to get smaller, and the acceleration will decrease until it reaches its equilibrium point, and then it'll have an acceleration of zero.
01:49
Next, we need to plug numbers into that and figure out what the acceleration actually will be.
01:55
So let's do that now.
01:56
So we have 6 .4 for k newtons per meter, and so we need to convert everything into kilograms and meters...