As shown in the figure, a block of mass M1=0.450 kg is initially at rest on a slab of mass M2=0

step 1 Once again, welcome to a new problem. This time we have forces. So force is the product of mass

As shown in the figure, a block of mass M1=0.450 kg is...

Key Concepts

Conservation of Momentum

The principle of conservation of momentum states that in the absence of external forces, the total momentum of a system remains constant. This concept is especially useful in analyzing systems with interacting components, where the internal forces (such as friction) may change the motion of individual parts but the total momentum of the system is conserved.

Relative Motion

Relative motion involves analyzing the movement of one object with respect to another rather than with respect to a fixed frame of reference. This concept is particularly important in systems where components may move in relation to each other, such as a block sliding on a moving slab, and helps in understanding the net effect of interactions between components.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle is fundamental when analyzing the dynamics of individual bodies as well as systems of bodies, as it requires identifying all forces acting on each object and understanding how these forces contribute to the acceleration of the objects.

Friction

Friction is the resistive force that occurs when two surfaces interact. The type of friction relevant in these problems can be static (which prevents motion) or kinetic (which opposes existing motion). Understanding friction is essential when determining whether objects start moving relative to each other or how they decelerate when sliding.

Free-Body Diagrams

Free-body diagrams are visual representations that isolate an object and illustrate all the external forces acting upon it. They are a key tool for decomposing complex problems into simpler parts, allowing one to apply fundamental laws of mechanics, such as Newton's Second Law, by clearly indicating the forces in play and their directions.

Transcript

00:02 Once again, welcome to a new problem.

00:06 This time we have forces.

00:08 So force is the product of mass and acceleration, and this is the same as newton's second law.

00:17 So the other thing that happens is that if we have equilibrium, then what's going to happen is that the sum of forces in the x direction is going to be zero, and the sum of forces in the y direction is also going to be zero.

00:34 So think about a block that sits on table.

00:38 It's going to have a mass m and so its weight is m.

00:42 Based off of newton's third law, action and reaction forces are equal and opposite.

00:51 So action and reaction forces are equal and opposite.

00:56 So action and reaction forces are equal and opposite.

01:00 So action and reaction forces are equal and opposite.

01:03 So if i apply a force word here, f, there's going to be an opposition for friction.

01:10 This is kinetic friction.

01:13 This is kinetic friction.

01:15 And it's the product of the coefficient of kinetic friction and the normal force.

01:22 And then also assuming that there is equilibrium, you're going to see those two values of the normal force and the weight being equivalent.

01:32 The other thing you could have is the static friction.

01:36 This is static friction.

01:40 And so the static friction is the product of coefficient of static friction times the normal force.

01:48 So assuming that we have a new problem and in this problem we have a block m2 and the block sits on a slab.

02:01 So this block sits on a slab.

02:04 So this is a block and this is a slab.

02:09 And the slab sits on a table.

02:12 And at the edge of the table we have a pulley.

02:18 So the pulley holds the string on the table.

02:26 And there's another block m3 that's hanging downwards.

02:30 This first block is m1.

02:35 This one is m2.

02:38 And so the mass of the first block is 0 .450 kilograms and it's at rest.

02:47 Both of them are at rest.

02:50 The mass of the second block happens to be 0 .820 kilograms and this is the slab.

02:57 This is a block.

03:02 This string that you're seeing right here we have a string of negligible negligible mass, so this string is of leg, did you go mass, and it's connected to the slab, as you can see.

03:23 And so the block is at rest, meaning that there's going to be static friction.

03:41 There's going to be static friction right there.

03:44 So the slab, there are two frictions.

03:49 There is one between the block and the slab and the slab and the table.

03:53 So the coefficient of kinetic friction is 3 .4, or that's for the slab.

04:02 And then the coefficient for the slab is static friction is 0 .560.

04:08 This is between the slab and the block or the slab and the table.

04:24 So they have the experience the same coefficient of the block.

04:30 So we'll say a given, given that m3 is released and pulls down the string, it's released and pulls down the string, causing an acceleration, causes an acceleration of the slab, and in turn, an acceleration, of the block, slab and the block determine the maximum mass of m3 that allows acceleration of the slab with the block sitting on top of it.

05:43 So the block, so the block, sitting on top of it.

05:51 So the block, not slide from the slab.

06:05 So that's what you're seeing right there.

06:07 The block doesn't slide from the slab.

06:10 So we have all these numbers that we're dealing with.

06:13 We'll start with the force diagram for the block and the weight of the block is m1g.

06:22 That's opposed by the normal force.

06:25 As m3 moves, there's going to be an acceleration.

06:28 And the only force acting on the block is the static friction provided by the second force diagram of the second slab of the slab.

06:39 So right here we do have the slab which has a weight m2g.

06:46 The slab also experiences the weight of the block in terms of its own normal, the weight of the block...